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Sparsity-based Image Deblurring with Locally Adaptive and Nonlocally Robust Regularization

Sparsity-based Image Deblurring with Locally Adaptive and Nonlocally Robust Regularization. Weisheng Dong a , Xin Li b , Lei Zhang c , Guangming Shi a a Xidian University, b West Virginia University, c HongKong Polytechnic University.

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Sparsity-based Image Deblurring with Locally Adaptive and Nonlocally Robust Regularization

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  1. Sparsity-based Image Deblurring with Locally Adaptive and Nonlocally Robust Regularization Weisheng Donga, Xin Lib, Lei Zhangc, Guangming Shia aXidian University, bWest Virginia University, cHongKong Polytechnic University This work is partially supported by NSF CCF-0914353, HK RGC General Research Fund (PolyU 5375/09E), NSFC (No. 60736043,61072104, 61070138,and 61071170), and the Fundamental Research Funds of the Central Universities of China (No. K50510020003)

  2. History of Image Restoration(Non-blind Image Deconvolution) Cameraman 256×256, 9×9 uniform blur, BSNR=40dB

  3. Lessons We Have Learned BM3D>DCT DCT>BM3D • “All models are wrong; but some are useful” – G. Box • Local models: wavelet/DCT, total-variation (TV), spatially-weighted TV (SWTV), … • Nonlocal models: nonlocal-mean, BM3D, nonlocal TV, ASDS-AR-NL (precursor of this work), …

  4. One Simple Message • Local variation and nonlocal invariance are two sides of the same coin Nonlocal invariance Local variation Kanizsa Triangle

  5. Local View: Dictionary Learning Bell&Sejnowski’ICA,1996 Do&Vetterli’s contourlet,2005 Daubechies’ wavelet,1988 Elad&Aharon’K-SVD,2006 Lagrange’s idea NP-hard the magic of l1 HOTTY

  6. Nonlocal View: Structural Clustering Kmeans-based clustering NLM denoising (Buades et al. CVPR’2005)

  7. Variational Formulation Structural clustering penalty term NL-similarity penalty term

  8. Key Derivations Typo in the paper Iterative thresholding (via surrogate functions)

  9. Summary of Algorithm

  10. Connection with Other Competing Works Patch-based Image Deconvolution Via Joint Modeling of Sparse Priors (ICIP’2011) Nonlocal total-variation for image restoration (UCLA Math TR) Deconvolution network (CVPR’2010) Handling Outliers in Non-Blind Image Deconvolution (ICCV”2011) Close the Loop: Joint Blind Image Restoration and Recognition with Sparse Representation Prior (ICCV’2011)

  11. Experimental Results MATLAB codes accompanying this work are available From my homepage: http://www.csee.wvu.edu/~xinl/

  12. Image Comparison Results (I) SWTV (28.96dB) original BM3D (30.22dB) LANL (31.33dB) L0-sparsity (29.04dB) Noisy and blurred

  13. Image Comparison Results (II) SWTV (27.96dB) original BM3D (27.22dB) LANL (29.15dB) L0-sparsity (27.12dB) Noisy and blurred

  14. Image Comparison Results (III) LANL (31.33dB) CSR (32.09dB) LANL (29.15dB) CSR (29.75dB)

  15. Conclusions and Perspectives • What should we care about? • Pursue even higher ISNR value for cameraman? • A collection of benchmark images? • Landweber vs. Lucy-Richardson • Application side: • Motion deblurring: from non-blind to blind image deconvolution? • What will be the next episode like the malfunctioned mirror of Hubble Space Telescope? • Dehazing: from linear blur to nonlinear hazing

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