Non-Asymptotic Guarantees for Correlation-Aware Support Detection

Abstract

This paper considers the problem of sparse support recovery in Multiple Measurement Vector (MMV) models, where the support size (K) can exceed the dimension (M) of individual measurement vectors. Existing results in this regime mostly establish asymptotic performance guarantees, where the number of measurement vectors $L\rightarrow\infty$ . In this paper, we develop non-asymptotic guarantees (finite $L$ ), and demonstrate that it is possible to recover supports of size $K= \mathcal{O}(M^{2})$ provided the sparse signals are statistically uncorrelated. In particular, the probability of detecting a wrong support is shown to approach zero exponentially fast in $L$ even when $K > M$ , for appropriately designed measurement matrices. Our analysis is based on a simple least squares estimation of signal powers, followed by hard thresholding to detect the support.