EM-based identification of sparse FIR systems having quantized data1

In this paper, we explore the identification of sparse FIR systems having quantized output data. Our approach is based on the use of regularization. We explore several aspects concerning the implementation of the Expectation-Maximization (EM) algorithm, including: i) a general framework, based on mean-variance Gaussian mixtures, for incorporating a regularization term that forces sparsity, ii) utilization of Markov Chain Monte Carlo techniques (namely a Gibbs sampler) and scenarios to implement the EM algorithm for multiple input multiple output systems. We show that for single input single output systems, it is possible to obtain closed form expressions for solving the EM algorithm.