Sparse deconvolution using Gaussian mixtures

We present a new algorithm to recover a sparse signal from a noisy register. The algorithm assumes a new model for the sparse signal that consists of a mixture of narrowband and broadband Gaussian noise both with zero mean. A penalty term which favors solutions driven from this model is added to the usual error cost function and the resultant global cost function is minimized with a gradient-type algorithm. We propose methods for updating the mixture parameters as well as for choosing the weighting parameter for the penalty term. Simulation experiments show that the accuracy of the proposed method is competitive with classical statistical detectors with a lower computational load. The proposed algorithm shows also a good performance when applied to a practical seismic deconvolution problem