Iteratively reweighted algorithms for compressive sensing

2008/03/01 by Rick Chartrand, Wotao Yin · 13 citations
Engineering · #Sparse and Compressive Sensing Techniques #Microwave Imaging and Scattering Analysis #Electrical and Bioimpedance Tomography

paper · doi:10.1109/icassp.2008.4518498

openalex publication_date 2008/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

The theory of compressive sensing has shown that sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. In [1], it was shown empirically that using ℓpminimization with p ≪ 1 can do so with fewer measurements than with p = 1. In this paper we consider the use of iteratively reweighted algorithms for computing local minima of the nonconvex problem. In particular, a particular regularization strategy is found to greatly improve the ability of a reweighted least-squares algorithm to recover sparse signals, with exact recovery being observed for signals that are much less sparse than required by an unregularized version (such as FOCUSS, [2]). Improvements are also observed for the reweighted-ℓ1approach of [3].

Citations

• Atomic Decomposition by Basis Pursuit
• The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data
• Atomic Decomposition by Basis Pursuit
• Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
• Compressed sensing

Cited by

• Robust Linear Regression via ℓ₀ Regularization
• Block Iterative Reweighted Algorithms for Super-Resolution of Spectrally Sparse Signals
• Matrix Coherency Graph: A Tool for Improving Sparse Coding Performance
• Enhancing Sparsity and Resolution via Reweighted Atomic Norm Minimization
• Alternating Minimization Algorithm with Automatic Relevance Determination for Transmission Tomography under Poisson Noise
• A Relaxation Argument for Optimization in Neural Networks and Non-Convex Compressed Sensing
• Nonconvex Regularization Based Sparse Recovery and Demixing with Application to Color Image Inpainting
• Type I and Type II Bayesian Methods for Sparse Signal Recovery Using Scale Mixtures
• Utilizing the wavelet transform’s structure in compressed sensing
• The Bernstein Function: A Unifying Framework of Nonconvex Penalization in Sparse Estimation
• Bayesian Hypothesis Testing for Sparse Representation
• Non-Local Euclidean Medians
• Iteratively reweighted least squares [wikipedia]

Related

• Noisy Signal Recovery via Iterative Reweighted L1-Minimization
• A Novel Algorithm for Compressive Sensing: Iteratively Reweighed Operator Algorithm (IROA)
• Enhancing Sparsity by Reweighted L1 Minimization
• Improving the Thresholds of Sparse Recovery: An Analysis of a Two-Step Reweighted Basis Pursuit Algorithm
• IRLS for Sparse Recovery Revisited: Examples of Failure and a Remedy