Sparse deconvolution using adaptive mixed-Gaussian models

In this paper we present a new algorithm to recover a sparse signal from a noisy register. The algorithm assumes a new prior distribution for the sparse signal that consists of a mixture of a narrow and a broad Gaussian 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 by means of a gradient-type algorithm. A condition is derived for the step-size parameter in order to ensure convergence. In the paper we also propose a method (based on the Expectation-Maximization algorithm) to update the mixture parameters. The estimation of the sparse signal and the optimization of the Gaussian mixture are combined in the proposed algorithm: in each iteration a new signal estimate and a new model (which approximates the distribution of the new estimate) are obtained. In this way, the proposed method can be used without any statistical knowledge about the signal. Simulation experiments show that the accuracy of the proposed method is competitive with classical statistical detectors with a lower computational load.