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Wavelet-Domain Video Denoising Based on Reliability Measures

Vladimir Zlokolica, Aleksandra Piˇzurica and Wilfried Philips

Circuits and Systems for Video Technology2006, Transaction on IEEE Journals

Outline

• Introduction• Proposed Video Denoising Method– Noise Estimation[36]– Reliability of MV Estimates– Motion Estimation– Recursive Temporal Filtering (RTF)– Adaptive Spatial Filtering

• Experimental Results• Conclusions

• Video denoising: spatial-temporal filters.• Filtering:– Nonseparable (fully 3-D) [2]–[6]– Separable (2-D +1-D) [7]–[14]• Combined: weighting for spatial and temporal?• Spatial-first: ringing or blurring at high noise levels.• Temporal-first

• We adopt the temporal-first approach, and develop a robust motion estimation method.

Introduction

Proposed Video Denoising Method

Noise Estimation• Assume that most frequent gradient amplitude

is predominately caused by noise:

• It can be related to the input noise level:

• Finally, we recursively update estimated σs :

[36]V. Zlokolica, A. Pizurica, and W. Philips, “Wavelet domain noise-robust motion estimation and noise estimation for video denoising,”presented at the 1st Int. Workshop Video Process. Quality Metrics Consum. Electron., Scotssdale, AZ, Jan. 2005, Paper no. 200.

• Parameters k1 = 0.001, k2 = 1.069 and k3 =2.213.• value is almost independent of image

context and strongly corresponds to noise level.

Noise Estimation

[36]V. Zlokolica, A. Pizurica, and W. Philips, “Wavelet domain noise-robust motion estimation and noise estimation for video denoising,”presented at the 1st Int. Workshop Video Process. Quality Metrics Consum. Electron., Scotssdale, AZ, Jan. 2005, Paper no. 200.



• The proposed method uses a nondecimated wavelet transform[35].

• Denote wavelet bands: WB={LL,HL,LH,HH}• The spatial position as: r = (x,y)• The decomposition level: l = 1,…,N

(1 denotes the finest scale and N the coarsest)• WBn: noisy band; WBtf: temporally filtered;

WBstf: spatio-temporally filtered band.

Reliability of MV Estimates• We define the MAD for each block s in the

wavelet band WB(l)(r,t), as follows:

– Bs : the set of r belonging to the given 8x8 block.– WB: {LL,HL,LH,HH}– N: the maximum decomposition level.

Reliability of MV Estimates• Define the horizontal θH and vertical θ V reliabilities of MV v:

– Where d1 = d2 = … = dN and

• Analogously, we define the “per wavelet band” WB(l) reliability of the estimated MV v:

• MAD→σn then θ→1 , MAD>>σn then θ→0.

Motion Estimation

• Wavelet-Domain Three-Step Method:– Estimates first MV field at the roughest scale and in the

following steps refines the MV field:

• vpi {∈ 0,s,s’,t,t’}; P(0) = 0, P(vpi) = 2.5

• v(1)cx , v(1)

cy {-8,-4,0,4,8}; ∈ v(2)cx , v(2)

cy {-4,-2,0,2,4};∈v(3)

cx , v(3)cy {-2,-1,0,1,2}; ∈

Motion Estimation• The cost function:

– Where the constants C1 and C2 are optimized to obtain a noise robust and smooth MV field: C1= 1, C2 = 1.45

– Assign more weight to the cost function for higher θH and θ V for the tested nonzero correction.


Recursive Temporal Filtering (RTF)

• Wavelet domain temporal filtering:

• When WB(l)tf(r-vb,t-1) has not all been filtered,

noisy wavelet coefficient will propagate.

Recursive Temporal Filtering (RTF)

• To solve this problem, we update α(l)WB(s,t,σn,vb) with a

correction function:

– When α(l)WB(r-vb,t-1) → 0, α(l)

WB*(r,t) →0.5:

Both frames are noisy, perform simple averaging.– When α(l)

WB(r-vb,t-1) → 1, α(l) WB

*(r,t) → α(l) WB(r,t).

– Furthermore, we apply α = 1 at least two time-recursions with reliable MVs have been applied in the last two frames.


Adaptive Spatial Filtering

• Let δ(rc) denote the neighborhood surrounding the central pixel rc :

– Where T = MAD(l)WB(s,t,vb) , km = 1.

– The lower MAD the for the corresponding wavelet band WB(l) and block s, the less we will average.

Experimenta

l Results

Fig. 4. Results for the 29th frame of “Bicycle” sequence with added Gaussian noise(σn= 15), processed by (c) WRTF filter and (d) 3RDS filter [16].

(a) Original image frame. (b) Noisy image frame.(c) WRTF(d) 3RDS filter [16]

Experimenta

l Results

Fig. 7. Results for the 75th frame of the processed “Flower Garden” sequence with added Gaussian noise (σn = 15), by (c) the 3DWTF algorithm, and (d) theWRSTF algorithm.

(a) Original image frame. (b) Noisy image frame.(c) 3DWTF(d) WRSTF

Experimental Results(a)

(c)

(b)

(d)

Experimental Results

Experimental Results

Conclusions

• We have proposed a new method for motion estimation and image sequence denoising in the wavelet domain.

• By robustly estimating motion and compensating, we efficiently remove noise without introducing visual artifacts.

• In future work, we intend to refine our motion estimation framework in order to deal with occlusion and moving block edges.