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Wavelet-Domain Video Denoising Based on Reliability Measures

Wavelet-Domain Video Denoising Based on Reliability Measures. Vladimir Zlokolica , Aleksandra Piˇ zurica and Wilfried Philips Circuits and Systems for Video Technology 2006 , Transaction on IEEE Journals. Outline. Introduction Proposed Video Denoising Method Noise Estimation[36]

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Wavelet-Domain Video Denoising Based on Reliability Measures

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  1. Wavelet-Domain Video Denoising Based on Reliability Measures Vladimir Zlokolica, Aleksandra Piˇzuricaand WilfriedPhilips Circuits and Systems for Video Technology2006, Transaction on IEEE Journals

  2. 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

  3. Introduction • 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-firstapproach, and develop a robust motion estimation method.

  4. Proposed Video DenoisingMethod

  5. Noise Estimation • Assumethat most frequent gradient amplitude is predominatelycaused by noise: • It can be related to the input noiselevel: • 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.

  6. Noise Estimation • Parameters k1 = 0.001, k2 = 1.069 and k3=2.213. • value is almost independent of image context and strongly corresponds to noise level. [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.

  7. Proposed Video DenoisingMethod

  8. Proposed Video DenoisingMethod • 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.

  9. Reliability of MV Estimates • We define the MADfor each block s in the wavelet band WB(l)(r,t), as follows: • Bs: the set ofr belonging to the given 8x8 block. • WB: {LL,HL,LH,HH} • N: the maximum decomposition level.

  10. Reliability of MV Estimates • Define the horizontal θHand vertical θV reliabilities of MV v: • Where d1 = d2 = … = dNand • 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.

  11. Motion Estimation • Wavelet-Domain Three-Step Method: • Estimates first MV field at the roughestscale 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};

  12. 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 θVfor the tested nonzero correction.

  13. Proposed Video DenoisingMethod

  14. Recursive Temporal Filtering (RTF) • Wavelet domain temporalfiltering: • When WB(l)tf(r-vb,t-1) has not all been filtered, noisywavelet coefficient will propagate.

  15. 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, performsimple averaging. • When α(l)WB(r-vb,t-1) → 1, α(l) WB*(r,t) → α(l) WB(r,t). • Furthermore, we applyα = 1 at least two time-recursions with reliable MVs have been appliedin the last two frames.

  16. Proposed Video DenoisingMethod

  17. 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.

  18. Experimental 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]

  19. Experimental 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) the WRSTF algorithm. (a) Original image frame. (b) Noisy image frame. (c) 3DWTF (d) WRSTF

  20. Experimental Results (a) (b) (c) (d)

  21. Experimental Results

  22. Experimental Results

  23. 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.

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