New Bounds on Image Denoising

VCIP 2012, New Bounds on Image Denoising: Viewpoint of Sparse
Representation and Non-Local Averaging, By J. Feng, Li Song, X. Huo, X. Yang and W. Zhang

Transcript

1. New Bounds on Image Denoising: Viewpoint of Sparse Representation and Non-Local Averaging Jianzhou Feng1, Li Song1, Xiaoming Huo2, Xiaokang Yang1 and Wenjun Zhang1 1 Shanghai Digital Media Processing and Transmission Key Lab 2 Georgia Institute of Technology, Atlanta, GA, U.S.A Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 1 / 20
2. Outline 1 Motivation and goal 2 Prior art vs requirements 3 New denoising bounds 4 Experiment results 5 Conclusion Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 2 / 20
3. Outline 1 Motivation and goal 2 Prior art vs requirements 3 New denoising bounds 4 Experiment results 5 Conclusion Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 3 / 20
4. Is Denoising Dead Have we reach the bound? Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 4 / 20
5. Patch Based Denoising Problem An image I is divided into N patches zi ∈ Rn. yi = zi + ηi (1) For a denoising algorithm f, MSE(f) = 1 nN i E ˆ zi(f) − zi 2 2 . (2) Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 5 / 20
6. Goal Ideal bound: min f∈F MSE(f) (3) Requirement of the new bound: 1 Establish F: Nowadays algorithms can be well approximated with f’s in it. 2 Derive the bound: No additional assumption on the image model. Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 6 / 20
7. Outline 1 Motivation and goal 2 Prior art vs requirements 3 New denoising bounds 4 Experiment results 5 Conclusion Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 7 / 20
8. Bayasian bound (Levin et.al CVPR 2011) A general prior p(z): from a large image dataset. ˆ zi = z p(yi|z)p(z)dz (4) Conflict with requirement 1: Nowadays algorithms already use adaptive prior, validated to be more efficient than a general one. Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 8 / 20
9. Affine bias model based bound(Chatterjee et.al TIP 2010) E zi − ˆ zi 2 ≥ Tr Ji + cov−1 k (z) −1 (5) Conflict with requirement 2: while calculating Ji, they made an assumption on image patches 1 Ni zj = zi, (6) where zj − zi 2 ≤ γ. (7) Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 9 / 20
10. Outline 1 Motivation and goal 2 Prior art vs requirements 3 New denoising bounds 4 Experiment results 5 Conclusion Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 10 / 20
11. Techniques for denoising Requirement 1: Establish F: Nowadays algorithms can be well approximated with f’s in it. Main techniques shared in nowadays algorithms: Technique Image Property Sparse representation Sparsity Non-local averaging Non-local Similarity Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 11 / 20
12. Our framework Denoising process under parameter set (K, {Ni, Uk,i}): 1 Clustering geometric similar patches into K groups, Locally Adaptive Regression Kernels as feature. 2 Apply PCA to each group to obtain Uk, Uk,i contains a few columns of Uk. 3 Find Ni radiometric similar patches of zi. 4 Wiener filtering: ˆ zi = ui + Covi(Covi + σ2I)−1(yi − ui), (8) where ui = 1 Ni j Uk,iUT k,i yj (9) and Covi = Uk,i[Cov({UT k,i yj}) − σ2I]+UT k,i . (10) Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 12 / 20
13. New bound vs. Requirement Denote F as all the previous parameterized algorithms. Nowadays algorithm is approximated by a certain f using parameter set (K, {Ni, Uk,i}). (Requirement 1 satisfied) We find minf∈F MSE(f) by enumerating (K, {Ni, Uk,i}). (Requirement 2 satisfied) Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 13 / 20
14. Outline 1 Motivation and goal 2 Prior art vs requirements 3 New denoising bounds 4 Experiment results 5 Conclusion Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 14 / 20
15. Parameters The patch size is 11 × 11, so n = 121. Parameter set search range: 1 K ∈ {5, 10, 15, 20, 25}. 2 Ni ∈ [1, 20]. 3 Uk,i could use any set of columns in Uk. Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 15 / 20
16. Images for testing parrot peppers house cameraman Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 16 / 20
17. New bounds result Table 1: MSE results under different images parrot peppers house cameraman BM3D 47.37 34.91 20.83 41.84 Bound 37.89 31.03 14.94 36.02 Bound* 38.51 31.50 16.56 36.68 σ = 15 Bound: find similar patches using clean patches. Bound*: find similar patches using denoised patches of BM3D. Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 17 / 20
18. New bounds result Averaged SNR gaps between BM3D and Bound: 0.9dB. Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 18 / 20
19. Outline 1 Motivation and goal 2 Prior art vs requirements 3 New denoising bounds 4 Experiment results 5 Conclusion Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 19 / 20
20. Conclusion We proposed a new bound in the viewpoint of sparse representation and non-local averaging. Experiments results show: there still leaves room for improvement. Finding image property other than sparsity and non-local similarity is encouraged. Jianzhou Feng et al. (SJTU) VCIP 2012 2012-11-30 20 / 20