Decomposition-based multiscale compressed sensing

This paper proposes a generalized decomposition-based measurement matrix (DMM) to capture multi-scale compressive measurements. In the proposed method, we linearly decompose the sensing image to various scales, and then adaptively sample it at each scale to capture essential information. The restricted isometric property of DMM is proven for structured sparse and compressible signals with various decomposition methods. Simulation results validate the recovery performance of the proposed method as well as the reduction in complexity.