Mismatch and resolution in compressive imaging

TL;DR

This paper introduces algorithms BOMP and BLOOMP that improve sparse signal reconstruction in highly coherent sensing matrices common in radar and medical imaging, with proven guarantees and demonstrated effectiveness.

Contribution

It proposes novel algorithms that enhance OMP for coherent matrices, providing theoretical guarantees and practical performance improvements.

Findings

BLOOMP outperforms traditional OMP in coherence scenarios

Algorithms have similar sparsity and computational costs as OMP

Numerical results confirm effectiveness in compressed sensing

Abstract

Highly coherent sensing matrices arise in discretization of continuum problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold as well as in using highly coherent, redundant dictionaries as sparsifying operators. Algorithms (BOMP, BLOOMP) based on techniques of band exclusion and local optimization are proposed to enhance Orthogonal Matching Pursuit (OMP) and deal with such coherent sensing matrices. BOMP and BLOOMP have provably performance guarantee of reconstructing sparse, widely separated objects {\em independent} of the redundancy and have a sparsity constraint and computational cost similar to OMP's. Numerical study demonstrates the effectiveness of BLOOMP for compressed sensing with highly coherent, redundant sensing matrices.