Hard thresholding pursuit: An algorithm for compressive sensing

SIAM Journal on Numerical Analysis

Volumn 49, Issue 6, 2011, Pages 2543-2563

  Foucart, Simon ^a  

^a DREXEL UNIVERSITY   (United States)

Author keywords

Compressive sensing; Iterative algorithms; Sparse recovery; Thresholding

Indexed keywords

COMPRESSIVE SAMPLING; COMPRESSIVE SENSING; EMPIRICAL PERFORMANCE; FINITE NUMBER; HARD THRESHOLDING; ITERATIVE ALGORITHM; LOW COMPLEXITY; MATCHING PURSUIT ALGORITHMS; MATRIX; NUMERICAL EXPERIMENTS; SPARSE RECOVERY; SPARSE SOLUTIONS; SUFFICIENT CONDITIONS; THRESHOLDING;

ALGORITHMS; CHANNEL ESTIMATION; LINEAR SYSTEMS; SIGNAL RECONSTRUCTION;

ITERATIVE METHODS;

EID: 84856034474     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/100806278     Document Type: Article

References (18)

1. R. Berinde, Advances in Sparse Signal Recovery Methods, Master's thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 2009.
2. T. Blumensath and M.E. Davies, Iterative thresholding for sparse approximations, J. Fourier Anal. Appl., 14 (2008), pp. 629-654.
3. T. Blumensath and M.E. Davies, Iterative hard thresholding for compressed sensing, Appl. Comput. Harmon. Anal., 27 (2009), pp. 265-274.
4. T. Blumensath and M.E. Davies, Normalized iterative hard thresholding: Guaranteed stability and performance, IEEE J. Sel. Top. Signal Process., 4 (2010), pp. 298-309.
5. T.T. Cai, L. Wang, and G. Xu, Shifting inequality and recovery of sparse signals, IEEE Trans. Signal Process., 58 (2010), pp. 1300-1308.
6. E. Candés and T. Tao, Decoding by linear programing, IEEE Trans. Inform. Theory, 51 (2005), pp. 4203-4215.
7. A. Cohen, W. Dahmen, and R.A. DeVore, Compressed sensing and best k-term approximation, J. Amer. Math. Soc., 22 (2009), pp. 211-231.
8. W. Dai and O. Milenkovic, Subspace pursuit for compressive sensing signal reconstruction, IEEE Trans. Inform. Theory, 55 (2009), pp. 2230-2249.
9. D. Donoho and J. Tanner, Precise undersampling theorems, Proc. IEEE, 98 (2010), pp. 913-924.
10. S. Foucart, A note on guaranteed sparse recovery via l1-minimization, Appl. Comput. Harmon. Anal., 29 (2010), pp. 97-103.
11. S. Foucart, Sparse recovery algorithms: Sufficient conditions in terms of restricted isometry constants, in Proceedings of the 13th International Conference on Approximation Theory, M. Neantu and L. Schumaker, eds., San Antonio, TX, 2010, Springer, accepted.
12. R. Garg and R. Khandekar, Gradient descent with sparsification: An iterative algorithm for sparse recovery with restricted isometry property, in Proceedings of the 26th International Conference on Machine Learning, L. Bottou and M. Littman, eds., ACM, New York, 2009, pp. 337-344.
13. A. Gilbert, M. Strauss, J. Tropp, and R. Vershynin, One sketch for all: Fast algorithms for compressed sensing, in Proceedings of the 39th Annual ACM Symposium on Theory of Computing, San Diego, CA, 2007, pp. 237-246. (Pubitemid 47630740)
14. S. Huang and J. Zhu, Hybrid Iterative Thresholding for Sparse Signal Recovery from Incomplete Measurements, Department of Mathematics and Systems, College of Science, National University of Defense Technology, Changsha, China, preprint.
15. P. Jain, R. Meka, and I. S. Dhillon, Guaranteed rank minimization via singular value projection: Supplementary material, in Advances in Neural Information Processing Systems 23, J. Lafferty, C.K.I. Williams, J. Shawe-Taylor, R.S. Zemel, and A. Culotta, eds., 2010, pp. 937-945.
16. A. Maleki, Coherence analysis of iterative thresholding algorithms, in Proceedings of the Allerton Conference on Communication, Control, and Computing, Monticello, IL, 2009, pp. 236-243.
17. S.G. Mallat and Z. Zhang, Matching pursuits with time-frequency dictionaries, IEEE Trans. Signal Process., 41 (1993), pp. 3397-3415.
18. D. Needell and J.A. Tropp, CoSaMP: Iterative signal recovery from incomplete and inaccurate samples, Appl. Comput. Harmon. Anal., 26 (2009), pp. 301-332.