A generalized iterated shrinkage algorithm for non-convex sparse coding

Proceedings of the IEEE International Conference on Computer Vision

Volumn , Issue , 2013, Pages 217-224

  Zuo, Wangmeng ^a,c   Meng, Deyu ^b   Zhang, Lei ^c   Feng, Xiangchu ^d   Zhang, David ^c  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

^c HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^d XIDIAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FACE RECOGNITION; IMAGE CLASSIFICATION; IMAGE RECONSTRUCTION; SHRINKAGE; TABLE LOOKUP;

1-NORM MINIMIZATIONS; ANALYTIC SOLUTION; ITERATIVELY REWEIGHTED LEAST SQUARES; LOOK UP TABLE; P-NORM MINIMIZATION; SOFT-THRESHOLDING OPERATORS; SPECIFIC VALUES; THRESHOLDING METHODS;

ITERATIVE METHODS;

EID: 84898776032     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICCV.2013.34     Document Type: Conference Paper

References (39)

1. M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo. Fast image recovery using variable splitting and constrained optimization. IEEE T-IP, 19(9):2345-2356, 2010.
2. A. Antoniadis. Wavelets in statistics: a review (with discussion). Italian Journal of Statistics, 6(2):97-130, 1997.
3. A. Beck and M. Teboulle. Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE T-IP, 18(11):2419-2434, 2009.
4. A. Beck and M. Teboulle. A fast iterative shrinkage/thresholding algorithm for linear inverse problems. SIAM J. Imag. Sci., 2(1):183-202, 2009.
5. J. Bioucas-Das and M. Figueiredo. A new twist: Two step iterative shrinkage/thresholding algorithms for image restoration. IEEE T-IP, 16(12):2992C-3004, 2007.
6. E. Candes and T. Tao. Near optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inf. Theory, 52(12):5406-5425, 2006.
7. E. J. Candes and J. Romberg. Quantitative robust uncertainty principles and optimally sparse decompositions. J. Foundations of Computational Mathematics, 6(2):227-254, 2006.
8. E. J. Candes, M. Wakin, and S. Boyd. Enhancing sparsity by reweighted-1 minimization. Journal of Fourier Analysis and Applications, 14(5):877C905, 2008.
9. M. Cetin and W. C. Karl. Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization. IEEE T-IP, 10(4):623-C631, 2001.
10. R. Chartrand. Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Process. Lett., 14(10):707C-710, 2007.
11. R. Chartrand and V. Staneva. Restricted isometry properties and nonconvex compressive sensing. Inverse Problems, 24(035020):1C-14, 2008.
12. R. Chartrand and W. Yin. Iteratively reweighted algorithms for compressive sensing. IEEE ICASSP, pages 3869C-3872, 2008.
13. T. Cho, C. Zitnick, N. Joshi, S. Kang, R. Szeliski, and W. Freeman. Image restoration by matching gradient distributions. IEEE T-PAMI, 34(4):683-C694, 2012.
14. T. S. Cho, N. Joshi, C. L. Zitnick, S. B. Kang, R. Szeliski, and W. T. Freeman. A content-aware image prior. Proc. CVPR, 2010.
15. I. Daubechies, M. Defrise, and C. D. Mol. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications on Pure and Applied Mathematics, 57:1413-C1457, 2004.
16. D. Donoho. De-noising by soft-thresholding. IEEE Trans. Inf. Theory, 41(3):613C-627, 1995.
17. D. L. Donoho. For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution. Communications on Pure and Applied Mathematics, 59(7):907-C934, 2006.
18. M. Elad. Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. Springer, 2010.
19. J. Fan. Comment on 'wavelets in statistics: A review' by A. Antoniadis. Italian Journal of Statistics, 6(2):131-C138, 1997.
20. S. Foucart and M. Lai. Sparsest solutions of underdetermined linear systems via-q minimization for 0
21. A. Georghiades, P. Belhumeur, and D. Kriegman. From few to many: Illumination cone models for face recognition under variable lighting and pose. IEEE T-PAMI, 23(6):643C-660, 2001.
22. I. F. Gorodnitsky and B. D. Rao. Sparse signal reconstruction from limited data using focuss: A re-weighted minimum norm algorithm. IEEE T-SP, 45(3):600-C616, 1997.
23. N. Joshi, C. L. Zitnick, R. Szeliski, and D. Kriegman. Image deblurring and denoising using color priors. Proc. CVPR, 2009.
24. D. Krishnan and R. Fergus. Fast image deconvolution using hyper-laplacian priors. Proc. NIPS, 2009.
25. M. Lai and J. Wang. An unconstrained-q minimization with 0
26. A. Levin, R. Fergus, F. Durand, and W. Freeman. Image and depth from a conventional camera with a coded aperture. ACM TOG, 26(3):70, 2007.
27. Q. Lv, Z. Lin, Y. She, , and C. Zhang. A comparison of typical-p minimization algorithms. Neurocomputing, 2013.
28. G. Marjanovic and V. Solo. On lq optimization and matrix completion. IEEE Trans. T-SP, 60(11):5714-5724, 2012.
29. R. Mazumder, J. H. Friedman, and T. Hastie. SparseNet: Coordinate descent with nonconvex penalties. Journal of the American Statistical Association, 106(495):1125-1138, 2011.
30. B. K. Natarajan. Sparse approximate solutions to linear systems. SIAM J. Comput., 24(2):227-234, 1995.
31. Y. She. Thresholding-based iterative selection procedures for model selection and shrinkage. Electronic Journal of Statistics, 3:384-C415, 2009.
32. Y. She. An iterative algorithm for fitting nonconvex penalized generalized linear models with grouped predictors. Computational Statistics & Data Analysis, 56(10):2976-2990, 2012.
33. E. Simoncelli and E. H. Adelson. Noise removal via bayesian wavelet coring. ICIP, pages 379C-382, 1996.
34. S. Wang, T. Hou, J. Border, H. Qin, and R. Miller. High-quality image deblurring with panchromatic pixels. ACM TOG, 31(5):120-1-11, 2012.
35. Y. Wang, J. Yang, W. Yin, and Y. Zhang. A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imag. Sci., 1(3):248C-272, 2008.
36. J. Wright, A. Yang, A. Ganesh, S. Sastry, and Y. Ma. Robust face recognition via sparse representation. IEEE T-PAMI, 32(2):210-227, 2009.
37. Z. Xu, X. Chang, F. Xu, and H. Zhang.-1/2 regularization: A thresholding representation theory and a fast solver. IEEE T-NNLS, 23(7):1013C-1027, 2012.
38. A. Y. Yang, S. S. Sastry, A. Ganesh, and Y. Ma. Fast l1-minimization algorithms for robust face recognition, 2012.
39. W. Zuo and Z. Lin. A generalized accelerated proximal gradient approach for total-variation-based image restoration. IEEE T-IP, 20(10):2748-2759, 2011.