1 Unsupervised Boosting of Supervised Denoising Networks

1

Unsupervised Boosting of Supervised DenoisingNetworks for Realistic Noise RemovalYuan Huang Jun Xu Li Liu Fan Zhu Ling Shao Xingsong Hou Wangmeng Zuo

AbstractmdashRecent deep image denoising networks highly relyon pairs of clean and noisy images to learn image priors and noisestatistics However the paired clean and noisy images cannotbe easily obtained in real-world scenarios Supervised imagedenoising networks deploying synthetic clean-noisy pairs sufferfrom a domain shift problem between real-world and synthesizednoisy images and fail to achieve satisfactory performance onrealistic noise removal In this paper to facilitate the supervisedimage denoising networks for real-world scenarios we introducea ldquoNoisy-As-Cleanrdquo (NAC) strategy to train supervised denoisingnetworks in an unsupervised manner ie using unpaired noisyimages To boost the denoising performance we propose aPrediction Augmentation (PA) strategy in the inference stageExtensive experiments demonstrate that with our NAC and PAstrategies our unsupervised networks achieve better performancethan previous leading unsupervised networks and is competitivewith state-of-the-art supervised ones on synthetic and real-world noisy image denoising Comprehensive ablation studiesalso validate the effectiveness of our unsupervised NAC and PAstrategies The code will be publicly released

Index TermsmdashImage denoising unsupervised learning deepconvolutional neural network

I INTRODUCTION

IMAGE denoising is a fundamental image processing prob-lem and plays a pre-requisite role in diverse multimedia

tasks such as image registration [25] surveillance [52] [71]image compression [19] and other image restoration prob-lems [48]ndash[50] etc It recovers the clean image x from itsnoisy observation y = x + n corrupted by the noise nOne assumption on noise corruption n is the additive whiteGaussian noise (AWGN) which is widely studied by previousimage denoising methods [10]ndash[13] [15] [17] [18] [20]ndash[22] [29]ndash[31] [34] [35] [37] [39] [40] [42] [45] [47][51] [53]ndash[57] [60] [63]ndash[67] [69] [73] With plenty ofpaired noisy and clean images deep networks [10] [12] [34][35] [40] [42] [47] [53] [60] [69] are achieving significantprogress on image denoising

Most of previous denoising networks are trained withnoisy-clean image pairs and noisy-noisy image pairs orunpaired noisy images With large amounts of noisy-cleanimage pairs supervised denoising networks are learned withpromising performance on synthetic additive white Gaussian

Yuan Huang and Xingsong Hou are with the School of Electronic andInformation Engineering Xirsquoan Jiaotong University Xirsquoan China Jun Xuis with College of Computer Science Nankai University Tianjin ChinaLi Liu Fan Zhu and Ling Shao are with Inception Institute of ArtificialIntelligence (IIAI) Abu Dhabi UAE Wangmeng Zuo is with School ofComputer Science and Technology Harbin Institute of Technology Jun Xu(nankaimathxujungmailcom) and Xingsong Hou are the correspondingauthors The first two authors contribute equally

(a) Clean Image

(b) Noisy

(c) Clean

(d) CDnCNN [69] 3519dB08881 (e) CDnCNN [69]+NACPA3643dB09151

Fig 1 Denoising results of CDnCNN [69] (c) and CDnCNNnetwork trained with our unsupervised NACPA scheme (d) onthe image Lena corrupted by AWGN noise (σ = 10) Bestresults of PSNR and SSIM [59] are highlighted in bold

noise (AWGN) [53] [69] Several unsupervised denoisingnetworks [36] trained with noisy-noisy image pairs evadingthe need on clean ground truth images However these net-works still require two independently sampled images on thesame scene [36] which cannot be easily obtained in mostreal-world scenarios Recently several unsupervised denoisingnetworks are trained with unpaired noisy images [9] [33][44] [58] [61] assuming that either image-specific networkstructures can resonate different degradation [58] or the noiseare signal independent in real photographs [9] [33] [61]But training these networks often requires fine-tuning a setof hyper-parameters for every image [58] or the independenceof captured image pixels [9] [33] Different from [58] thework of [61] is a more stable solution for unsupervised imagedenoising but not efficient enough in practice Despite theirpromising performance existing denoising networks [9] [33][34] [36] [40] [69] are mainly designed for signal indepen-dent noise (eg AWGN) and cannot guarantee to performwell on realistic noise which is signal-dependent To alleviatethis problem several supervised denoising networks [10] [26]simulate the realistic noise either in mixed Gaussian and Pois-son distribution [23] or by data-driven generative models [5]

2

[14] The training of these networks usually need ground-truthclean images [1] [6] However the ground-truth images ofreal-world noisy images can hardly be accurately collected inoutdoor environments since they need hundreds of captureson the same scene under controlled environment [46] [62] orexhaustive manipulations of the captured image pairs [1] [6]

In this work to utilize the supervised networks for real-istic noise removal we introduce an unsupervised ldquoNoisy-As-Cleanrdquo (NAC) strategy to train these supervised networksin an unsupervised manner Our NAC strategy evades therequirements of fine-grained collected ground-truth clean im-ages in the training and inference stages of supervised im-age denoising networks Specifically in our NAC strategywe directly take the real-world noisy images as the targetswhich previously are usually clean ground truth images whilesynthesizing the corresponding noisy image by adding to thenoisy images similar noise again To boost our unsuperviseddenoising networks we propose a Prediction Augmentation(PA) strategy in the inference stage while previous methodsperform data augmentation in the training stage Combiningour NAC and PA strategies we propose an unsupervisedtraining scheme (we call it NACPA) to boost previous super-vised image denoising networks on realistic noise removal Toillustrate the effectiveness of our NACPA scheme we comparethe denoised images of CDnCNN [69] and the CDnCNNtrained with our NACPA scheme on the image ldquoLenardquo inFigure 4 We observe that with our unsupervised NACPAscheme boosts the performance of CDnCNN on the results ofvisual quality PSNR and SSIM [59] Extensive experimentson benchmark datasets demonstrate that several representativesupervised denoising networks trained by our NACPA schemeachieve similar or even better performance than the originalsupervised networks on removing ldquoweakrdquo synthetic noise andrealistic noise Comprehensive ablation studies validate theeffectiveness of our strategies

In summary our contributions are mainly three-foldbull We introduce a ldquoNoisy-As-Cleanrdquo (NAC) strategy

to evade the requirements on ground truth cleanimages in training supervised denoising networks Inthe NAC strategy we replace the training targets fromground truth clean images to the syntheticcaptured noisyimages (syntheticreal-world) while synthesizing the cor-responding noisy images by adding to the noisy imagessimilar noise degradation Our NAC strategy transformsthe supervised denoising networks into unsupervised onesby only changing their training inputs and targets

bull We propose a Prediction Augmentation (PA) strategyto boost the performance of unsupervised denoisingnetworks trained by our NAC Since most superviseddenoising networks employ data augmentation techniquesduring training our PA strategy can be seamlessly em-bedded into these networks to improve their performanceon image denoising

bull With our NACPA scheme previous supervised denois-ing networks achieve better performance by beingtrained in an unsupervised manner Experiments onbenchmark datasets show that the unsupervised networkstrained with our NACPA scheme achieve competitive or

even better performance on synthetic and realistic noiseremoval over state-of-the-art unsupervised and superviseddenoising networks

The rests of this paper are organized as follows In sectIIwe introduce the related work In sectIII we present our un-supervised NACPA training scheme for boosting supervisednetworks on image denoising Extensive experiments are con-ducted in sectIV to evaluate the effectiveness of our strategieson synthetic and real photograph denoising datasets Theconclusion is given in sectV

II RELATED WORK

A Supervised denoising networksThe work of [12] [34] [40] [42] [47] [53] [60] [69]

[70] employ noisy and clean image pairs as the trainingdata as plotted in Figure 2a The differences among thesenetworks are mainly the network architectures they employedEarly work [12] [60] applied multi-layer perception (MLP) fordeep learning based image denoising The layers of MLP areusually less than 10 and the famous ldquogradient vanishing prob-lemrdquo [27] largely restrict their depth In order to obtain deeperconvolution networks for better denoising performance [42]utilizes skip connections between multiple convolution layersand deconvolution layers The authors of [53] introduced amemory block containing a recursive unit and a gate unitto build consistent and adaptive connection between differentlayers achieving better performance Inspired by the residualnetwork [27] the work of [69] learned to predict the noisemap instead of the clean images Later Zhang et al [70]introduced a more flexible and faster solution by using anestimated noise map and the down-sampling of the noisyimage as input [34] further exploited the non-local selfsimilarity priors of natural images for training superviseddenoising networks This is implemented by k-Nearest Neigh-bors (kNN) for feature matching which is non-differentiableduring training To alleviate this problem [47] introduceda neural nearest neighbors block a continuous extensionof discrete kNN to perform differentiable feature matchingduring training Different from [34] [47] [40] implementedthe non-local matching by using a recurrent neural networkallowing efficient propagating of the correlated features thoughthe recurrent states

Recently supervised denoising networks tackle the realisticnoise removal with the release of benchmark datasets [1][6] [62] on real-world noisy images and corresponding cleanground-truth images The CBDNet [26] trains a noise estima-tion sub-network to obtain the realistic noise map and a de-noising network accordingly for realistic noise removal In [5]a generative flow network is employed to synthesis realisticnoise In [7] a feature attention module was proposed to tacklethe synthesis and realistic noise These supervised denoisingnetworks [5] [7] [26] are effective upon the availability ofthe ground truth clean images to the corresponding real-worldnoisy images But these clean images are difficult to collect inmost real-world scenes In summary the training of superviseddenoising networks requires plenty of noisy-clean image pairsbut collecting the ground-truth clean images are difficult inmany real-world scenarios

3

(a) Supervised ldquoNoisy-To-Cleanrdquo Strategy [53] [69] (b) Unsupervised ldquoNoise2Noiserdquo Strategy [36]

(c) Unsupervised ldquoNoise2Selfrdquo Strategy [9] (d) Our Unsupervised ldquoNoisy-As-Cleanrdquo Strategy

Fig 2 Comparison of different strategies of training deep image denoising networks The plus sign in a green circle indicatesthe element-wise addition (a) In ldquoNoisy-To-Cleanrdquo strategy noisy and clean image pairs are used for training superviseddenoising networks (b) The ldquoNoise2Noiserdquo strategy uses the noisy image pairs (the same scene but different noise) for trainingunsupervised denoising networks (c) The ldquoNoise2Selfrdquo strategy uses the single noisy image itself for training unsuperviseddenoising networks (d) Our ldquoNoisy-As-Cleanrdquo strategy uses pairs of more noisy (add a observed noise on the original noisyimage) and the original noisy image for training unsupervised denoising networks

B Unsupervised denoising networks

Due to the aforementioned limitations researchers havebegan to train unsupervised denoising networks with noisyimage pairs as plotted in Figure 2b In [36] under theassumption of AWGN pairs of noisy images on the samescene were generated independently as the training data Bybeing trained with 300 000 iterations on BSD300 [8] theNoise2Noise network is capable of denoising diverse synthesisnoise However capturing two independent images of the samescene is difficult for real-world outdoor scenes and medicalscenes The work of Deep Image Prior [58] learned an image-specific denoising network using multi-channels of randomnoise as input and the test noisy image as target But thismethod perform the inference by early-stopping the trainingBesides it should assign suitable network architectures andtraining settings for different test images The work of [44]trains the denoising network using unpaired noisy images Thiswork requires to know the noise statistics eg additive whiteGaussian noise or multiplicative Bernoulli noise from thedegraded image However this is impractical in complex real-world scenarios since realistic noise is hard to be modeled [1][6] [46] [64] As illustrated in Figure 2c [9] [33] are twoself-supervised denoising network trained by using the noisyimages as both inputs and targets While self-supervision is apromising way for unsupervised denoising both [9] and [33]can only achieve comparable performance with [36]

In unsupervised denoising networks for realistic noiseremoval [14] restore real-world noisy images by a two-stage framework firstly training a generative adversarial net-

work [24] to generate noise samples similar to the test realisticnoise and then train the denoising network with the cleanimage to form the noisy and clean image pairs But [14] iseffective on the additive white noise which is not the case inmost real photograph

III PROPOSED UNSUPERVISED BOOSTING STRATEGY

In this section we introduce the proposed ldquoNoisy-As-Cleanrdquo (NAC) and Prediction Augmentation (PA) strategiesfor training unsupervised image denoising networks Thecombination of NAC and PA strategies (we call it the NACPAscheme) are employed in the training stage and inference stagerespectively We first present the NAC strategy in sectIII-A Thenwe present the PA strategy in sectIII-B Finally in sectIII-C wedescribe the application of our unsupervised NACPA schemeonto boosting representative supervised denoising networks bybeen trained with only noisy images

A Proposed ldquoNoisy-As-Cleanrdquo Strategy

Due to the unavailability of ground truth clean images inmany real-world imaging scenarios we propose to train unsu-pervised denoising networks by regarding the ldquoNoisyrdquo imagesdirectly ldquoAsrdquo the ldquoCleanrdquo targets The proposed ldquoNoisy-As-Cleanrdquo strategy trains denoising networks by taking noisyimages as targets and generating more noisy images basedon the noisy images as inputs The more noisy images aregenerated by adding to the ldquotargetrdquo noisy images the simulatednoise similar to the corrupted noise on that noisy image Asillustrated in Figure 2 our NAC strategy can be easily utilized

4

Fig 3 Pipeline of the proposed NACPA scheme for supervised image denoising networks The NACPA scheme containstwo parts the ldquoNoisy-As-Cleanrdquo (NAC) strategy is applied in the training stage (upper) while the Prediction Augmentation(PA) strategy is performed in the inference stage (lower) of the unsupervised denoising networks

by mangy supervised denoising networks to evade the groundtruth clean images As will be shown in the experimentalsection sectIV transforming these supervised denoising networksinto unsupervised ones by our NAC degrades little theirperformance on ldquoweakrdquo noise However by avoiding groundtruth images these unsupervised denoising networks can bemore adaptive to real-world scenarios

Previous supervised denoising networks [34] [40] [69]learn a mapping function fθ with a set of parameters θ bytaking the noisy images yiNi=1 as inputs and targeting atcorresponding clean images xiNi=1 with a loss function L

argminθ

Nsumi=1

L(fθ(yi)xi) (1)

However the ldquonoise-freerdquo ground truth images are usually dif-ficult to collect in real-world scenarios To ease this problemit is more feasible to train an unsupervised denoising networkwithout resorting to xi As studied in [9] [33] [36] [61]noisy images can be directly taken as targets for networktraining Noise2Noise [36] trains the denoising network withpairs of noisy images corrupted by independent noise

yi1 = xi + n1 yi2 = xi + n2 (2)

where xi is the i-th clean image n1 and n2 are two in-dependent AWGN noise yi1 and yi2 are the noisy imagepairs used as training target and input respectively But it ishard to guarantee that the two independent samples share thesame ground truth xi especially for scenes that have outdoormoving objects A more practical alternative is to capture thescene only once for real photographs

In our NAC the noisy images yi1 are taken as the traininginputs while a more noisy image yi2 is taken as the inputThis is formulated as follows

yi1 = xi + n1 yi2 = yi1 + n2 (3)

where the noise n2 is very close to n1 n2 asymp n1 Here we donot require that the noise n1n2 to be zero mean Since thetraining target yi1 is itself noisy images our NAC strategyis more suitable for ldquoweakrdquo noise The original superviseddenoising network fθ can be transferred into an unsupervisedone by our NAC as follows

yi1 = fθ(yi2) (4)

With (3) (4) can be written as

yi1 = fθ(yi1 + n2) (5)

This indicates that after training the network fθ has thecapacity to remove the noise n2 from yi1 By assuming that

5

(a) Noisy Image (b) Clean Image (c) CDnCNN [69] 2950dB08912 (d) CDnCNN [69]+NACPA3261dB09365

Fig 4 Denoising results of CDnCNN [69] network and CDnCNN with our NACPA scheme on the image ldquokodim13rdquo (fromthe Koda24 [2] dataset) corrupted by AWGN noise (σ = 20) Best results of PSNR and SSIM [59] are highlighted in bold

n2 and n1 are weak and similar the network fθ is feasible toremove the noise n1 from yi1 ie xi = fθ(xi + n1) asymp xiHowever in most situation such assumption can be hardlysatisfied In sectIV we will verify the effectiveness of our NACstrategy on synthetic and realistic noise removal

With applying our NAC at training stage previous super-vised denoising networks can be directly trained with real-world noisy images [34] [40] [69] Though the realistic noisen1 is complex [23] [41] it can be modeled by mixed Gaussianand Poisson noise [23] [41] or learned by variational genera-tive models [68] The former solution acquires to process theRAW image by in-camera processing pipeline (ISP) [26] aswell as corresponding inverse operators to simulate the processthat realistic noise are generated in sensors With the real-world noisy images and synthetic more noisy images corruptedagain by similar noise the unsupervised denoising networkstrained with our NAC strategy are very effective on real-worldimage des as will be demonstrated in sectIV Note that previousunsupervised denoising networks [9] [33] [36] [58] requirethe noise to be zero-mean while our NAC strategy can learnto remove non-zero mean noise

B Proposed Prediction Augmentation Strategy

To further boost the performance of unsupervised networkswe propose a Prediction Augmentation (PA) strategy whichaugments and fuses the inference predictions for better denois-ing performance Note that our PA strategy is different fromthe widely used data augmentation (DA) techniques [28] DAaims to boost training performance by providing more trainingdata to evade over-fitting and reduce the domain gap betweenthe training and test data Built upon DA our PA providesmore inference predictions for each augmented training inputand is thus able to fuse the complementary denoising resultsfor better performance

Similar strategy is also studied by the famous Deep ImagePrior (DIP) [58] in an online learning-while-inference mannerin which the inference is performed via a weighted averageof inferences in thousands learning iterations This onlineinference strategy indeed improves the final prediction ofDIP but is time-consuming and infeasible for offline training

networks With DA our PA strategy naturally obtains differentinference predictions of the denoised images During thetraining each training input is rotated or flipped for dataaugmentation The same noisy pixels (ie pixels in the samepositions of original image) of different augmented imagesare restored using different receptive fields in all augmentedimages and are thus averaged in a complementary manner toproduce better results

For the PA strategy in inference stage two ways of aug-mentation can be explored The Strategy 1 performs dataaugmentation during model training to augmented the noisyinput image with rotation and flip into 8 images Then theaugmented images go through the denoising model and areaveraged to output the mean image This strategy is also usedin image super-resolution community [38] [72] in an ensemblemanner Different from the Strategy 1 the Strategy 2 is tocomplement the clean image or an estimated clean imageby 8 augmented images and then add them with the sameobserved noise We evaluate the above two trategies based onthe CDnCNN [69] and CDnCNN with our NAC strategy in thesame training settings the results are provided in Table I FromTable I both strategies show clear improvements over thenetworks only with the original inference results The Strategy2 demonstrates higher improvements since the noise is ableto sample different pixels by adding to the augmentation ofthe clean images While CDnCNN [69] with NAC and thefirst inference strategy can still achieve better results than theoriginal supervised trained CDnCNN [69] at σ = 10 15 20Since the Strategy 2 achieves better performance we takethe Strategy 2 as our PA strategy studied in the experimentalsection

As illustrated in Figure 5 built upon general data augmen-tation techniques [28] our PA strategy augments the inferencepredictions by rotating 90 180 270 andor flipping verti-callyhorizontally With the noisy image yi = xai + n2 (n2 isthe observed noise xai is an approximation of xi) we augmentthe xai to xai1 xai8 Then we generate the augmentationof the inference images for input as (6)

yai aug 1 = xai1 + n2 yai aug 8 = xai8 + n2 (6)

The outputs of these augmented inference images are rotated

6

TABLE I The average PSNR (dB) and SSIM [59] results of blind denoising network CDnCNN [69] and CDnCNN [69]with NAC applied with two different inference strategies for color image denoising tested on Koda24 [2] dataset undernoise levels σ = 5 10 15 20 Higher results are highlighted in bold The Strategy 1 directly augments the noisy image forcomplementary inferences The Strategy 2 firstly separates the noisy image into a denoised image and the roughly removednoise and then augmented the denoised image for complementary inferences

Test Noise Level σ = 5 σ = 10 σ = 15 σ = 20Set Metric PSNRuarr SSIMuarr PSNRuarr SSIMuarr PSNRuarr SSIMuarr PSNRuarr SSIMuarr

Koda24

CDnCNN 4060 09729 3678 09469 3468 09223 3326 09013CDnCNN+Strategy 1 4070 09734 3698 09489 3485 09250 3342 09040CDnCNN+Strategy 2 4316 09812 3932 09633 3706 09441 3571 09311CDnCNN+NAC 4043 09725 3675 09467 3458 09193 3310 08971CDnCNN+NAC+Strategy 1 4053 09729 3688 09480 3477 09223 3331 09016CDnCNN+NAC+Strategy 2 4296 09812 3924 09632 3672 09390 3566 09306

andor flipped back to be averaged as the final inferenceprediction as follows

yfinal =1

N

Nsumn=1

fθ(yai aug n) (7)

Our PA strategy improves the prediction performance forimage denoising in the NACPA scheme and can also be appliedto many other supervised trained image denoising networksas will be shown in the experimental section Please refer toFigure VII for a direct comparisons of the networks with orwithout our PA inference strategy

C Training Unsupervised Denoising Networks

Our NACPA scheme can be seamlessly embedded intoexisting supervised denoising networks During the inferencestage we only change the input-output of these networks fromnoisy-clean image pairs to noisier-noisy ones During trainingthe `2 loss function is used to optimize the unsupervisednetworks

L =

Nsumi=1

||fθ(yi2)minus yi1||22 (8)

More implementation details are described in the experimentalsection to deal with synthetic and realistic noise removal

IV EXPERIMENTS

In this section extensive experiments on diverse benchmarkdatasets are performed to evaluate the effectiveness of theproposed NACPA scheme on both synthetic and realistic noiseremoval By our unsupervised NACPA scheme we boostseveral supervised denoising networks and compare them withthe original supervised denoising networks We also conductcomprehensive ablation studies to gain more insights of ourNACPA scheme

A Synthetic Noise Removal

Implementation details In training stage we apply ourNAC strategy to several representative supervised denoisingnetworks to evaluate its effectiveness on these networksand compare their performance with the original supervisedtrained denoising models For the color image denoising

Algorithm 1 Unsupervised boosting of supervised denoisingnetworks by our NACPA scheme

Generate noisy image pairs for training with noisy image yiand the observed noise n2 yi2 = yi1 + n2 to form noisy pairsas yi2yi1Ni=1 N indicates the number of the training imagesLearning noisy image pairs as inputs and targets yi2yi1Ni=1θ larr Initialize network fθ parametersrepeat

Network training using noisy image pairs for training opti-mized the parameters θ in the denoising models fθ according tothe loss function

until Convergencereturn fθ

Inference Input noisy image yi = xai + na2 where n2 is aobserved noise of the noisy input imageGenerate multiple augmentation rotate and flip xa togenerate(xai1 x

ai8) then add with n2

yai aug 1 = xai1 + n2 yai aug 8 = xai8 + n2

Testing thought the denoising model take (yai aug 1 yai aug 8)

though the trained network fθ and get the correspondence output(yai1 y

ai8)

De-augmentation inverse the rotation and flipped for (yi1 yi8)Final output compute the average of the (yi1 yi8) and get thefinal inference result yfinal

the employed networks are CDnCNN [69] MemNet [53]RedNet [42] and a simplified version of RCAN [72] (orig-inally used in image super resolution) with 10 resblocks inthe network and represents as RCAN While for gray-scaleimage denoising we use CDnCNN [69] MemNet [53] andRCAN [72] in our experiments For fair comparison thenetwork architectures and training settings of these networksare kept unchanged

In inference stage our PA strategy produces 8 augmen-tations of rotating 90 180 270 andor flipping verti-callyhorizontally of the original noisy image which are addedwith the observed noise as the input test images Two widelyused evaluation metrics are the Peak Signal to Noise Ratio(PSNR) and Structure Similarity Index (SSIM) [59] All thenetworks are implemented in PyTorch [3] and trained on asingle NVIDIA V100 GPUDatasets The training is performed individually on theCBSD400 [43] (400 RGB images) for color image denoising

7

Fig 5 Proposed Prediction Augmentation (PA) strategy augments the inference prediction images by rotating 90 180270 andor flipping verticallyhorizontally

and on BSD400 [43] (400 gray-scale images) for gray-scaleimage denoising Each image is used to generate the syntheticnoisier-noisy image pairs for training by our NAC strategyHere we test additive white Gaussian noise (AWGN) withdifferent standard deviations (stds) The testing is performedon CBSD68 [43] Kodak24 [2] and Urban100 [32] datasetsfor color image denoising The denoising model for gray-scalewere tested on BSD68 [43] gray-scale version of Kodak24 [2]and Urban100 [32] datasets

Results We test on AWGN noise with stds σ = 5 10 15 20to evaluate the effectiveness of our NACPA scheme appliedon different denoising networks For denoising RGB imagesCBSD400 as the training set and tested the denoising modelon CBSD68 [43] Koda24 [2] and Urban100 [32] datasetsThe original denoising models were trained supervised usingthe synthesis noise while the denoising model applied withNACPA scheme trained unsupervised The results are listedin Table II We observe that with our NACPA scheme theunsupervised trained networks exceed the original supervisedtrained models in the cases of low noise levels σ = 5 10 15However the improvements decline as the noise becomesstronger The reason is that with the increasing of the noiselevels the input noisy images are doubly degraded with thenoise as the training inputs making the latent clean image isdifficult to be recovered from the noisy image

For gray-scale image denoising the BSD400 dataset [43]is utilized to train the denoising networks The test results onBSD68 [43] and the gray-scale version of Urban100 [32] andKoda24 [2] datasets are listed in Table III We observe thatthe supervised denoising networks are clearly boosted by ourunsupervised NACPA strategies Similar phenomenon appearsin gray-scale image denoising that the denoising networkswith the NACPA scheme achieved a superior performance atthe most noise level compared with the original supervisedtrained denoising models The performance becomes com-parable when σ=20 More visual comparison and qualitativeevaluation comparison of the denoising results are presentedin the supplementary file

Speed Our NAC strategy does not affect the training speedBut in testing our PA strategy requires multiple inferencesand hence the inference time of our unsupervised boostednetworks will be larger than the original supervised denoisingones The running time of the comparison methods are listed inTable IV One can see that the unsupervised networks require

more time to obtain better denoising performance

B Realistic Noise Removal

Implementation details For real photograph denoising ourNACPA scheme is applied on CDnCNN [69] and RCAN [72]for realistic noise removal To implied our NACPA schemea similar observed noise is needed to build the noisy imagepairs for training Here we employ the work of [68] to estimatethe noise and generate an observed noise for the real-worldnoisy image For fair comparison the network architecturesand training settings of these networks are kept unchangedDatasets For real photograph denoising the training set in-cluding 5000 selected images from the SIDD small dataset [6]The test sets including the DND [1] (1000 images) SIDDvalidation set [6] (1280 images) and the SIDD Benchmarktest set [4] (1280 images)Results Comparison Here we compare the performance ofRCAN [72] applied with NACPA scheme based unsuperviseddenoising with the traditional method CBM3D [16] unsuper-vised denoising networks [14] [36] and supervised ones suchas CDnCNN [69] and RCAN [72] (both supervised trainedwith SIDD small dataset [6]) for realistic noise removal Thecomparisons of these methods on PSNR (dB) and SSIM [59]are listed in Table V

In Figures 7-8 we demonstrate visual and quantitativedenoised results of these methods on test images of DND [1]and SIDD [6] datasets One can see that in the task ofrealistic noise removal for DND [1] dataset which do notprovide similar training data no ldquonoisy-cleanrdquo image pairslike SIDD dataset [6] applied with NACPA scheme indeedboosted the original supervised trained model and acquireda 02dB of improvement and surpass the other state-of-the-art unsupervised denoising methods While for testing resultson SIDD validation set [6] and SIDD Benchmark set [4] thesupervised trained with SIDD training set denoising modelshows a higher performance Both the CDnCNN [69] withNACPA and RCAN [72] with NACPA scheme achievea highest performance among other unsupervised denoisingmethods Figure 8 shows a visual comparison of the denoisedresults from SIDD Validation set we observe that supervisedtrained models have higher PSNR (dB)SSIM but both theCDnCNN [69] with NACPA and RCAN [72] with NACPAdeliver a more clear vision of the text in the image This

8

(a) Noisy Image (b) CDnCNN [69]3556dB09467

(c) RCAN [72] 332309125 (d) MemNet [53]2975dB08068

(e) Rednet [42] 3416dB09320

(f) Clean Image (g) CDnCNN [69]+NACPA3909dB09717

(h) RCAN [72] + NACPA3594dB09511

(i) MemNet [53]+NACPA3464dB09457

(j) Rednet [42]+NACPA3570dB09422

Fig 6 Denoising results of a typical images (ldquokodim14rdquo) of different denoising networks with the proposed NACPA schemeon Koda24 [2] test set corrupted by AWGN noise (σ = 10)

demonstrate the effectiveness of our unsupervised NAC andPA strategies for real photograph denoising

C Validation of the Proposed Method

Here we conduct more detailed examinations and analysisof our proposed NACPA scheme on image denoising to gainmore insights of our unsupervised training and inferencescheme Specifically we assess 1) the effectiveness of ourNAC strategy 2) applied PA strategy to other image denoisingnetworks 3) NACPA for blind denoising 4) how inaccurateobserved noise affect the denoising performance All theexperiments are performed by training the networks on theCBSD400 dataset and testing them on the Kodak24 [2] andCBSD68 [43] datasets1) Effectiveness of our NAC Strategy on image denoisingThe proposed NAC strategy works as an important role totransform the supervised networks into unsupervised onesWith our NAC previous denoising networks [69] are trainedwith the noisy-noisy image pairs without the requirementsof clean ground truth images To evaluate the effectivenessof our NAC strategy we applied it to several [69] (withoutthe PA strategy) under the same settings The noise levels areσ = 5 10 15 20 As shown in Table VI the performanceof the unsupervised denoising networks with our NAC arecomparable to the original supervised denoising networksbearing little sacrifice on denoising performance Howeverour NAC strategy evades the requirements on clean groundtruth images which are hardly available in real scenarios2) Improvements of our PA strategy on image denoisingnetworks While our NAC strategy provides an unsupervised

training method for image denoising networks Our PA strat-egy is proposed to further improve the unsupervised denoisingperformance While the Table II in sectIII already demonstratesthat the proposed NACPA scheme can improve the qualitativeperformance of unsupervised image denoising networks herewe further study the contribution of our PA strategy applied onthe other supervised image denoising networks As shown inFigure VII by applying our PA strategy to the supervised net-works such as CDnCNN [69] RCAN [72] and MemNet [53]all their PSNR and SSIM results are clearly improved withoutadditional training strategies This demonstrates that our PAstrategy indeed helps improving the denoising performance ofthe supervised denoising networks3) How is the effects of our NACPA scheme for blind imagedenoising The above synthetic denoising experiments wereperformed on specific noise levels ie the training and testnoise levels (σ) are known and exactly the same However inreal photograph denoising scenarios we can hardly know thenoise levels To further exploit the potential of our NACPAscheme we trained a blind denoising network in unsupervisedmanner based on CDnCNN-B [69] In the training stage theAWGN noise is randomly generated with σ isin [0 55] Thenat inference stage the network is tested on the Koda24 [2]CBSD68 [43] and Urban100 [32] datasets As shown inTable VIII the blindly trained network can still achievessatisfactory results on specific noise levels even comparablewith the original supervised trained denoising model4) How inaccurate observed noise affects the denoisingperformance In the above presentation of the proposedframework for synthesis noise denoising the observed noisewere described as the noise with the same statistics while for

9

TABLE II Average PSNR (dB) and SSIM [59] results of different denoising networks applied with and without our NACPAscheme for color image denoising tested on Koda24 [2] CBSD68 [43] and Urban100 [32] datasets under AWGN withσ = 5 10 15 20


Koda24

CDnCNN 4060 09729 3678 09469 3468 09223 3326 09013CDnCNN+NACPA 4296 09812 3924 09632 3672 09390 3566 09306RCAN 3721 09420 3372 08812 3102 08217 2965 07754RCAN+NACPA 4123 09778 3656 09341 3393 08701 3122 07927MemNet 3790 09420 3287 09047 3080 08840 2895 08578MemNet+NACPA 3965 09730 3500 09342 3203 08682 2869 07995RED 3874 09566 3510 09243 3303 08844 3108 08346RED+NACPA 4157 09775 3656 09321 3343 08754 3151 08193

CBSD68


Urban100


TABLE III Average PSNR (dB) and SSIM [59] results of different denoising networks applied with and without NACPA schemefor gray-scale image denoising tested on gray-scale version of Koda24 [2] BSD68 [43] gray-scale version of Urban100 [32]datasets with AWGN levels σ = 5 10 15 20


Koda 24

DnCNN 3873 09628 3493 09255 3286 08911 3147 08610DnCNN+NACPA 4101 09751 3638 09387 3389 09003 3221 08950RCAN 3751 09504 3178 08265 2701 06245 2424 05022RCAN+NACPA 4056 09724 3615 09224 3277 08445 3023 07613MemNet 3607 09193 3291 08691 3033 07923 2871 07186MemNet+NACPA 4012 09690 3403 08781 3116 07931 2862 07007RED 3791 09857 3405 09117 3164 08563 2979 07940RED+NACPA 3940 09664 3502 09176 3236 08597 3090 08062

BSD68


Urban100


TABLE IV Running time (in seconds) of different denoising networks and those trained with our NACPA scheme on RGBimages of size 256times256 and 512times512

Image Size CDnCNN CDnCNN+NACPA RCAN RCAN+NACPA256times256times3 00038 00405 03038 2446512times512times3 00171 01568 1200 9657

most cases it is hard to acquire the same statistics noise Tofurther discover the impact of inaccurate observed noise wouldaffect the denoising performance In Table IX and Table X we

applied the NACPA scheme to CDnCNN [69] and training forimage denoising The first column represent the specific σ thatthe model original trained for while the first row represent the

10

TABLE V Average PSNR (dB) and SSIM [59] results on realistic noise removal on the DND [1] SIDD Validation [6] andSIDD Benchmark [4] datasets ldquoSrdquo indicates supervised models and ldquoUrdquo indicates unsupervised models

DND [1] SIDD Val [6] SIDD Benchmark [4]Method SU PSNRuarr SSIMuarr PSNRuarr SSIMuarr PSNRuarr SSIMuarrCBM3D [16] U 3451 08507 3088 07025 2565 06850N2N [36] U 3310 08110 2427 03527 2450 05050GCBD [14] U 3558 09217 - - - -CDnCNN [69] S 3721 09297 3636 08858 3661 09270CDnCNN [69]+NAC U 3332 08159 2781 05287 2786 06660CDnCNN [69]+NACPA U 3616 09003 3239 07273 3242 08260RCAN [72] S 3589 09128 3491 08278 3490 09000RCAN [72]+NAC U 3362 08237 2860 05431 2855 06870RCAN [72]+NACPA U 3610 09104 3169 06945 3151 08090

TABLE VI Average PSNR (dB) and SSIM [59] results of color image denoising with our NAC strategy on Koda24 [2]and CBSD68 [43] datasets The noise levels are σ = 5 10 15 20


Koda24 CDnCNN 4060 09729 3678 09469 3468 09223 3326 09013CDnCNN+NAC 4043 09725 3675 09467 3458 09193 3310 08971

CBSD68 CDnCNN 4019 09800 3599 09545 3389 09292 3219 09060CDnCNN+NAC 4010 09797 3594 09541 3363 09136 3210 09033

TABLE VII Average PSNR (dB) and SSIM [59] of different supervised denoising networks with our PA strategy and testedon Koda24 [2] and CBSD68 [43] datasets The noise levels are σ = 5 10 15 20 Higher results are highlighted in bold


Koda24

CDnCNN 4060 09729 3678 09469 3468 09223 3326 09013CDnCNN+ PA 4316 09812 3932 09633 3706 09441 3571 09311RCAN 3721 09420 3372 08812 3102 08217 2965 07754RCAN+ PA 4123 09778 3656 09341 3393 08701 3122 07927MemNet 3790 09420 3287 09047 3080 08840 2895 08578MemNet+ PA 3980 09687 3510 09361 3349 08731 2974 08051

CBSD68 CDnCNN 4019 09800 3599 09545 3389 09292 3219 09060CDnCNN+ PA 4319 09879 3883 09715 3635 09528 3478 09375RCAN 3697 09519 3337 09017 3066 08507 2910 07943RCAN+ PA 4191 09831 3692 09467 3379 08922 3116 08270MemNet 3815 09680 3330 09062 3088 08520 2927 07873MemNet+ PA 3973 09730 3570 09539 3347 09200 3075 08833

TABLE VIII Average PSNR (dB) and SSIM [59] results of blind denoising network CDnCNN-B [69] and CDnCNN-B [69]with NACPA scheme for color image denoising tested on Koda24 [2] CBSD68 [43] and Urban100 [32] datasets The noiselevels are σ = 5 10 15 20 Higher results are highlighted in bold


Koda24 CDnCNN-B 3973 09686 3638 09428 3441 09180 3303 08951CDnCNN-B+NACPA 4181 09746 3647 09203 3334 08535 3104 07817

CBSD68 CDnCNN-B 3985 09779 3591 09528 3371 09280 3221 09044CDnCNN-B+NACPA 4169 09786 3634 09290 3320 08772 3092 08166

Urban100 CDnCNN-B 3700 09681 3450 09497 3288 09237 3167 09167CDnCNN-B+NACPA 4089 09756 3609 09290 3312 08769 3092 08233

noisy image with different σ of noises that tested on The best performance evaluated by PSNR and SSIM were highlighted

11

(a) CBM3D [16] 3350dB09461 (b) Noise2Noise [36] 2978dB08563 (c) CDnCNN [69] 3582dB09793 (d) CDnCNN [69]+NAC3367dB09393

(e) CDnCNN [69]+NACPA3590dB09736

(f) RCAN [72] 3315dB09678 (g) RCAN [72]+NAC 3305dB09641 (h) RCAN [72]+NACPA3581dB09747

Fig 7 Denoising results of image ldquo0044 1rdquo from DND [1] dataset of different methods The ground-truth image is notreleased but PSNR (dB)SSIM results are publicly provided on the DND Benchmark Best results of PSNR and SSIM [59]are highlighted in bold

For σ=5 the best performance acquired by training with thesame level of noise While for σ=10 20 the best performancewere acquired by training with lower level of noises

TABLE IX Average PSNR (dB) and SSIM [59] results ofCDnCNN [69] with our NACPA scheme trained with noiselevels σ = 5 10 15 20 and cross tested on Koda24 [2]with noise levels σ = 5 10 15 20 The highest results arehighlighted in bold

Noise Level Metric σ=5 σ=10 σ=15 σ=20

σ=5 PSNR 4296 3910 3436 3107SSIM 09812 09570 08788 07848

σ=10 PSNR 3857 3924 3748 3393SSIM 09520 09632 09449 08738

σ=15 PSNR 3536 3590 3672 3628SSIM 09108 09213 09396 09376

σ=20 PSNR 3400 3436 3499 3566SSIM 08877 08965 09117 09306

TABLE X Average PSNR (dB) and SSIM [59] results ofCDnCNN [69] with our NACPA scheme trained under noiselevels σ = 5 10 15 20 and cross tested on CBSD68 [43]under noise levels σ = 5 10 15 20 The highest results arehighlighted in bold


σ=5 PSNR 4309 3888 3431 3106SSIM 09878 09647 08999 08211

σ=10 PSNR 3819 3867 3694 3371SSIM 09613 09709 09534 08947

σ=15 PSNR 3477 3526 3597 3547SSIM 09203 09306 09472 09439

σ=20 PSNR 3333 3367 3422 3478SSIM 08975 09061 09205 09376

V CONCLUSION

In this paper we proposed the ldquoNoisy-As-Cleanrdquo (NAC) andPrediction Augmentation (PA) strategies to transform original

12

(a) Clean Image (b) Noisy Image (c) CBM3D [16]2655dB04303

(d) CDnCNN [69]3521dB09048

(e) CDnCNN [69] +NAC3083dB06849

(f) CDnCNN [69] + NACPA3519dB08499

(g) Noise2Noise [36]2743dB05160

(h) RCAN [72]3575dB08719

(i) RCAN [72]+NAC3189dB07197

(j) RCAN [72]+NACPA3505dB08495

Fig 8 Denoising results of different methods on image ldquo8 15rdquo from SIDD Validation set [6] Best results of PSNR andSSIM [59] are highlighted in bold

supervised denoising networks into unsupervised ones toevade the cumbersome requirements on the clean groundtruth images in real-world image denoising problem Weintegrate our two strategies into a NACPA scheme Throughapplying the proposed NACPA scheme to denoising networkstrained with only noisy images provide an alternative solu-tion for unsupervised real-world image denoising problemExperiments also shows that our NACPA scheme boosts thesupervised image denoising networks to achieve competitiveor even superior performance when compared to their originalsupervised ones In our NACPA scheme the PA strategyoffers a practical inference strategy to further improve theirunsupervised denoising performance It can also be easilyapplied to other image denoising models for performanceimprovement Extensive experiments on both synthesis andrealistic noise removal demonstrated that the effectivenessof the proposed framework With our NACPA scheme theunsupervised trained image denoising networks achieves betterperformance than previous state-of-the-art unsupervised imagedenoising networks and comparable to the supervised onesComprehensive ablation studies validated our contributions

ACKNOWLEDGMENT

This work was supported by the NSFC (61872286and 61701391) the National Key RD Program of China(2017YFF0107700) and Natural Science Basic Research Planin Shaanxi Province of China (2018JM6092)

REFERENCES

[1] Darmstadt Noise Dataset Benchmark httpsnoisevisinftu-darmstadtdebenchmarkresults srgb 2 3 7 10 11

[2] Kodak lossless true color image suite httpsnoisevisinftu-darmstadtdebenchmarkresults srgb 5 6 7 8 9 10 11

[3] PyTorch httpspytorchorg 6[4] Smartphone Image Denoising Dataset Benchmark httpr0kus

graphicskodak 7 10[5] A Abdelhamed M A Brubaker and M S Brown Noise flow Noise

modeling with conditional normalizing flows In Proceedings of theIEEE International Conference on Computer Vision 2019 1 2

[6] A Abdelhamed S Lin and M S Brown A high-quality denoisingdataset for smartphone cameras In Proceedings of the IEEE Conferenceon Computer Vision and Pattern Recognition 2018 2 3 7 10 12

[7] S Anwar and N Barnes Real image denoising with feature attention InProceedings of the IEEE International Conference on Computer Vision2019 2

[8] P Arbelaez M Maire C Fowlkes and J Malik Contour detection andhierarchical image segmentation IEEE transactions on pattern analysisand machine intelligence 33(5)898ndash916 2011 3

[9] J Batson and L Royer Noise2Self Blind denoising by self-supervisionarXiv preprint arXiv190111365 2019 1 3 4 5

[10] T Brooks B Mildenhall T Xue J Chen D Sharlet and J T BarronUnprocessing images for learned raw denoising In Proceedings of theIEEE Conference on Computer Vision and Pattern Recognition pages9446ndash9454 2019 1

[11] A Buades B Coll and J M Morel A non-local algorithm for imagedenoising In Proceedings of the IEEE Conference on Computer Visionand Pattern Recognition volume 2 pages 60ndash65 2005 1

[12] H C Burger C J Schuler and S Harmeling Image denoising Canplain neural networks compete with BM3D In Proceedings of the IEEEConference on Computer Vision and Pattern Recognition pages 2392ndash2399 2012 1 2

13

[13] P Chatterjee and P Milanfar Clustering-based denoising with lo-cally learned dictionaries IEEE Transactions on Image Processing18(7)1438ndash1451 2009 1

[14] J Chen J Chen H Chao and M Yang Image blind denoising withgenerative adversarial network based noise modeling In Proceedingsof the IEEE Conference on Computer Vision and Pattern Recognitionpages 3155ndash3164 2018 1 3 7 10

[15] S I Cho and S J Kang Geodesic path-based diffusion acceleration forimage denoising IEEE Transactions on Multimedia 20(7)1738ndash17502017 1

[16] K Dabov A Foi V Katkovnik and K Egiazarian Color imagedenoising via sparse 3D collaborative filtering with grouping constraintin luminance-chrominance space In IEEE International Conference onImage Processing pages 313ndash316 IEEE 2007 7 10 11 12

[17] K Dabov A Foi V Katkovnik and K Egiazarian Image denoising bysparse 3D transform-domain collaborative filtering IEEE Transactionson Image Processing 16(8)2080ndash2095 2007 1

[18] K Dabov A Foi V Katkovnik and K Egiazarian Bm3d image de-noising with shape-adaptive principal component analysis In Structureand parsimony for the adaptive representation of signals 2009 1

[19] Y Dar A M Bruckstein M Elad and R Giryes Postprocessing ofcompressed images via sequential denoising IEEE Transactions onImage Processing 25(7)3044ndash3058 2016 1

[20] W Dong L Zhang G Shi and X Li Nonlocally centralized sparserepresentation for image restoration IEEE Transactions on ImageProcessing 22(4)1620ndash1630 2013 1

[21] B Du M Zhang L Zhang R Hu and D Tao Pltd Patch-based low-rank tensor decomposition for hyperspectral images IEEE Transactionson Multimedia 19(1)67ndash79 2016 1

[22] M Elad and M Aharon Image denoising via sparse and redundantrepresentations over learned dictionaries IEEE Transactions on Imageprocessing 15(12)3736ndash3745 2006 1

[23] A Foi M Trimeche V Katkovnik and K Egiazarian Practicalpoissonian-gaussian noise modeling and fitting for single-image raw-data IEEE Transactions on Image Processing 17(10)1737ndash1754 20081 5

[24] I Goodfellow J Pouget-Abadie M Mirza B Xu D Warde-FarleyS Ozair A Courville and Y Bengio Generative adversarial nets InAdvances in neural information processing systems pages 2672ndash26802014 3

[25] M Guizar-Sicairos S T Thurman and J R Fienup Efficient subpixelimage registration algorithms Optics letters 33(2)156ndash158 2008 1

[26] S Guo Z Yan K Zhang W Zuo and L Zhang Toward convolutionalblind denoising of real photographs In Proceedings of the IEEEConference on Computer Vision and Pattern Recognition 2019 1 2 5

[27] K He X Zhang S Ren and J Sun Deep residual learning for imagerecognition In Proceedings of the IEEE Conference on Computer Visionand Pattern Recognition pages 770ndash778 2016 2

[28] Z He L Xie X Chen Y Zhang Y Wang and Q Tian DataAugmentation Revisited Rethinking the Distribution Gap between Cleanand Augmented Data arXiv e-prints page arXiv190909148 Sep 20195

[29] Y Hou J Xu M Liu G Liu L Liu F Zhu and L Shao Nlh A blindpixel-level non-local method for real-world image denoising 2019 1

[30] B Hu L Li H Liu W Lin and J Qian Pairwise-comparison-basedrank learning for benchmarking image restoration algorithms IEEETransactions on Multimedia 2019 1

[31] D Huang L Kang Y Frank Wang and C Lin Self-learning basedimage decomposition with applications to single image denoising IEEETransactions on multimedia 16(1)83ndash93 2013 1

[32] J Huang A Singh and N Ahuja Single image super-resolution fromtransformed self-exemplars In In Proceedings of the IEEE Conferenceon Computer Vision and Pattern Recognition pages 5197ndash5206 20157 8 9 10

[33] A Krull T Buchholz and F Jug Noise2void-learning denoisingfrom single noisy images In Proceedings of the IEEE Conference onComputer Vision and Pattern Recognition pages 2129ndash2137 2019 13 4 5

[34] S Lefkimmiatis Non-local color image denoising with convolutionalneural networks In Proceedings of the IEEE Conference on ComputerVision and Pattern Recognition pages 3587ndash3596 2017 1 2 4 5

[35] S Lefkimmiatis Universal denoising networks A novel cnn architecturefor image denoising In Proceedings of the IEEE Conference onComputer Vision and Pattern Recognition 2018 1

[36] J Lehtinen J Munkberg J Hasselgren S Laine T Karras M Aittalaand T Aila Noise2Noise Learning image restoration without cleandata In International Conference on Machine Learning pages 2971ndash2980 2018 1 3 4 5 7 10 11 12

[37] C Li C Guo J Guo P Han H Fu and R Cong Pdr-netPerception-inspired single image dehazing network with refinement

IEEE Transactions on Multimedia 2019 1[38] B Lim S Son H Kim S Nah and K Mu Lee Enhanced deep residual

networks for single image super-resolution In Proceedings of the IEEEconference on computer vision and pattern recognition workshops pages136ndash144 2017 5

[39] C Liu R Szeliski S Kang C L Zitnick and W T FreemanAutomatic estimation and removal of noise from a single image IEEEtransactions on pattern analysis and machine intelligence 30(2)299ndash314 2008 1

[40] D Liu B Wen Y Fan C C Loy and T S Huang Non-local recurrentnetwork for image restoration In Advances in Neural InformationProcessing Systems pages 1673ndash1682 2018 1 2 4 5

[41] X Liu M Tanaka and M Okutomi Practical signal-dependent noiseparameter estimation from a single noisy image IEEE Transactions onImage Processing 23(10)4361ndash4371 2014 5

[42] X Mao C Shen and Y Yang Image restoration using convolutionalauto-encoders with symmetric skip connections In Advances in NeuralInformation Processing Systems 2016 1 2 6 8

[43] D Martin C Fowlkes D Tal and J Malik A database of humansegmented natural images and its application to evaluating segmentationalgorithms and measuring ecological statistics In Proceedings of theIEEE International Conference on Computer Vision volume 2 pages416ndash423 July 2001 6 7 8 9 10 11

[44] N Moran D Schmidt Y Zhong and P Coady Noisier2NoiseLearning to Denoise from Unpaired Noisy Data arXiv e-prints pagearXiv191011908 Oct 2019 1 3

[45] I Mosseri M Zontak and M Irani Combining the power of internaland external denoising In International Conference on IntelligentComputer Communication and Processing pages 1ndash9 2013 1

[46] S Nam Y Hwang Y Matsushita and S J Kim A holistic approachto cross-channel image noise modeling and its application to imagedenoising In Proceedings of the IEEE Conference on Computer Visionand Pattern Recognition pages 1683ndash1691 2016 2 3

[47] T Plotz and S Roth Neural nearest neighbors networks In Advancesin Neural Information Processing Systems 2018 1 2

[48] D Ren K Zhang Q Wang Q Hu and W Zuo Neural blinddeconvolution using deep priors arXiv preprint arXiv1908021972019 1

[49] D Ren W Zuo Q Hu P Zhu and D Meng Progressive imagederaining networks a better and simpler baseline In Proceedings of theIEEE Conference on Computer Vision and Pattern Recognition pages3937ndash3946 2019 1

[50] D Ren W Zuo D Zhang J Xu and L Zhang Partial deconvolutionwith inaccurate blur kernel IEEE Transactions on Image Processing27(1)511ndash524 2018 1

[51] D Ren W Zuo D Zhang L Zhang and M-H Yang Simultaneousfidelity and regularization learning for image restoration IEEE Trans-actions on Pattern Analysis and Machine Intelligence 2019 1

[52] S K Roy N Bhattacharya B Chanda B B Chaudhuri and SBanerjee Image denoising using fractal hierarchical classification InAnnual Convention of the Computer Society of India pages 631ndash645Springer 2018 1

[53] Y Tai J Yang X Liu and C Xu Memnet A persistent memorynetwork for image restoration In Proceedings of the IEEE InternationalConference on Computer Vision 2017 1 2 3 6 8

[54] H Talebi and P Milanfar Global image denoising IEEE Transactionson Image Processing 23(2)755ndash768 2014 1

[55] C Tian L Fei W Zheng Y Xu W Zuo and C-W Lin Deep learningon image denoising An overview arXiv preprint arXiv1912131712019 1

[56] C Tian Y Xu Z Li W Zuo L Fei and H Liu Attention-guided cnnfor image denoising Neural Networks 2020 1

[57] C Tian Y Xu and W Zuo Image denoising using deep cnn with batchrenormalization Neural Networks 121461ndash473 2020 1

[58] D Ulyanov A Vedaldi and V Lempitsky Deep image prior InProceedings of the IEEE Conference on Computer Vision and PatternRecognition pages 9446ndash9454 2018 1 3 5

[59] Z Wang A C Bovik H R Sheikh and E P Simoncelli Imagequality assessment from error visibility to structural similarity IEEETransactions on Image Processing 13(4)600ndash612 2004 1 2 5 6 79 10 11 12

[60] J Xie L Xu and E Chen Image denoising and inpainting with deepneural networks In Advances in Neural Information Processing Systemspages 341ndash349 2012 1 2

[61] J Xu Y Huang L Liu F Zhu X Hou and L Shao Noisy-As-CleanLearning Unsupervised Denoising from the Corrupted Image arXive-prints page arXiv190606878 Jun 2019 1 4

[62] J Xu H Li Z Liang D Zhang and L Zhang Real-world noisy imagedenoising A new benchmark arXiv preprint arXiv180402603 2018

14

2[63] J Xu L Zhang and D Zhang External prior guided internal prior

learning for real-world noisy image denoising IEEE Transactions onImage Processing 27(6)2996ndash3010 June 2018 1

[64] J Xu L Zhang and D Zhang A trilateral weighted sparse codingscheme for real-world image denoising In European Conference onComputer Vision 2018 1 3

[65] J Xu L Zhang D Zhang and X Feng Multi-channel weighted nuclearnorm minimization for real color image denoising In Proceedings ofthe IEEE International Conference on Computer Vision 2017 1

[66] J Xu L Zhang W Zuo D Zhang and X Feng Patch groupbased nonlocal self-similarity prior learning for image denoising InProceedings of the IEEE International Conference on Computer Visionpages 244ndash252 2015 1

[67] J L Yin B H Chen and Y Li Highly accurate image reconstructionfor multimodal noise suppression using semisupervised learning on bigdata IEEE Transactions on Multimedia PP(99)1ndash1 2018 1

[68] Z Yue H Yong Q Zhao D Meng and L Zhang Variational denoisingnetwork Toward blind noise modeling and removal In Advances in

Neural Information Processing Systems pages 1688ndash1699 2019 5 7[69] K Zhang W Zuo Y Chen D Meng and L Zhang Beyond a Gaussian

denoiser Residual learning of deep cnn for image denoising IEEETransactions on Image Processing 2017 1 2 3 4 5 6 7 8 9 1011 12

[70] K Zhang W Zuo and L Zhang Ffdnet Toward a fast and flexiblesolution for cnn based image denoising IEEE Transactions on ImageProcessing 2018 2

[71] L Zhang S Vaddadi H Jin and S K Nayar Multiple view imagedenoising In 2009 IEEE Conference on Computer Vision and PatternRecognition pages 1542ndash1549 IEEE 2009 1

[72] Y Zhang K Li K Li L Wang B Zhong and Y Fu Image super-resolution using very deep residual channel attention networks InEuropean Conference on Computer Vision 2018 5 6 7 8 10 1112

[73] F Zhu G Chen and P A Heng From noise modeling to blind imagedenoising In Proceedings of the IEEE Conference on Computer Visionand Pattern Recognition pages 420ndash429 2016 1

2

[14] The training of these networks usually need ground-truthclean images [1] [6] However the ground-truth images ofreal-world noisy images can hardly be accurately collected inoutdoor environments since they need hundreds of captureson the same scene under controlled environment [46] [62] orexhaustive manipulations of the captured image pairs [1] [6]

In this work to utilize the supervised networks for real-istic noise removal we introduce an unsupervised ldquoNoisy-As-Cleanrdquo (NAC) strategy to train these supervised networksin an unsupervised manner Our NAC strategy evades therequirements of fine-grained collected ground-truth clean im-ages in the training and inference stages of supervised im-age denoising networks Specifically in our NAC strategywe directly take the real-world noisy images as the targetswhich previously are usually clean ground truth images whilesynthesizing the corresponding noisy image by adding to thenoisy images similar noise again To boost our unsuperviseddenoising networks we propose a Prediction Augmentation(PA) strategy in the inference stage while previous methodsperform data augmentation in the training stage Combiningour NAC and PA strategies we propose an unsupervisedtraining scheme (we call it NACPA) to boost previous super-vised image denoising networks on realistic noise removal Toillustrate the effectiveness of our NACPA scheme we comparethe denoised images of CDnCNN [69] and the CDnCNNtrained with our NACPA scheme on the image ldquoLenardquo inFigure 4 We observe that with our unsupervised NACPAscheme boosts the performance of CDnCNN on the results ofvisual quality PSNR and SSIM [59] Extensive experimentson benchmark datasets demonstrate that several representativesupervised denoising networks trained by our NACPA schemeachieve similar or even better performance than the originalsupervised networks on removing ldquoweakrdquo synthetic noise andrealistic noise Comprehensive ablation studies validate theeffectiveness of our strategies

In summary our contributions are mainly three-foldbull We introduce a ldquoNoisy-As-Cleanrdquo (NAC) strategy

to evade the requirements on ground truth cleanimages in training supervised denoising networks Inthe NAC strategy we replace the training targets fromground truth clean images to the syntheticcaptured noisyimages (syntheticreal-world) while synthesizing the cor-responding noisy images by adding to the noisy imagessimilar noise degradation Our NAC strategy transformsthe supervised denoising networks into unsupervised onesby only changing their training inputs and targets

bull We propose a Prediction Augmentation (PA) strategyto boost the performance of unsupervised denoisingnetworks trained by our NAC Since most superviseddenoising networks employ data augmentation techniquesduring training our PA strategy can be seamlessly em-bedded into these networks to improve their performanceon image denoising

bull With our NACPA scheme previous supervised denois-ing networks achieve better performance by beingtrained in an unsupervised manner Experiments onbenchmark datasets show that the unsupervised networkstrained with our NACPA scheme achieve competitive or

even better performance on synthetic and realistic noiseremoval over state-of-the-art unsupervised and superviseddenoising networks

The rests of this paper are organized as follows In sectIIwe introduce the related work In sectIII we present our un-supervised NACPA training scheme for boosting supervisednetworks on image denoising Extensive experiments are con-ducted in sectIV to evaluate the effectiveness of our strategieson synthetic and real photograph denoising datasets Theconclusion is given in sectV

II RELATED WORK

A Supervised denoising networksThe work of [12] [34] [40] [42] [47] [53] [60] [69]

[70] employ noisy and clean image pairs as the trainingdata as plotted in Figure 2a The differences among thesenetworks are mainly the network architectures they employedEarly work [12] [60] applied multi-layer perception (MLP) fordeep learning based image denoising The layers of MLP areusually less than 10 and the famous ldquogradient vanishing prob-lemrdquo [27] largely restrict their depth In order to obtain deeperconvolution networks for better denoising performance [42]utilizes skip connections between multiple convolution layersand deconvolution layers The authors of [53] introduced amemory block containing a recursive unit and a gate unitto build consistent and adaptive connection between differentlayers achieving better performance Inspired by the residualnetwork [27] the work of [69] learned to predict the noisemap instead of the clean images Later Zhang et al [70]introduced a more flexible and faster solution by using anestimated noise map and the down-sampling of the noisyimage as input [34] further exploited the non-local selfsimilarity priors of natural images for training superviseddenoising networks This is implemented by k-Nearest Neigh-bors (kNN) for feature matching which is non-differentiableduring training To alleviate this problem [47] introduceda neural nearest neighbors block a continuous extensionof discrete kNN to perform differentiable feature matchingduring training Different from [34] [47] [40] implementedthe non-local matching by using a recurrent neural networkallowing efficient propagating of the correlated features thoughthe recurrent states

Recently supervised denoising networks tackle the realisticnoise removal with the release of benchmark datasets [1][6] [62] on real-world noisy images and corresponding cleanground-truth images The CBDNet [26] trains a noise estima-tion sub-network to obtain the realistic noise map and a de-noising network accordingly for realistic noise removal In [5]a generative flow network is employed to synthesis realisticnoise In [7] a feature attention module was proposed to tacklethe synthesis and realistic noise These supervised denoisingnetworks [5] [7] [26] are effective upon the availability ofthe ground truth clean images to the corresponding real-worldnoisy images But these clean images are difficult to collect inmost real-world scenes In summary the training of superviseddenoising networks requires plenty of noisy-clean image pairsbut collecting the ground-truth clean images are difficult inmany real-world scenarios

3












4




argminθ

Nsumi=1

L(fθ(yi)xi) (1)


yi1 = xi + n1 yi2 = xi + n2 (2)



yi1 = xi + n1 yi2 = yi1 + n2 (3)


yi1 = fθ(yi2) (4)


yi1 = fθ(yi1 + n2) (5)


5













6



Koda24



yfinal =1

N

Nsumn=1

fθ(yai aug n) (7)




L =

Nsumi=1



IV EXPERIMENTS













ai8)




7










8


(c) RCAN [72] 332309125 (d) MemNet [53]2975dB08068

(e) Rednet [42] 3416dB09320


(h) RCAN [72] + NACPA3594dB09511








9



Koda24


CBSD68


Urban100




Koda 24


BSD68


Urban100






10









Koda24









11








σ=5 PSNR 4296 3910 3436 3107SSIM 09812 09570 08788 07848

σ=10 PSNR 3857 3924 3748 3393SSIM 09520 09632 09449 08738

σ=15 PSNR 3536 3590 3672 3628SSIM 09108 09213 09396 09376

σ=20 PSNR 3400 3436 3499 3566SSIM 08877 08965 09117 09306



σ=5 PSNR 4309 3888 3431 3106SSIM 09878 09647 08999 08211

σ=10 PSNR 3819 3867 3694 3371SSIM 09613 09709 09534 08947

σ=15 PSNR 3477 3526 3597 3547SSIM 09203 09306 09472 09439

σ=20 PSNR 3333 3367 3422 3478SSIM 08975 09061 09205 09376

V CONCLUSION


12


(d) CDnCNN [69]3521dB09048

(e) CDnCNN [69] +NAC3083dB06849



(h) RCAN [72]3575dB08719

(i) RCAN [72]+NAC3189dB07197




ACKNOWLEDGMENT


REFERENCES













13




















































14














3












4




argminθ

Nsumi=1

L(fθ(yi)xi) (1)


yi1 = xi + n1 yi2 = xi + n2 (2)



yi1 = xi + n1 yi2 = yi1 + n2 (3)


yi1 = fθ(yi2) (4)


yi1 = fθ(yi1 + n2) (5)


5













6



Koda24



yfinal =1

N

Nsumn=1

fθ(yai aug n) (7)




L =

Nsumi=1



IV EXPERIMENTS













ai8)




7










8


(c) RCAN [72] 332309125 (d) MemNet [53]2975dB08068

(e) Rednet [42] 3416dB09320


(h) RCAN [72] + NACPA3594dB09511








9



Koda24


CBSD68


Urban100




Koda 24


BSD68


Urban100






10









Koda24









11








σ=5 PSNR 4296 3910 3436 3107SSIM 09812 09570 08788 07848

σ=10 PSNR 3857 3924 3748 3393SSIM 09520 09632 09449 08738

σ=15 PSNR 3536 3590 3672 3628SSIM 09108 09213 09396 09376

σ=20 PSNR 3400 3436 3499 3566SSIM 08877 08965 09117 09306



σ=5 PSNR 4309 3888 3431 3106SSIM 09878 09647 08999 08211

σ=10 PSNR 3819 3867 3694 3371SSIM 09613 09709 09534 08947

σ=15 PSNR 3477 3526 3597 3547SSIM 09203 09306 09472 09439

σ=20 PSNR 3333 3367 3422 3478SSIM 08975 09061 09205 09376

V CONCLUSION


12


(d) CDnCNN [69]3521dB09048

(e) CDnCNN [69] +NAC3083dB06849



(h) RCAN [72]3575dB08719

(i) RCAN [72]+NAC3189dB07197




ACKNOWLEDGMENT


REFERENCES













13




















































14














4




argminθ

Nsumi=1

L(fθ(yi)xi) (1)


yi1 = xi + n1 yi2 = xi + n2 (2)



yi1 = xi + n1 yi2 = yi1 + n2 (3)


yi1 = fθ(yi2) (4)


yi1 = fθ(yi1 + n2) (5)


5













6



Koda24



yfinal =1

N

Nsumn=1

fθ(yai aug n) (7)




L =

Nsumi=1



IV EXPERIMENTS













ai8)




7










8


(c) RCAN [72] 332309125 (d) MemNet [53]2975dB08068

(e) Rednet [42] 3416dB09320


(h) RCAN [72] + NACPA3594dB09511








9



Koda24


CBSD68


Urban100




Koda 24


BSD68


Urban100






10









Koda24









11








σ=5 PSNR 4296 3910 3436 3107SSIM 09812 09570 08788 07848

σ=10 PSNR 3857 3924 3748 3393SSIM 09520 09632 09449 08738

σ=15 PSNR 3536 3590 3672 3628SSIM 09108 09213 09396 09376

σ=20 PSNR 3400 3436 3499 3566SSIM 08877 08965 09117 09306



σ=5 PSNR 4309 3888 3431 3106SSIM 09878 09647 08999 08211

σ=10 PSNR 3819 3867 3694 3371SSIM 09613 09709 09534 08947

σ=15 PSNR 3477 3526 3597 3547SSIM 09203 09306 09472 09439

σ=20 PSNR 3333 3367 3422 3478SSIM 08975 09061 09205 09376

V CONCLUSION


12


(d) CDnCNN [69]3521dB09048

(e) CDnCNN [69] +NAC3083dB06849



(h) RCAN [72]3575dB08719

(i) RCAN [72]+NAC3189dB07197




ACKNOWLEDGMENT


REFERENCES













13




















































14














5













6



Koda24



yfinal =1

N

Nsumn=1

fθ(yai aug n) (7)




L =

Nsumi=1



IV EXPERIMENTS













ai8)




7










8


(c) RCAN [72] 332309125 (d) MemNet [53]2975dB08068

(e) Rednet [42] 3416dB09320


(h) RCAN [72] + NACPA3594dB09511








9



Koda24


CBSD68


Urban100




Koda 24


BSD68


Urban100






10









Koda24









11








σ=5 PSNR 4296 3910 3436 3107SSIM 09812 09570 08788 07848

σ=10 PSNR 3857 3924 3748 3393SSIM 09520 09632 09449 08738

σ=15 PSNR 3536 3590 3672 3628SSIM 09108 09213 09396 09376

σ=20 PSNR 3400 3436 3499 3566SSIM 08877 08965 09117 09306



σ=5 PSNR 4309 3888 3431 3106SSIM 09878 09647 08999 08211

σ=10 PSNR 3819 3867 3694 3371SSIM 09613 09709 09534 08947

σ=15 PSNR 3477 3526 3597 3547SSIM 09203 09306 09472 09439

σ=20 PSNR 3333 3367 3422 3478SSIM 08975 09061 09205 09376

V CONCLUSION


12


(d) CDnCNN [69]3521dB09048

(e) CDnCNN [69] +NAC3083dB06849



(h) RCAN [72]3575dB08719

(i) RCAN [72]+NAC3189dB07197




ACKNOWLEDGMENT


REFERENCES













13




















































14














6



Koda24



yfinal =1

N

Nsumn=1

fθ(yai aug n) (7)




L =

Nsumi=1



IV EXPERIMENTS













ai8)




7










8


(c) RCAN [72] 332309125 (d) MemNet [53]2975dB08068

(e) Rednet [42] 3416dB09320


(h) RCAN [72] + NACPA3594dB09511








9



Koda24


CBSD68


Urban100




Koda 24


BSD68


Urban100






10









Koda24









11








σ=5 PSNR 4296 3910 3436 3107SSIM 09812 09570 08788 07848

σ=10 PSNR 3857 3924 3748 3393SSIM 09520 09632 09449 08738

σ=15 PSNR 3536 3590 3672 3628SSIM 09108 09213 09396 09376

σ=20 PSNR 3400 3436 3499 3566SSIM 08877 08965 09117 09306



σ=5 PSNR 4309 3888 3431 3106SSIM 09878 09647 08999 08211

σ=10 PSNR 3819 3867 3694 3371SSIM 09613 09709 09534 08947

σ=15 PSNR 3477 3526 3597 3547SSIM 09203 09306 09472 09439

σ=20 PSNR 3333 3367 3422 3478SSIM 08975 09061 09205 09376

V CONCLUSION


12


(d) CDnCNN [69]3521dB09048

(e) CDnCNN [69] +NAC3083dB06849



(h) RCAN [72]3575dB08719

(i) RCAN [72]+NAC3189dB07197




ACKNOWLEDGMENT


REFERENCES













13




















































14














7










8


(c) RCAN [72] 332309125 (d) MemNet [53]2975dB08068

(e) Rednet [42] 3416dB09320


(h) RCAN [72] + NACPA3594dB09511








9



Koda24


CBSD68


Urban100




Koda 24


BSD68


Urban100






10









Koda24









11








σ=5 PSNR 4296 3910 3436 3107SSIM 09812 09570 08788 07848

σ=10 PSNR 3857 3924 3748 3393SSIM 09520 09632 09449 08738

σ=15 PSNR 3536 3590 3672 3628SSIM 09108 09213 09396 09376

σ=20 PSNR 3400 3436 3499 3566SSIM 08877 08965 09117 09306



σ=5 PSNR 4309 3888 3431 3106SSIM 09878 09647 08999 08211

σ=10 PSNR 3819 3867 3694 3371SSIM 09613 09709 09534 08947

σ=15 PSNR 3477 3526 3597 3547SSIM 09203 09306 09472 09439

σ=20 PSNR 3333 3367 3422 3478SSIM 08975 09061 09205 09376

V CONCLUSION


12


(d) CDnCNN [69]3521dB09048

(e) CDnCNN [69] +NAC3083dB06849



(h) RCAN [72]3575dB08719

(i) RCAN [72]+NAC3189dB07197




ACKNOWLEDGMENT


REFERENCES













13




















































14














8


(c) RCAN [72] 332309125 (d) MemNet [53]2975dB08068

(e) Rednet [42] 3416dB09320


(h) RCAN [72] + NACPA3594dB09511








9



Koda24


CBSD68


Urban100




Koda 24


BSD68


Urban100






10









Koda24









11








σ=5 PSNR 4296 3910 3436 3107SSIM 09812 09570 08788 07848

σ=10 PSNR 3857 3924 3748 3393SSIM 09520 09632 09449 08738

σ=15 PSNR 3536 3590 3672 3628SSIM 09108 09213 09396 09376

σ=20 PSNR 3400 3436 3499 3566SSIM 08877 08965 09117 09306



σ=5 PSNR 4309 3888 3431 3106SSIM 09878 09647 08999 08211

σ=10 PSNR 3819 3867 3694 3371SSIM 09613 09709 09534 08947

σ=15 PSNR 3477 3526 3597 3547SSIM 09203 09306 09472 09439

σ=20 PSNR 3333 3367 3422 3478SSIM 08975 09061 09205 09376

V CONCLUSION


12


(d) CDnCNN [69]3521dB09048

(e) CDnCNN [69] +NAC3083dB06849



(h) RCAN [72]3575dB08719

(i) RCAN [72]+NAC3189dB07197




ACKNOWLEDGMENT


REFERENCES













13




















































14














9



Koda24


CBSD68


Urban100




Koda 24


BSD68


Urban100






10









Koda24









11








σ=5 PSNR 4296 3910 3436 3107SSIM 09812 09570 08788 07848

σ=10 PSNR 3857 3924 3748 3393SSIM 09520 09632 09449 08738

σ=15 PSNR 3536 3590 3672 3628SSIM 09108 09213 09396 09376

σ=20 PSNR 3400 3436 3499 3566SSIM 08877 08965 09117 09306



σ=5 PSNR 4309 3888 3431 3106SSIM 09878 09647 08999 08211

σ=10 PSNR 3819 3867 3694 3371SSIM 09613 09709 09534 08947

σ=15 PSNR 3477 3526 3597 3547SSIM 09203 09306 09472 09439

σ=20 PSNR 3333 3367 3422 3478SSIM 08975 09061 09205 09376

V CONCLUSION


12


(d) CDnCNN [69]3521dB09048

(e) CDnCNN [69] +NAC3083dB06849



(h) RCAN [72]3575dB08719

(i) RCAN [72]+NAC3189dB07197




ACKNOWLEDGMENT


REFERENCES













13




















































14














10









Koda24









11








σ=5 PSNR 4296 3910 3436 3107SSIM 09812 09570 08788 07848

σ=10 PSNR 3857 3924 3748 3393SSIM 09520 09632 09449 08738

σ=15 PSNR 3536 3590 3672 3628SSIM 09108 09213 09396 09376

σ=20 PSNR 3400 3436 3499 3566SSIM 08877 08965 09117 09306



σ=5 PSNR 4309 3888 3431 3106SSIM 09878 09647 08999 08211

σ=10 PSNR 3819 3867 3694 3371SSIM 09613 09709 09534 08947

σ=15 PSNR 3477 3526 3597 3547SSIM 09203 09306 09472 09439

σ=20 PSNR 3333 3367 3422 3478SSIM 08975 09061 09205 09376

V CONCLUSION


12


(d) CDnCNN [69]3521dB09048

(e) CDnCNN [69] +NAC3083dB06849



(h) RCAN [72]3575dB08719

(i) RCAN [72]+NAC3189dB07197




ACKNOWLEDGMENT


REFERENCES













13




















































14














11








σ=5 PSNR 4296 3910 3436 3107SSIM 09812 09570 08788 07848

σ=10 PSNR 3857 3924 3748 3393SSIM 09520 09632 09449 08738

σ=15 PSNR 3536 3590 3672 3628SSIM 09108 09213 09396 09376

σ=20 PSNR 3400 3436 3499 3566SSIM 08877 08965 09117 09306



σ=5 PSNR 4309 3888 3431 3106SSIM 09878 09647 08999 08211

σ=10 PSNR 3819 3867 3694 3371SSIM 09613 09709 09534 08947

σ=15 PSNR 3477 3526 3597 3547SSIM 09203 09306 09472 09439

σ=20 PSNR 3333 3367 3422 3478SSIM 08975 09061 09205 09376

V CONCLUSION


12


(d) CDnCNN [69]3521dB09048

(e) CDnCNN [69] +NAC3083dB06849



(h) RCAN [72]3575dB08719

(i) RCAN [72]+NAC3189dB07197




ACKNOWLEDGMENT


REFERENCES













13




















































14














12


(d) CDnCNN [69]3521dB09048

(e) CDnCNN [69] +NAC3083dB06849



(h) RCAN [72]3575dB08719

(i) RCAN [72]+NAC3189dB07197




ACKNOWLEDGMENT


REFERENCES













13




















































14














13




















































14














14














Documents

1 Unsupervised Boosting of Supervised Denoising Networks