A divide-and-conquer approach for sparse recovery of high dimensional signals

Abstract

Compressed sensing (CS) techniques demand significant storage and computational resources, when recovering high-dimensional sparse signals. Block CS (BCS), a special class of CS, addresses both the storage and complexity issues by partitioning the sparse recovery problem into several sub-problems. In this paper, we derive a Welch bound-based guarantee on the reconstruction error with BCS. Our guarantee reveals that the reconstruction quality with BCS monotonically reduces with an increasing number of partitions. To alleviate this performance loss, we propose a sparse recovery technique that exploits correlation across the partitions of the sparse signal. Our method outperforms BCS in the moderate SNR regime, for a modest increase in the storage and computational complexities.