Compressed sensing reconstruction of convolved sparse signals

This paper addresses the problem of efficient sampling and reconstruction of sparse spike signals, which have been convolved with low-pass filters. A modified compressed sensing (CS) framework is proposed, termed dictionary-based deconvolution CS (DDCS) to achieve this goal. DDCS builds on the assumption that a low-pass filter can be represented sparsely in a dictionary of blurring atoms. Identification of both the sparse spike signal and the sparsely parameterized blurring function is performed by an alternating scheme that minimizes each variable independently, while keeping the other constant. Simulation results reveal that the proposed DDSS scheme achieves an improved reconstruction performance when compared to traditional CS recovery.