On the role of sparsity in inverse problems

Journal of Inverse and Ill-Posed Problems

Volumn 17, Issue 1, 2009, Pages 61-68

  Lorenz, D A ^a  

^a UNIVERSITY OF BREMEN   (Germany)

Author keywords

Error estimates; Inverse problems; Sparsity constraints

Indexed keywords

EID: 59449088843     PISSN: 09280219     EISSN: None     Source Type: Journal    
DOI: 10.1515/JIIP.2009.007     Document Type: Article

References (12)

1. K. Bredies and D. A. Lorenz, Linear convergence of iterated soft-thresholding. Journal of Fourier Analysis and Applications (to appear).
2. E. J. Candès and T. Tao, Decoding by linear programming. IEEE Transaction on Information Theory 51, 12 (2005), 4203-4215. (Pubitemid 41800353)
3. I. Daubechies, M. Defrise, and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications in Pure and Applied Mathematics 57, 11 (2004), 1413-1457. (Pubitemid 39427442)
4. D. Donoho, Compressed sensing. IEEE Transactions on Information Theory 52, 4 (2006), 1289-1306.
5. H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems. Kluwer Academic Publishers Group, Dordrecht, 2000.
6. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, Gradient projection for sparse reconstruction: Applications to compressed sensing and other inverse problems. IEEE Journal of Selected Topics in Signal Processing 4 (2007), 586-597.
7. R. Griesse and D. A. Lorenz, A semismooth Newton method for Tikhonov functionals with sparsity constraints. Inverse Problems 24 (2008), 035007 (19pp).
8. M. Hintermüller, K. Ito, and K. Kunisch, The primal-dual active set strategy as a semismooth Newton method. SIAM Journal on Optimization 13, 3 (2003), 865-888. (Pubitemid 36971115)
9. 1-regularized least squares problems with applications in signal processing and statistics. IEEE Journal on Selected Topics in Signal Processing 1, 606-617.
10. D. A. Lorenz, Non-convex variational denoising of images: Interpolation between hard and soft wavelet shrinkage. Current Development in Theory and Application of Wavelets 1, 1 (2007), 31-56.
11. D. A. Lorenz, Convergence rates and source conditions for Tikhonov regularization with sparsity constraints. J. Inv. Ill-Posed Problems 16, 5 (2008), 463-478.
12. R. T. Rockafellar and R. J.-B. Wets, Variational Analysis. Springer, 1998.