A Modest Overview of Image De-noising Methods

1. A Modest Overview of Image De-noising Methods PengfeiWan* and YukihikoYamashita** *Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology **Department of International Development Engineering, Tokyo Institute of Technology

2. OUTLINE • What is image noise? • Why image de-nosing? • How to remove noise? • Experiments • Conclusions

3. What is image noise? • Noise means any unwantedsignal. • Image noise: caused by thermal vibrations of atoms in conductors etc caused by bit errors in transmission etc Salt & Pepper Noise (SPN) Additive White Gaussian Noise (AWGN)

4. OUTLINE • What is image noise? • Why image de-nosing? • How to remove noise? • Experiments • Conclusions

5. Why Image de-noising? • Because image noise is: • Visually unpleasant (obviously) • Bad for compression (introduces extra high frequency components) • Bad for analysis (e.g. feature extraction, object recognition, etc)

6. OUTLINE • What is image noise? • Why image de-nosing? • How to remove noise? • Experiments • Conclusions

7. How to Remove SP Noise? Salt & Pepper Noise removal is easy: Median Filter: .

8. How to Remove AWGN Noise? • Isotropic Filter • Bilateral Filter • Non-local Filter • TV Minimization • BM3D • … AWGN removal is much harder…

9. Isotropic Filter • . • The most famous isotropic filter is the Gaussian Filter: where

10. Bilateral Filter (or SUSAN Filter) • . • The weights for filtering is not only decided by spatial distance, but also range distance:

11. Non-local Filter • . • Make use of a much wider neighborhood to achieve better performance:

12. Total Variation Minimization • Enforce element-wise smoothness using L-1 norm: where

13. Block Matching and 3D filtering (BM3D) • The state-of-the-art image de-noisngalgorithm. • Basic Idea: • Enhanced sparse representation in transform domain. • Basic Procedure: • Group similar 2D image blocks into 3D arrays. • Apply a 3D transform to each group. • Threshold the transform coefficients. • Transform back to produce block estimates. • Return the estimates to their original positions. • Average the obtained estimates that are overlapping. • *3D transform is composed by a basic 2D transform and a 1D Haar transform on the third dimension.

14. Block Matching and 3D filtering (BM3D)

15. OUTLINE • What is image noise? • Why image de-nosing? • How to remove noise? • Experiments • Conclusions

16. Experiments

17. OUTLINE • What is image noise? • Why image de-nosing? • How to remove noise? • Experiments • Conclusions

18. Conclusions • BM3D achieves apparently the best objective de-noising performance. • TVM and Bilateral filter (BL) achieve the better–than–average performance. • Performance of Isotropic filter (IF) and Non-local filter (NL) is relatively poorer. • More specifically: • When the noise variance is relatively small, we have: • When the noise variance is relatively large, we have:

19. [1] http://en.wikipedia.org/wiki/Main_Page/ [2] http://www.cs.tut.fi/~foi/GCF-BM3D/ [3] V. Katkovnik, A. Foi, K. Egiazarian, and J. Astola, “From local kernel to nonlocal multiple-model image denoising”, IJCV 2010. [4] K. Dabov, A. Foi, “Image denoising by sparse 3D transform-domain collaborative filtering.” IEEE Trans. Image Processing 2007 [5] M. Lindenbaum, M. Fischer, “On Gabor contribution to image enhancement.” Pattern Recognition, 1994. [6] P. Perona, J. Malik, “Scale space and edge detection using anisotropic diffusion.” IEEE Trans. PAMI 1990. [7] A. Buades, B. Coll, “A non-local algorithm for image denoising.” Proc. CVPR 2005. [8] S. Smith, J. Brady, “SUSAN-a new approach to low level image processing,” IJCV 1997 [9] C. Tomasi, R. Manduchi, “Bilateral filtering for gray and color images,” Proc. ICCV 1998 [10] L. Rudin, S. Osher, “Total variation based image restoration with free local constrains,” Proc. ICIP. 1994. [11] S. Osher, M. Burger, “Using Geometry and iterated refinement for inverse problems: Total variation based image restoration,” JSIAM.2004

20. Thank you ! Q&A