  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.
