Restricted isometry properties and nonconvex compressive sensing

By Rick Chartrand, Valentina Staneva. 2007

677 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/a3aa36919ba22867189e37294dc614a1abddabcf

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In Biomedical Engineering

In Computational Mechanics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Fast Image Deconvolution using Hyper-Laplacian Priors (2009, background): “Chartrand [1, 2] has introduced non-convex compressive sen sing, where the usual l1 norm on the signal to be recovered is replaced with a lp quasi-norm, wherep < 1.”
A Systematic Review of Compressive Sensing: Concepts, Implementations and Applications (2018, neutral): “[48].”
Iterative reweighted algorithms for matrix rank minimization (2012, methodology): “It was empirically observed (Chartrand and Staneva, 2008; Chartrand and Yin, 2008) that IRLS-p shows a better recovery performance than ℓ 1 minimization for p < 1 and has a similar performance as the reweighted ℓ 1 algorithm when p is set to zero.”
The null space property for sparse recovery from multiple measurement vectors (2011, neutral): “Indeed, in [9], Chartrand demonstrated this fact by numerical examples with Gaussian random matrices and in [10], Chartrand and Staneva showed in theory that the p minimization (8) can recover the exact sparse solution by using a fewer measurements when”
Iteratively reweighted least squares minimization for sparse recovery (2008, background): “Then the map z 7→ z ℓ Nτ deﬁnes a quasi-norm for R N , in particular the triangle inequality holds up to a constant, i.e.,”
A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding (2013, background): “Actually, both theoretical analysis and numerical experiments [9, 10, 11] have shown that the solution of (cid:2) p -norm sparse coding (0 ≤ p 1) min is close to that of the (cid:2) 1 -minimization and it is sparser.”
$L_{1/2}$ Regularization: A Thresholding Representation Theory and a Fast Solver (2012, neutral): “It often introduces extra bias in estimation [14], and cannot recover a signal with the least measurements when applied to compressed sensing [15], [7].”
Analysis of Orthogonal Matching Pursuit Using the Restricted Isometry Property (2009, methodology): “When it is satisfied, the RIP for a matrix Φ provides a sufficient condition to guarantee successful sparse recovery using a wide variety of algorithms [8, 11–19].”
Minimization of ℓ1-2 for Compressed Sensing (2015, background): “Non-convex (concave) functions, such as lp (quasi-)norm (p < 1) [12, 13] and log-det functional [10], have also been proposed as alternatives to l0.”