Compressive MUSIC: A Missing Link Between Compressive Sensing and Array Signal Processing

TL;DR

This paper introduces compressive MUSIC, a unified approach bridging compressive sensing and array signal processing, improving support recovery with fewer sensors and approaching optimal bounds.

Contribution

It presents a novel algorithm that combines CS and array processing techniques, revealing a missing link and enhancing support recovery performance.

Findings

Requires fewer sensors than existing CS methods

Approaches the optimal l0-bound with finite snapshots

Unifies probabilistic CS with deterministic array processing

Abstract

The multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. Even though MMV problems had been traditionally addressed within the context of sensor array signal processing, the recent trend is to apply compressive sensing (CS) due to its capability to estimate sparse support even with an insufficient number of snapshots, in which case classical array signal processing fails. However, CS guarantees the accurate recovery in a probabilistic manner, which often shows inferior performance in the regime where the traditional array signal processing approaches succeed. The apparent dichotomy between the {\em probabilistic} CS and {\em deterministic} sensor array signal processing have not been fully understood. The main contribution of the present article is a unified approach that unveils a {missing link} between CS and array signal processing. The new algorithm, which we call {\em compressive MUSIC}, identifies the parts of support using CS, after which the remaining supports are estimated using a novel generalized MUSIC criterion. Using a large system MMV model, we show that our compressive MUSIC requires a smaller number of sensor elements for accurate support recovery than the existing CS methods and can approach the optimal $l_0$-bound with finite number of snapshots.