A* Orthogonal Matching Pursuit: Best-First Search for Compressed Sensing Signal Recovery

TL;DR

This paper introduces A*OMP, a novel best-first search algorithm for compressed sensing that improves sparse signal recovery accuracy over traditional methods by using a tree search with dynamic cost functions and pruning techniques.

Contribution

The paper proposes A*OMP, a semi-greedy, best-first search algorithm for compressed sensing that enhances recovery performance with dynamic cost functions and pruning, outperforming existing methods.

Findings

A*OMP achieves lower reconstruction error than BP, OMP, and SP.

A*OMP has higher exact recovery frequency.

Dynamic cost functions improve reconstruction results.

Abstract

Compressed sensing is a developing field aiming at reconstruction of sparse signals acquired in reduced dimensions, which make the recovery process under-determined. The required solution is the one with minimum $\ell_0$ norm due to sparsity, however it is not practical to solve the $\ell_0$ minimization problem. Commonly used techniques include $\ell_1$ minimization, such as Basis Pursuit (BP) and greedy pursuit algorithms such as Orthogonal Matching Pursuit (OMP) and Subspace Pursuit (SP). This manuscript proposes a novel semi-greedy recovery approach, namely A* Orthogonal Matching Pursuit (A*OMP). A*OMP performs A* search to look for the sparsest solution on a tree whose paths grow similar to the Orthogonal Matching Pursuit (OMP) algorithm. Paths on the tree are evaluated according to a cost function, which should compensate for different path lengths. For this purpose, three different auxiliary structures are defined, including novel dynamic ones. A*OMP also incorporates pruning techniques which enable practical applications of the algorithm. Moreover, the adjustable search parameters provide means for a complexity-accuracy trade-off. We demonstrate the reconstruction ability of the proposed scheme on both synthetically generated data and images using Gaussian and Bernoulli observation matrices, where A*OMP yields less reconstruction error and higher exact recovery frequency than BP, OMP and SP. Results also indicate that novel dynamic cost functions provide improved results as compared to a conventional choice.