Rank Awareness in Joint Sparse Recovery

In this paper we revisit the sparse multiple measurement vector (MMV) problem, where the aim is to recover a set of jointly sparse multichannel vectors from incomplete measurements. This problem has received increasing interest as an extension of single channel sparse recovery, which lies at the heart of the emerging field of compressed sensing. However, MMV approximation has origins in the field of array signal processing as we discuss in this paper. Inspired by these links, we introduce a new family of MMV algorithms based on the well-know MUSIC method in array processing. We particularly highlight the role of the rank of the unknown signal matrix X in determining the difficulty of the recovery problem. We begin by deriving necessary and sufficient conditions for the uniqueness of the sparse MMV solution, which indicates that the larger the rank of X the less sparse X needs to be to ensure uniqueness. We also show that as the rank of X increases, the computational effort required to...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Mike E. Davies, Yonina C. Eldar
• Keywords: CORR 2010, Education, Sparse, Sparse Mmv Solution, Sparse Multichannel Vectors