ORIGINAL PAPER

AWavelet-Based Mammographic Image Denoisingand Enhancement with Homomorphic Filtering

Pelin Gorgel & Ahmet Sertbas & Osman N. Ucan

Received: 8 January 2009 /Accepted: 8 May 2009 /Published online: 6 June 2009# Springer Science + Business Media, LLC 2009

Abstract Breast cancer continues to be a significant publichealth problem in the world. The diagnosing mammogra-phy method is the most effective technology for earlydetection of the breast cancer. However, in some cases, it isdifficult for radiologists to detect the typical diagnosticsigns, such as masses and microcalcifications on themammograms. This paper describes a new method formammographic image enhancement and denoising basedon wavelet transform and homomorphic filtering. Themammograms are acquired from the Faculty of Medicineof the University of Akdeniz and the University of Istanbulin Turkey. Firstly wavelet transform of the mammograms isobtained and the approximation coefficients are filtered byhomomorphic filter. Then the detail coefficients of thewavelet associated with noise and edges are modeled byGaussian and Laplacian variables, respectively. The con-sidered coefficients are compressed and enhanced usingthese variables with a shrinkage function. Finally using aproposed adaptive thresholding the fine details of themammograms are retained and the noise is suppressed.The preliminary results of our work indicate that thismethod provides much more visibility for the suspiciousregions.

Keywords Image enhancement . Mammography . Imagedenoising .Wavelet transform

Introduction

In recent years, breast cancer has caused a significantnumber of deaths in woman population and constitutedmore than 30% of cancer incidences in both developing anddeveloped countries [1]. In order to detect breast cancer atearly stages, mammography is the best radiographic methodavailable today. Mammography is indispensable for womenolder than 40 years as the risk of breast cancer is increased.However it is not always perfect and adequate because ofthe fuzzy nature of the mammograms and the low contrastbetween the breast cancer and its surroundings. Detectionof small malignancies is especially difficult in youngerwomen who tend to present denser breast tissue. On theother hand, lesions like calcifications have high attenuationproperties and low local contrast, but are small in size. So,the visibility of small tumors, and any associated micro-calcifications, is a problem in the mammography technol-ogy based on analog film. Therefore many research centersare developing several new technologies to detect breasttumors including digital mammography, where computersassist in the interpretation of the X-rays. The critical andessential contrast enhancement process can be improvedusing digital mammography [2, 3]. Several approacheshave been proposed for enhancement in the literature. In theapproach of Wirth et al. [4], the enhancement of digitalmammograms was based on morphological enhancement.The difference between the original image and its grayscaleopening were performed by means of non-flat structuralelements. In order to improve the contrast of the micro-calcifications, the breast region was isolated and morpho-

J Med Syst (2010) 34:993–1002DOI 10.1007/s10916-009-9316-3

P. Gorgel (*) :A. SertbasComputer Engineering Department, Engineering Faculty,Istanbul University,34320Avcilar,Istanbul, Turkeye-mail: paras@istanbul.edu.tr

O. N. UcanElectrical and Electronics Engineering Department,Engineering Faculty, Istanbul University,34320Avcilar,Istanbul, Turkey

www.Matlabi.ir

logical pre-processing was used to suppress the backgroundartifacts. Using deterministic fractal approach, Huai Li et al.[5] improved enhancement by modelling the mammograph-ic patterns. The background noise was measured by thestandard derivation. Removal was performed by subtractinga low pass filtered version of the image from itself. Lena etal. [6] proposed an enhancement system using local non-linear modification of multiscale gradient magnitudesprovided by the wavelet transform. Denoising was accom-plished by adaptive soft-thresholding and contrast enhance-ment by a local non-linear gain operator. In the study ofElsherif and Elsayad [7], a non-linear enhancement func-tion based on the soft-thresholding scheme was applied tothe images decomposed by the wavelet transform. Theenhancement transformation was cumulative and monoton-ically increasing which preserved the order of intensityinformation. After the wavelet packet coefficients were softthresholded, the coefficients were filtered with sharpeningfilter. The technique was applied especially to the irregularbreast masses. Papadopoulos et al. [8] tested five imageenhancement algorithms introducing the contrast limitedadaptive histogram equalization, the local range modifica-tion, the discrete wavelet linear stretching and shrinkagealgorithms. They achieved the highest performance in twomammographic datasets, for the local range modificationand the wavelet-based linear stretching methodology. InDominguez and Nandi’s [9] enhancement routine, statisticalmeasures of the pixel intensities in local neighborhoodswere employed to automatically set the parameters of thetransform applied to each pixel. In order to obtain effectiveenhancement over all mammographic structures of differentsizes, the enhancement routine was wrapped into a multi-scale processing framework. The objective of the procedurein [9] was to increase the contrast between mammogramstructures and their background, while providing a relative-ly uniform intensity to all of the structures.

The main problem of the approaches mentioned above isthe need of the noise estimation, which may be difficult toobtain in some situations, especially for images havinginherent noise. One of the faults encountered when usingthese approaches [4–9] is that they invariably enhance thenoise while trying to improve the contrast and sharpeningthe edges or eliminate the fine details while trying todenoise.

Scharcanski and Jung [10] described a new method formammographic image enhancement based on the wavelettransform. At each resolution, coefficients associated withnoise and coefficients associated with edges were modelledby Gaussian and Laplacian random variables respectively,and a shrinkage function was assembled based on posteriorprobabilities. The shrinkage functions at consecutive scaleswere combined, and then applied to the wavelets coef-ficients. The purpose was eliminating the noise while

enhancing the fine details in the mammograms. But theirtechnique is inadequate to perform this task. Becausedenoising is not an alternative of enhancement. When theexperimental results are analyzed it can be seen that thenoise is partly suppressed and the enhancement of the edgedetails is not implemented efficiently. Therefore in thispaper, we advance the Scharcanski and Jung’s [10]approach to perform the contrast enhancement by combin-ing their denoising method with homomorphic filtering andthe proposed adaptive thresholding. In our method, thedecomposed approximation coefficients are passed througha homomorphic filter. This filter provides an efficientenhancement that emphasizes the suspicious regions withlow contrast. Next, while the detail coefficients areconsidered to be distributed according to the Gaussianprobability density function (pdf), the edge and fine dataare considered to be distributed according to the Laplacianpdf. A shrinkage function is constituted based on Bayesianposterior probability using the remodelled detail coeffi-cients. Finally an adaptive thresholding function is appliedto these coefficients after the inverse wavelet transform sothe remainder noise resembling very small points iseliminated. Thus the image is pre-processed to improve itslocal contrast and the discrimination of subtle details. Onthe other hand Scharcanski and Jung [10] use a poor globalthresholding that can not perform a sufficient result tosuppress the noise in small edge details and the approachhas a limited effect on high density tissues. The explanatoryflow chart of our study is demonstrated in Fig. 1. Theexperiments demonstrate that the proposed method caneffectively enhance the contours and fine details of themammographic features which will be useful for breastcancer diagnosis.

The rest of the paper is organized as follows. The“Discrete wavelet transform” section gives a description ofthe wavelet transform. The “Proposed denoising andenhancement method” section describes the proposedmethod. The “Experimental results” section presents theexperimental results and finally the “Conclusions” sectiongives our conclusions.

Discrete wavelet transform

To compute the wavelet transform with two detail images[10], a smoothing function ϕ(x, y) and two wavelets ψi(x, y)are needed. The dilation of these functions are denoted by:

ft x; yð Þ ¼ 1t2 f

xt ;

yt

� �;y i

t x; yð Þ ¼ 1t2 y

i xt ;

yt

� �; i ¼ 1; 2; ð1Þ

t demonstrates the scale and equals to 2j.The dyadic wavelet transform f(x, y) at the t scale has

two detail components, given by:

994 J Med Syst (2010) 34:993–1002

Wi2j f x; yð Þ ¼ f � y i

2j� �

x; yð Þ; i ¼ 1; 2; ð2Þand one low-pass component, given by:

T2j f x; yð Þ ¼ f � f2jð Þ x; yð Þ ð3ÞThe details in the x and y directions are represented by

the coefficients W 12j f x; yð Þ and W 2

2j f x; yð Þ respectively. Inthis way the image gradient at the resolution 2j can beapproximated by:

W2 j f x; yð Þ ¼ W 12 j f x; yð Þ

W 22 j f x; yð Þ

!: ð4Þ

In this work, the discrete wavelet transform (DWT) is usedsince we are dealing with the digital images f[n, m]. The basicidea of the DWT is approximating a signal through a set ofbasic mathematical functions. In DWT the signal’s multi-resolution decomposition is implemented into four subbandscalled the approximation (low frequency component) anddetails (high frequency component). The approximation Aindicates a low resolution of the original image. The detail

coefficients are horizontal (H), vertical (V) and diagonal (D).This decomposition is repeated to further increase thefrequency resolution. The approximation coefficients aredecomposed with high and low pass filters and then down-sampled [11]. This is represented as a binary tree with nodespointing a sub-space with different time–frequency localiza-tion. The tree is known as a filter bank as seen in Fig. 2.

Proposed denoising and enhancement method

After the wavelet transformation of a given digital image f[n, m], we obtain a decomposed detail coefficient groupconsists of one level horizontal detail WH

21 f n;m½ �, one levelvertical detail WV

21 f n;m½ �, one level diagonal detailWD

21 f n;m½ �, two level horizontal detail WH22 f n;m½ �, two level

vertical detail WV22 f n;m½ � and finally two level diagonal

detail WD22 f n;m½ �. We propose the first step of enhancement

by applying the homomorphic filter to the approximationswhile shrinking the details based on posteriori probabilitiesto discriminate coefficients associated with edges fromcoefficients associated with noise. The adjusted approxi-mation and details are adaptively thresholded so the objectscan be separated from the background and suspicious areascan be identified much more easily. Finally we compute theinverse wavelet transform to obtain the processed image.

Homomorphic filtering

A good deal of control over the illumination and reflectancecomponents is able to be gained with a homomorphic filter.This control requires specification of a filter function H(u,v) that affects the low and high frequency components ofthe Fourier transform in different ways. An image f(x, y)can be expressed as the product of illumination andreflectance components [12]:

f x; yð Þ ¼ i x; yð Þr x; yð Þ ð5Þand we define:

z x; yð Þ ¼ ln f x; yð Þ ¼ ln i x; yð Þ þ ln r x; yð Þ; ð6Þ

Z u; vð Þ ¼ Fi u; vð Þ þ Fr u; vð Þ; ð7Þ

Fig. 2 Wavelet decomposition tree

Fig. 1 Flow chart of the proposed method

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Z(u, v), Fi(u, v), and Fr(u, v) demonstrates the Fouriertransforms of z(x, y).

If is processed by means of a filter function H(u, v), isthe Fourier transform of the result:

S u; vð Þ ¼ H u; vð ÞZ u; vð Þ¼ H u; vð ÞFi u; vð Þ þ H u; vð ÞFr u; vð Þð8Þ

So s(x, y) is the inverse Fourier transform of and can beexpressed in the form:

s x; yð Þ ¼ i ¶ x; yð Þ þ r ¶ x; yð Þ ð9ÞFinally, our desired enhanced image, denoted by that is:

g x; yð Þ ¼ es x;yð Þ¼ ei ¶ x;yð Þ � er ¶ x;yð Þ¼ i0 x; yð Þr0 x; yð Þ: ð10ÞIn this particular application, the key to the approach is

the separation of the illumination and reflectance compo-nents achieved in the form shown in Eq. 7. Thehomomorphic filter function H(u, v) can then operate onthese components separately as indicated in Eq. 8. The filterH(u, v) can be shown as:

H u; vð Þ ¼ gH � gLð Þ 1� e�c D2 u;vð Þ=D20ð Þh i

þ gL ð11Þ

where D0 is a specified distance from the origin of thetransform, D(u, v) is the distance from point (u, v) to thecenter of the frequency rectangle, constant c has beenintroduced to control the sharpness of the slope of the filterfunction as it transitions between γL and γH. A brief of thehomomorphic filtering process is given in Fig. 3.

Wavelet shrinkage

The wavelet shrinkage is a signal denoising techniquebased on the idea of adjusting the wavelet coefficients. Theaim is to produce signal with lesser amount of noise. Anonlinearity that reduces low amplitude values and retainshigh amplitude values is implemented. Our detail coef-

ficients WH21 f n;m½ �, W V

21 f n;m½ �, WD21 f n;m½ �, WH

22 f n;m½ �,W V

22 f n;m½ � and WD22 f n;m½ � are shrunk according to the

Eq. 12 for j=1,2:

WH2 j f n;m½ � ¼ WH

2 j f n;m½ �SH2j n;m½ �WV

2 j f n;m½ � ¼ WV2 j f n;m½ �SV2j n;m½ �

WD2 j f n;m½ � ¼ WD

2 j f n;m½ �SD2j n;m½ �ð12Þ

where Si2j n;m½ � are called shrinkage factors for i=H, V, D.In order to determine a shrinkage function S(x) the

distribution coefficients are analyzed. In this work wemodel the mammographic image noise by an additive zero-mean Gaussian noise [10]. The detail coefficients of animage constituted only by Gaussian noise may be consid-ered Gaussian distributed with standard deviation σnoise.Under these circumstances, the probability density functionthat models the coefficient distribution is given by:

p xjnoiseð Þ ¼ 1

snoise

ffiffiffiffiffi2p

p e�x2=2s2noise ð13Þ

Hence, p(x|noise) represents the distribution coefficientsconsidering that image consists of the noise only. On theother hand, the distribution of the wavelet coefficients fornoise-free images is sharply peaked near the origin and haslong tail due to image edges. So we model such coefficientswith Laplacian probability density function, given by:

p xjedgeð Þ ¼ 1

2be� x�mj j

b ; b ¼ 1

N

XNi¼1

xi � mj j: ð14Þ

Here, N is the number of independent and identicallydistributed samples μ is the sample median and b is themaximum likelihood estimator. p(x|edge) represents thedistribution of coefficients assuming that only edges andhomogeneous regions are present in the image. Conse-quently we consider modeling the decomposed waveletcoefficients of images containing noisy edges and homo-geneous regions affected by noise. The coefficients belong-ing to the tail of the distribution are likely to be edge relatedand coefficients close to the origin of the histogram arelikely to be related to noise [10]. The origin of thehistogram is of course Gaussian shaped. We compute theshrinkage function S(x) by the posterior probability functionp(x|edge) using Bayesian theorem as follows:

S xð Þ ¼ 1� lð Þp xjedgeð Þ1� lð Þp xjedgeð Þ þ lp xjnoiseð Þ : ð15Þ

Here λ is an unknown parameter of the overallcoefficient distribution (0≤λ≤1). In this work, we choosethe value of near 1 such as 0.8. Because the image isconsidered that it may have more fine details than noise.

Adaptive thresholding

The proposed denoising technique described above can beextended to local contrast enhancement which preservesedges and other high frequency parts of the mammographicimages. It is a nonlinear enhancement method that areas oflow contrast are enhanced more than high contrast areasand sharp edges are not blurred. The key point of thewavelet denoising method is that in the wavelet domain thenoise is spread fairly uniformly among all coefficients,Fig. 3 Homomorphic filtering

996 J Med Syst (2010) 34:993–1002

whereas the signal is quite sparse, being concentrated into asmall number of coefficients. This is the practical motivationfor thresholding of the detail coefficients [13]. We useadaptive local thresholding (LT) which is better for massdetection than global thresholding, because a local thresholdvalue is determined locally for each pixel based on theintensity values of the surrounding pixels [14]. Two variablesof the local thresholding should be considered; the windowsize around the pixel and thresholding value. Local thresholdvalue T is based on a recent denoising result by Birgé andMassart [15], and can be viewed as a variant of the fixed

form strategy of the wavelet shrinkage. The local thresholdTlocal applied to the denoised detail coefficients for a givenfixed decomposed tree, is defined by:

Tlocal ¼ c t�ð Þj jwith

t� ¼ argmin �sum c2 kð Þ; k < t� �þ 2vt a þ log

n

t

� �� �;

t ¼ 1; . . . ; n

24

35;

ð16Þ

Fig. 4 a Original image; b enhancement with histogram equalization; c image denoised and enhanced using the proposed method

Fig. 5 a Original image; b enhancement with histogram equalization; c image denoised and enhanced using the proposed method

J Med Syst (2010) 34:993–1002 997

where the sparsity parameter, α is chosen 1.5 for this work.The coefficients are sorted in decreasing order of theirabsolute value v, the noise variance.

In order to define an enhancement function, first wecalculate the local mean mlocal and the local standarddeviation σlocal for 5×5 pixel matrix neighbourhood. Then tstandard deviation is determined regarding to the coeffi-cient x being larger or smaller than the local mean. It isnecessary to specify that if x is small, very small, large orvery large. To achieve that, our starting point is dividing the256 gray levels into 20 sequential parts. The number oflevels is demonstrated by k (k=1,2,3,…,20). We find the

number k1 of the suitable gray level interval which thesmallest x larger than mlocal and satisfying equationx ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2local þ m2

local

q. In the same way the number k2 is

found for largest x which is smaller than mlocal andsatisfying the equation x ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffim2

local � s2local

q. Afterwards the

number of tolerance level ktol is determined. The informa-tion about how large or small of the x coefficient comparedto the values in its neighborhood is related to whether x islarger than (k1+ktol)

th or smaller than (k2−ktol)th levelinterval. The mentioned proposed enhancement functionwhich applies the threshold Tlocal with a neighborhood of5×5 pixel matrix is given by the following rule:

Edetail2j ¼

x ¼ x� Tlocal; ifx � mlocal and sx � s local and x � arrayðk1þktolÞth ½first�� �

x ¼ xþ Tlocal;

if x � mlocal and sx � s local and x < arrayðk1þktolÞth ½first� or

if x � mlocal and sx < s local or

if x < mlocal and sx < s local and x � arrayðk2�ktolÞth ½first�:

0BBB@

1CCCA

x;if x < mlocal and sx < s local and x < arrayðk2�ktolÞth ½first� or

if x < mlocal and sx � s local

!

8>>>>>>>>>>>>><>>>>>>>>>>>>>:

ð17Þ

Here, arrayk th is the set of values in kth gray level andarrayk th first½ � the first element of this array. σx is equal toffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

x2 � m2local

qfor x≥mlocal and

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffim2

local � x2q

for x<mlocal.

This enhancement rule is used to update the denoisedwavelet coefficients for detail=H,V,D and j=1,2 and finally,the inverse wavelet transform is applied to obtain thedenoised–enhanced image.

Experimental results

The proposed method has been implemented in MATLABand the approach has been tested on the mammogramsacquired from the Department of Radiodiagnostic of theFaculty of Medicine in the University of Akdeniz, and the

Faculty of Medicine in the University of Istanbul on which

Fig. 6 a Original image; b enhancement with histogram equalization; c image denoised and enhanced using the proposed method

998 J Med Syst (2010) 34:993–1002

masses were previously marked by experienced radiolog-ists. The used imaging device is a special system named“IMS Giotto Image Full Field Digital MammographySystem”. Each digital mammogram has the size of 85 μmand 2,560×4,096 pixel matrix. The modulation transfervalue and the quantum efficiency is 5 lp/mm and the spatialresolution is 6 lp/mm. There are 55 mammograms in thedatabase taken from 20 different patients.

The implemented method consists of two main steps.Firstly, the original image normalized to grayscale range([0,255]) is denoised using an approach based on a“bior3.7” wavelet transformation. A homomorphic filteris applied to the approximation coefficients by usingEq. 11 for γH=2 and γL=1.5. On the other hand the noisein the detail coefficients is assumed to distribute accordingas Gaussian and the edge data is as Laplacian distribution.

The fine detail probability function is calculated usingthe Bayesian posterior probability depending on Eq. 15for λ=0.8. This step provides noise reduction as a pre-process of denoising and enhancement system. Wepropose a local adaptive thresholding enhancement meth-od that behaves according to the information of how largeor small the coefficient gray scale numbers are. After theimplemented denoising-enhancement method is applied tothe mammogram in Fig. 4a, the brightness of the maligntumor gets larger while it gets smaller for the tissue aroundit as seen in Fig. 4c, so distinguishing the mass from thebackground is not as difficult as in the original image.There is a low contrast malign mass at the top of themammogram in Fig. 5a owing to the dense breast and as itcan be noticed, this mass is not sharp enough to diagnose.However as demonstrated in Fig. 5c after image denoising

Fig. 8 a Original image; b enhancement with histogram equalization; c image denoised and enhanced using the proposed method

Fig. 7 a Original image; b enhancement with histogram equalization; c image denoised and enhanced using the proposed method

J Med Syst (2010) 34:993–1002 999

and enhancement, the local contrast has been increasedsuccessfully so the malign mass can be clearly outlined ina first visual evolution. Also after the denoising andenhancement of Fig. 6a which represents a mammogramwith a few malign lesions, the result is illustrated inFig. 6c. In the original mammogram the mass at the top isnot able to be detected with a naked eye because it ishidden in the blurry breast tissue. In the Fig. 6c, one cannotice the mass boundary inside the frame more clearlythan in the original image. Also the other lesions whichseem like microcalcifications, get brighter after theprocess. The mammogram in Fig. 7a presents a massappears to be a bulge. As seen in Fig. 7c the irregularbottom border of the tumor can be detected easier. As weknow, it is essential in diagnosis to decide whether theboundary is regular or irregular. Besides the contrast of thetissue surrounding the mass is enhanced. In Fig. 8c similar

enhancement results are observed. Although the mass inthe original image in Fig. 8a has a very poor contrast, itgets sharpened successfully to guide the radiologist’svisual evolution accurately. Figure 9a shows a mammo-gram presenting two suspicious circular nodules at the topwith indistinct borders and a mass under them. In Fig. 9cwe can see the result of the proposed method that thebrightness of the masses is much more increased than thebrightness of the surrounding tissue in order to enhancethe visibility. Unlikely, in the region of interest in Fig. 10athe result achieved before adaptive thresholding is given.When it is compared to Fig. 10b one can realize that withthe thresholding process the edge and fine detail areenhanced and the regions which have low contrast aresharpened.

Next we compare the results of the proposed methodwith histogram equalization (HE) which is one of the well

Fig. 9 a Original image; b enhancement with histogram equalization; c image denoised and enhanced using the proposed method

Fig. 10 a The denoised imageusing the proposed methodwithout adaptive thresholding; bimage denoised and enhancedusing the proposed method

1000 J Med Syst (2010) 34:993–1002

known enhancement techniques commonly used for med-ical images. HE is a common enhancement method used toimprove the intensity contrast in medical images. Given aninput image, it stretches the dynamic range of the imageby virtue of the image’s cumulative distribution func-tion, thereby improving the image contrast [16–18]. HEis also used as a comparing enhancement method againstthe methods based on wavelet shrinkage [10, 19, 20].Besides there are recently published studies in which thenew techniques are developed based on HE [21, 22].However as seen in Figs. 4b, 5b, 6b, 7b, 8b and 9b,histogram equalization is inadequate for the local contrastand has a limited effect on high density tissues. Thereforeto distinguish the nodules from the background andoutline the shapes and the boundaries seem more difficult.The experimental results demonstrate that the proposedmethod produces more efficient results than HE fordiagnosing. As mentioned in the “Introduction” sectionearly detection and treatment of breast cancer are the mostsignificant methods to reduce mortality. The preliminaryexperimental results indicate that our method can helpimproving the local contrast, making morphologicaldetails of the masses more evident in order to successearly detection.

Conclusions

In the images belonging to the mammography technologysome important image features indicating malignant lesionsmight be lost or significantly attenuated, especially if themalignant region is located inside an almost homogeneoushigh intensity image region with very poor contrast. Forassistance in early detection of breast cancer we havedeveloped a denoising and enhancement method thatimproves the transparency of high density tissues, keepingenough contrast to characterize adequately the fine detailsand the morphology of masses. To demonstrate theeffectiveness of the proposed system, we have comparedthe results with the histogram equalization enhancementtechnique which causes losing small details and invisibilityby over brightening and increasing the contrast of the tissuearound the mass. According to the comparative work, it isseen that we provide better results with the proposedmethod in which low contrast features are more enhancedthan the high contrast areas without blurring fine imagedetails such as edges. On the other hand, histogramequalization resulted in losing small details and invisibilityby over brightening and increasing the contrast of the tissuearound the mass. As a conclusion, the proposed methodcould better assist mammography specialists to implementcomputer aided diagnosis of breast cancer.

Acknowledgement This research is supported by Istanbul Univer-sity, Research Fund., with Project No: 2477.

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