Improving A*OMP: Theoretical and Empirical Analyses With a Novel Dynamic Cost Model

TL;DR

This paper provides theoretical conditions and empirical evidence demonstrating the superior recovery performance of the A*OMP algorithm in compressed sensing, especially with a novel cost model and residue-based termination.

Contribution

It introduces a RIP-based recovery condition, develops online guarantees, and evaluates an adaptive cost model that enhances A*OMP's accuracy and speed.

Findings

A*OMP achieves high recovery accuracy with the AMul cost model.

Residue-based termination improves recovery performance.

AMul cost model speeds up the search process.

Abstract

Best-first search has been recently utilized for compressed sensing (CS) by the A* orthogonal matching pursuit (A*OMP) algorithm. In this work, we concentrate on theoretical and empirical analyses of A*OMP. We present a restricted isometry property (RIP) based general condition for exact recovery of sparse signals via A*OMP. In addition, we develop online guarantees which promise improved recovery performance with the residue-based termination instead of the sparsity-based one. We demonstrate the recovery capabilities of A*OMP with extensive recovery simulations using the adaptive-multiplicative (AMul) cost model, which effectively compensates for the path length differences in the search tree. The presented results, involving phase transitions for different nonzero element distributions as well as recovery rates and average error, reveal not only the superior recovery accuracy of A*OMP, but also the improvements with the residue-based termination and the AMul cost model. Comparison of the run times indicate the speed up by the AMul cost model. We also demonstrate a hybrid of OMP and A?OMP to accelerate the search further. Finally, we run A*OMP on a sparse image to illustrate its recovery performance for more realistic coefcient distributions.