Exact Reconstruction of Sparse Signals via Nonconvex Minimization

By Rick Chartrand. IEEE Signal Processing Letters, 2007

1,372 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/821f2919bef4bbb810a705cf01f7b5ed1c8e3f7e

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Citations in the corpus

Accelerating SENSE using compressed sensing (2009, background): “The average signal-to-noise ratios (SNR) were inﬁnity (no noise), 30, 15, and 7.5.”
Smoothing methods for nonsmooth, nonconvex minimization (2012, background): “An increasing number of practical problems require minimizing a nonsmooth, nonconvex function on a convex set, including image restoration, signal reconstruction, variable selection, optimal control, stochastic equilibrium problems and spherical approximations [1,8,10,11,13,21,29,30,33,42,44,61,76,8”
Deblending of Simultaneous-source Seismic Data using Fast Iterative Shrinkage-thresholding Algorithm with Firm-thresholding (2016, neutral): “12, where 0 p 1 (Chartrand 2007).”
MR Image Reconstruction From Highly Undersampled k-Space Data by Dictionary Learning (2011, background): “Other algorithms, for which similar theoretical performance guarantees may not be available, often provide even better empirical performance [36]‐[ 40 ].”
Non-convex Optimization for Machine Learning (2017, methodology): “A popular approach in this direction uses Lq regularization with 0 q 1 [Chartrand, 2007, Foucart and Lai, 2009, Wang et al., 2011].”
Compressive sensing: From theory to applications, a survey (2013, background): “Non-convex local minimization techniques recover CS signals from far less measurements by replacing l 1 -norm by l p - norm where p ≤ 1 [47].”
Weighted Schatten $p$ -Norm Minimization for Image Denoising and Background Subtraction (2015, background): “Despite the convexity of the NNM model, it has been indicated in [28], [31], [29], [26] that the recovery performance of such a convex relaxation will degrade in the presence of measurement noise, and the solution can seriously deviate from the original solution of rank minimization problem.”
Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data (2009, background): “Results of Candès et al. [1] and Donoho [2] demonstrated that sparse images can be reconstructed from fewer linear measurements than previously thought possible, in what is now known as compressive sensing (among other related terms).”
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”
Sparsest solutions of underdetermined linear systems via ℓq-minimization for 0 (2009, background): “Chartrand [7] studied it in terms of Restricted Isometry Constants.”
Infrared Dim and Small Target Detection via Multiple Subspace Learning and Spatial-Temporal Patch-Tensor Model (2021, methodology): “First, the NNM method used in the IPI method penalizes all the singular values with the same weight, which would shrink too much the low-rank component in noisy cases [26], and this phenomenon is called over-shrinkage problem [27].”
L1−2 minimization for exact and stable seismic attenuation compensation (2018, background): “The matrix can be considered as sensing matrix, which is required to satisfy the restricted isometry property (RIP) with small restricted isometry constants (Candes & Tao 2005; Chartrand & Staneva 2010).”
Sparse Array Beampattern Synthesis via Alternating Direction Method of Multipliers (2018, methodology): “Motivated by the excellent sparsity property of the l p norm [31]–[34], we introduce the l p norm of the array weight vector as the objective function of the beampattern synthesis problem to enhance sparsity”
Highly Undersampled Magnetic Resonance Image Reconstruction via Homotopic $\ell_{0}$ -Minimization (2009, methodology): “Following assertions made in [2] and that (assuming 00 = 0) the zero quasi-norm is commonly defined as ‖v‖0 = lim p→0 ∑ x∈Ω |v(x)|p, (10) Chartrand [22] proposed use of the ℓp semi-norm (0 p ≤ 1) class of sparsity priors within a basis pursuit reconstruction framework and showed asymptotic converg”