TV-min and Greedy Pursuit for Constrained Joint Sparsity and Application to Inverse Scattering

TL;DR

This paper introduces a unified compressed sensing framework for constrained joint sparsity, including TV-min, providing error bounds and extending exact recovery results to noisy Fourier data.

Contribution

It develops a general CJS framework encompassing TV-min, deriving error bounds and extending exact recovery proofs to noisy inverse scattering problems.

Findings

Derived ambient dimension-independent error bounds for CJS Basis Pursuit and OMP.

Extended exact recovery results to noisy Fourier data for piecewise constant objects.

Unified framework for TV-min and joint sparsity in compressed sensing.

Abstract

This paper proposes a general framework for compressed sensing of constrained joint sparsity (CJS) which includes total variation minimization (TV-min) as an example. TV- and 2-norm error bounds, independent of the ambient dimension, are derived for the CJS version of Basis Pursuit and Orthogonal Matching Pursuit. As an application the results extend Cand`es, Romberg and Tao's proof of exact recovery of piecewise constant objects with noiseless incomplete Fourier data to the case of noisy data.