Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Subspace pursuit for compressive sensing signal reconstruction
IEEE Transactions on Information Theory
On recovery of sparse signals via l1 minimization
IEEE Transactions on Information Theory
Coherence analysis of iterative thresholding algorithms
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Lower bounds on the maximum cross correlation of signals (Corresp.)
IEEE Transactions on Information Theory
Sparse representations in unions of bases
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Fast image deconvolution using closed-form thresholding formulas of Lq(q=12,23) regularization
Journal of Visual Communication and Image Representation
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Finding the sparset solution of an underdetermined system of linear equations y=Ax has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the most efficient and important classes of algorithms. This is mainly due to their low computational complexities, especially for large scale applications. The aim of this paper is to provide guarantees on the global convergence of a wide class of iterative thresholding algorithms. Since the thresholds of the considered algorithms are set adaptively at each iteration, we call them adaptively iterative thresholding (AIT) algorithms. As the main result, we show that as long as A satisfies a certain coherence property, AIT algorithms can find the correct support set within finite iterations, and then converge to the original sparse solution exponentially fast once the correct support set has been identified. Meanwhile, we also demonstrate that AIT algorithms are robust to the algorithmic parameters. In addition, it should be pointed out that most of the existing iterative thresholding algorithms such as hard, soft, half and smoothly clipped absolute deviation (SCAD) algorithms are included in the class of AIT algorithms studied in this paper.