Maximum likelihood estimation of a class of non-Gaussian densities with application to Ip deconvolution

The properties of the maximum likelihood estimator of the generalized p-Gaussian (GPG) probability density function from N independent identically distributed samples is investigated, especially in the context of the deconvolution problem under GPG white noise. Specifically, the properties in the estimator are first described independently of the application. Then the solution of the above-mentioned deconvolution problem is obtained as the solution of a minimum norm problem in an l_p normed space. It is shown that such minimum norm solution is the maximum-likelihood estimate of the system function parameters and that such an estimate is unbiased, with the lower bound of the variance of the error equal to the Cramer-Rao lower bound, and the upper bound derived from the concept of a generalized inverse. The results are illustrated by computer simulations