Maximum likelihood for blind separation and deconvolution of noisy signals using mixture models

In this paper, an approximate maximum likelihood method for blind source separation and deconvolution of noisy signal is proposed. This technique relies upon a data augmentation scheme, where the (unobserved) input are viewed as the missing data. In the technique described in this contribution, the input signal distribution is modeled by a mixture of Gaussian distributions, enabling the use of explicit formula for computing the posterior density and conditional expectation and thus avoiding Monte-Carlo integrations. Because this technique is able to capture some salient features of the input signal distribution, it performs generally much better than third-order or fourth-order cumulant-based techniques.