GRID matching in Monte Carlo Bayesian compressive sensing

Sparse signal reconstruction from compressive measurements assumes a grid of possible support points from which to estimate the signal support set. However, reconstruction of high measurement resolution waveforms is very sensitive to small grid offsets and assuming a fixed grid may result to information loss. On the other hand, identifying sparse elements over a very fine grid to minimize information loss is computationally prohibitive. In this work grid matching is performed via a computationally efficient multi-stage Monte Carlo sampling approach. The multistage sampling method identifies sparse signal elements and chooses the appropriate grid using information from compressively acquired measurements and any prior information on the signal structure. The effectiveness of the method in reconstructing high resolution waveforms, after compressive acquisition, is demonstrated via a simulation study.