Large-scale sparse reconstruction through partitioned compressive sensing

Compressive sensing (CS) finds broad applications in various sparse reconstruction problems. It has been clearly established that CS techniques achieve improved quality and resolution for many radar imaging problems where the scene is sparse or can be sparsely represented. One of the major issues that limits the applicability of CS techniques in radar systems is the prohibitive complexity in large-scale imaging problems encountered in, for example, synthetic aperture radar. However, as the actual scene and the back-projection images are associated with the point spreading function which has a finite support, it becomes possible to reconstruct the sparse scene based only on local observations. In this paper, we develop a novel segmented CS technique that achieves nearly optimal sparse reconstruction performance with significant reduction of computation complexity and memory requirements. The effect of interference from neighboring segments is examined, and the conditions of interference-free reconstruction of segmented compressive sensing are devised. The effectiveness of the proposed technique is verified by simulation results.