SMLR-Type Blind Deconvolution of Sparse Pulse Sequences Under a Minimum Temporal Distance Constraint

We consider Bayesian blind deconvolution (BD) of an unknown sparse sequence convolved with an unknown pulse. Our goal is to detect the positions where the sparse input sequence is nonzero and to estimate the corresponding amplitudes as well as the pulse shape. For this task, we propose a novel evolution of the single most likely replacement (SMLR) algorithm. Our method uses a modified Bernoulli-Gaussian prior that incorporates a minimum temporal distance constraint. This prior simultaneously induces sparsity and enforces a prescribed minimum distance between the pulse centers. The minimum distance constraint provides an effective way to avoid overfitting (i.e., spurious detected pulses) and improve resolution. The proposed BD method overcomes certain weaknesses of the traditional SMLR-based BD method, which is verified experimentally to result in improved detection/estimation performance and reduced computational complexity. Our simulation results also demonstrate performance and complexity advantages relative to the iterated window maximization (IWM) algorithm and a recently proposed partially collapsed Gibbs sampler method.