Nonlocally centralized simultaneous sparse coding

Abstract

The concept of structured sparse coding noise is introduced to exploit the spatial correlations and nonlocal constraint of the local structure. Then the model of nonlocally centralized simultaneous sparse coding(NC-SSC) is proposed for reconstructing the original image, and an algorithm is proposed to transform the simultaneous sparse coding into reweighted low-rank approximation. Experimental results on image denoisng, deblurring and super-resolution demonstrate the advantage of the proposed NC-SSC method over the state-of-the-art image restoration methods.

Keywords

sparse representation / image restoration / low-rank approximation / alternative direction method

References

[1] Zibulevsky M, Elad M. L ₁-L ₂ optimization in signal and image processing[J]. IEEE Signal Processing Magazine, 2010, 27(3): 76-88.

[2] Bioucas-Dias J M, Figueiredo M A T. A new TwIST: Twostep iterative shrinkage/thresholding algorithms for image restoration[J]. IEEE Transactions on Image Processing, 2007, 16(12): 2992-3004.

[3] Mairal J, Elad M, Sapiro G. Sparse represenation for color image restoration[J]. IEEE Transactions on Image Processing, 2008, 17(1): 53-69.

[4] Dabov K, Foi A, Katkovnik V, et al. Image denoising by sparse 3-D transform-domain collaborative filtering[J]. IEEE Transactions on Image Processing, 2007, 16(8): 2080-2095.

[5] Elad M, Aharon M. Image denoising via sparse and redundant representations over learned dictionaries[J]. IEEE Transactions on Image Processing, 2006, 15(12): 3736-3745.

[6] Dabov K, Foi A, Katkovnik V, et al. Image restoration by sparse 3D transform-domain collaborative filtering[J]. SPIE Proceedings, 2008, 6812: 681207

[7] Dong W, Zhang L, Shi G, et al. Image deblurring and supper-resolution by adaptive sparse domain selection and adaptive regularization[J]. IEEE Transactions on Image Processing, 2011, 20(7): 1838-1857.

[8] Dong W, Zhang L, Shi G. Centralized sparse representation for image restoration[C]. Proceedings of IEEE International Conference on Computer Vision, 2011.

[9] Yang J, Wright J, Huang T S, et al. Image super-resolution via sparse representation[J]. IEEE Transactions on Image Processing, 2010, 19(11): 2861-2873.

[10] Dong W, Zhang L, Shi G, et al. Nonlocally centralized sparse representation for image restoration[J]. IEEE Transactions on Image Processing, 2013, 22(4): 1620-1630.

[11] Dong W, Shi G, Li X. Nonlocal image restoration with bilateral variance estimation: A low-rank approach[J]. IEEE Transactions on Image Processing, 2013, 22(2): 700-711.

[12] Candes E J, Tao T. Near-optimal signal recovery from random projections: Universal encoding strategies?[J]. IEEE Transactions on Information Theory, 2006, 52(12): 5406-5425.

[13] Donoho D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.

[14] Candes E J, Romberg J, Tao T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.

[15] Buades A, Coll B, Morel J M. A non-local algorithm for image denoising[C]. Proceedings of IEEE International Conference on Computer Vision, 2005.

[16] Mairal J, Bach F, Ponce J, et al. Non-local sparse models for image restoration[C]. Proceedings of IEEE International Conference on Computer Vision, 2009.

[17] Katkovnik V, Foi A, Egiazarian K, et al. From local kernel to nonlocal multiple-model image denoising[J]. International Journal of Computer Vision, 2010, 86(1): 1-32.

[18] Dabov K, Foi A, Katkovnik V, et al. BM3D image denoising with shape-adaptive principal component analysis[C]. Proceedings of Workshop on Signal Processing with Adaptive Sparse Structured Representations, 2009.

[19] Beck A, Teboulle M. Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems[J]. IEEE Transactions on Image Processing, 2009, 18(11): 2419-2434.

[20] Portilla J. Image restoration through l0 analysis-based sparse optimization in tight frames[C]. Proceedings of IEEE International Conference on Computer Vision, 2009.

[21] Danielyan A, Katkovnik V, Egiazarian K. BM3D frames and variational image deblurring[J]. IEEE Transactions on Image Processing, 2012, 21(4): 1715-1728.

[22] Marquina A, Osher S J. Image super-resolution by TV-regularization and Bregman iteration[J]. Journal of Scientific Computing, 2008, 37(3): 367-382.