Optimal Sparse Recovery for Multi-Sensor Measurements

Many practical sensing applications involve multiple sensors simultaneously acquiring measurements of a single object. Conversely, most existing sparse recovery guarantees in compressed sensing concern only single-sensor acquisition scenarios. In this paper, we address the optimal recovery of compressible signals from multi-sensor measurements using compressed sensing techniques, thereby confirming the benefits of multi- over single-sensor environments. Throughout the paper, we consider a broad class of sensing matrices, and two fundamentally different sampling scenarios (distinct and identical respectively), both of which are relevant to applications. For the case of diagonal sensor profile matrices (which characterize environmental conditions between a source and the sensors), this paper presents two key improvements over existing results. First, a simpler optimal recovery guarantee for distinct sampling, and second, an improved recovery guarantee for identical sampling, based on the so-called sparsity in levels signal model.