Fast Recursive Greedy Methods for Sparse Signal Recovery

Theory and algorithms of greedy methods for sparse signal recovery using <inline-formula><tex-math notation="LaTeX">\ell_{0}</tex-math></inline-formula>-minimization are developed. The theoretical analysis shows that <inline-formula><tex-math notation="...

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Vydané v:IEEE transactions on signal processing Ročník 72; s. 4381 - 4394
Hlavní autori: Xiang, Min, Zhang, Zhenyue
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
active set updating
Adaptive algorithms
adaptive pursuing
Algorithms
Convergence
fast recursion
Greedy algorithms
Indexes
Iterative methods
Matching pursuit algorithms
Optimization
Recovery
Signal processing algorithms
Signal reconstruction
Sparse signal recovery
Sparsity
Thresholding (Imaging)
Vectors
ISSN:1053-587X, 1941-0476
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Shrnutí:Theory and algorithms of greedy methods for sparse signal recovery using <inline-formula><tex-math notation="LaTeX">\ell_{0}</tex-math></inline-formula>-minimization are developed. The theoretical analysis shows that <inline-formula><tex-math notation="LaTeX">\ell_{0}</tex-math></inline-formula>-minimization is more suitable for sparse signal recovery and that the greedy method based on active set updating can solve <inline-formula><tex-math notation="LaTeX">\ell_{0}</tex-math></inline-formula>-minimization problems under weak conditions. A fast recursive algorithm RASU is given to greedily update the active set with a given sparsity level, and an adaptive strategy is proposed to escape from the local minima achieved by RASU. RASU is further applied to minimize the residual. The algorithm FRASM repeats this procedure, using multiple starting points to enhance the efficiency. A fast algorithm SHTP is proposed to provide the multiple choices for FRASM, and itself is also an efficient algorithm solving the sparse problem. By combining an adaptive updating rule to estimate the sparsity of the sparsest signal, the FRASM is adopted to minimize the sparsity level subject to a residual constraint, yielding the algorithm SASSP. Numerical experiments demonstrate the superior performance of FRASM and SASSP compared to other sparse algorithms.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2024.3419132