Multi-Branch Matching Pursuit with applications to MIMO radar

TL;DR

The paper introduces Multi-Branch Matching Pursuit (MBMP), an algorithm for sparse recovery in redundant dictionaries that combines greedy, rank-aware, and multi-branch strategies, enabling efficient recovery with fewer measurements.

Contribution

It proposes MBMP, a novel multi-branch algorithm that exploits subspace information and offers a new recovery condition, MB-coherence, requiring fewer measurements than existing criteria.

Findings

MBMP guarantees recovery under MB-coherence condition.

MBMP outperforms traditional methods in incoherent dictionaries.

The algorithm balances hardware and computational complexity.

Abstract

We present an algorithm, dubbed Multi-Branch Matching Pursuit (MBMP), to solve the sparse recovery problem over redundant dictionaries. MBMP combines three different paradigms: being a greedy method, it performs iterative signal support estimation; as a rank-aware method, it is able to exploit signal subspace information when multiple snapshots are available; and, as its name foretells, it leverages a multi-branch (i.e., tree-search) strategy that allows us to trade-off hardware complexity (e.g. measurements) for computational complexity. We derive a sufficient condition under which MBMP can recover a sparse signal from noiseless measurements. This condition, named MB-coherence, is met when the dictionary is sufficiently incoherent. It incorporates the number of branches of MBMP and it requires fewer measurements than other conditions (e.g. the Neuman ERC or the cumulative coherence). As such, successful recovery with MBMP is guaranteed for dictionaries that do not satisfy previously known conditions.