Correlation-Aware Joint Support Recovery With Separation Prior

Abstract

Sparse support recovery from multiple measurement vectors (MMV) is studied in this paper. For years, a noticeable mismatch exists between the theories and algorithms in the research of super-resolution and direction-of-arrival (DOA) estimation that variants of separation conditions are assumed to ensure stable recovery while the corresponding algorithms rarely exploit such structural constraints. Due to the discrete nature of the separation condition, we propose to incorporate such prior information in a Mixed Integer Programming (MIP) problem with an <inline-formula><tex-math notation="LaTeX">$\ell _{0}$</tex-math></inline-formula>-based constraint. We develop a specialized branch and bound (B&amp;B) algorithm that can efficiently exploit the separation prior with guaranteed complexity reduction. Moreover, we show that computational complexity can be further reduced by leveraging the sparse array idea along with a particular perspective formulation of the MIP. The superior performance of the proposed algorithm is demonstrated via numerical experiments.