Thresholded Landweber Iteration (TLI) is an attractive algorithm since it has the advantage of simplicity for the problem of sparse reconstruction. However, this algorithm depends heavily on the coherence property of the redundant ictionary, and its convergence rate is slow. In this paper, we develop a modified version of TLI by using a sensing dictionary. The proposed algorithm significantly improves the reconstruction performance and the convergence roperties when compared to the classical TLI. We provide a sufficient condition for which the modified TLI algorithm an be guaranteed to exactly identify the correct atoms and also discuss the convergence properties for this agorithm. Finally, simulation results are presented to demonstrate the superior performance of the proposed lgorithm.
2. Zhang, Y., Q. Wan, and A. Huang, "Localization of narrow band sources in the presence of mutual coupling sparse solution finding," Progress In Electromagnetics Resaerch, Vol. 86, 243-257, 2008.
3. Pati, Y. C., R. Rezaiifar, and P. S. Krishnaprasad, Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition, Proc. 27th Annu. Asilomar Conf. Signals, Systems, and Computers, Vol. 1, 40-44, Pacific Grove, CA, Nov. 1993.
4. Daubechies, I., M. Defrise, and C. De Mol, "An iterative thresholding algorothm for linear inverse problems," Comm. Pure Appl. Math., Vol. 57, No. 11, 1413-1457, Aug. 2004.
5. Hunter, D. and K. Lange, "A tutorial on MM algorithms," Amer. Statist., Vol. 58, 30-37, 2004.
6. Bioucas-Dias, J., "Bayesian wavelet-based image deconvolution: A GEM algorithm exploiting a class of heavy-tailed priors," IEEE Trans. Image Process., Vol. 15, No. 4, 937-951, Apr. 2006.
7. Adeyemi, T. and M. E. Davies, Sparse representations of images using overcomplete complex wavelets, IEEE SP 13th Workshop on Statistical Signal Processing, 805-809, Jul. 2006.
8. Herrity, K. K., A. C. Gilbert, and J. A. Tropp, Sparse approximation via iterative thresholding, IEEE International Conference on ICASSP, Vol. 3, 14-19, May 2006.
9. Schnass, K. and P. Vandergheynst, "Dictionary preconditioning for greedy algorithms," IEEE Trans. Signal Process., Vol. 56, No. 5, 1994-2002, May 2008.