Probing the Pareto Frontier for Basis Pursuit Solutions

By Ewout van den Berg, Michael P. Friedlander. SIAM Journal on Scientific Computing, 2008

2,086 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e081ffcb596cf897b896b5fbc779936df52b8494

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In Atomic and Molecular Physics, and Optics

In Computational Mechanics

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Citations in the corpus

Convex Structure Learning in Log-Linear Models: Beyond Pairwise Potentials (2010, background): “This has been shown to give good performance in a variety of related applications (Figueiredo et al., 2007; van den Berg and Friedlander, 2008; Schmidt et al., 2008).”
Extension of SBL Algorithms for the Recovery of Block Sparse Signals With Intra-Block Correlation (2012, methodology): “December 21, 2013 DRAFT at low SNR and high SNR situations is due to some sub-optimal default parameters in the Group Basis Pursuit program [5].”
Fast randomized full-waveform inversion with compressive sensing (2012, methodology): “For this purpose, we follow van den Berg and Friedlander (2008); Hennenfent et al. (2008) and introduce the function v(τ), which parametrizes the `2-norm of the optimal residual in equation 3 as a function of the sparsity level τ .”
Fast and Efficient Compressive Sensing Using Structurally Random Matrices (2011, positive): “Linear programming [1], [2] and other convex optimization algorithms [3], [4], [5] have been proposed to solve the l1 minimization.”
Projected Newton-type methods in machine learning (2011, background): “Indeed, due to its strong empirical performance, SPG has recently also been explored in several other applications (Dai and Fletcher, 2005; Figueiredo et al., 2007; van den Berg and Friedlander, 2008).”
A Fast Projection onto the Simplex and the l 1 Ball (2015, background): “An improvement of Algorithm 1 was proposed in [20], by noticing that it is not useful to sort y completely, since only its largest elements are involved in the determination of τ .”
Compressed sensing imaging techniques for radio interferometry (2008, methodology): “For each value ofǫ, there exists a valueτ such that the solutions of the constrained and unconstrainedℓ1 sparsity problems are identical (van den Berg & Friedlander 2008).”
A Field Guide to Forward-Backward Splitting with a FASTA Implementation (2014, methodology): “marriage of FBS with an adaptive stepsize produces the spectral projected gradient method (SPG) [24]. SPG was further specialized to handle the case of ‘ 1 constraints by van den Berg and Friedlander [16,17]. The authors of [25] present a spectral stepsize rule that handles the case g= jj. The resul”
Compressed Sensing for Real-Time Energy-Efficient ECG Compression on Wireless Body Sensor Nodes (2011, methodology): “Many algorithms were introduced to solve this reconstruction problem, including interior-point algorithms [24], [25], gra-”
Projection Onto A Simplex (2011, background): “[2, 5], which has has similar formulation and is in general easier to solve.”
Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset (2015, methodology): “Factorized Robust Matrix Completion (FRMC) Spectral Projected Gradient Iterations (SPG) Oiter=Unknown, Opre=Unknown, Oconv=Unknown Mansour and Vetro [256] Berg and Friedlander [23] Motion-Assisted Matrix Completion (MAMC(19)) ALM-ADM Framework Oiter(mnmin(m, n)), Opre=unknown, Oconv(1/μT ) Yang et a”
Templates for convex cone problems with applications to sparse signal recovery (2010, methodology): “To show this, we compared the AT first-order variant with SPGL1 [7], chosen because recent and extensive tests in [5] suggest that it is one of the best available methods.”
Optimally Tuned Iterative Reconstruction Algorithms for Compressed Sensing (2009, methodology): “In this project, we did not attempt to document what is possible today using such solvers; an interesting follow-up project might involve the tuning of purported solvers like Bregman iteration [26] to see if they really can achieve the transition; another interesting follow-up project would be to ca”