Multichannel blind deconvolution of nonminimum-phase systems using filter decomposition

In this paper, we present a novel method-filter decomposition approach for multichannel blind deconvolution of nonminimum-phase systems. We decompose a doubly finite filter into a cascade form of two filters: a nonsausal FIR filter and a causal FIR filter. A Lie group and Riemannian metre are introduced on the manifold of the FIR filters. Using the isometry of the Riemannian metric, we derive the natural gradient on the FIR manifold. Then, we develop a novel natural gradient algorithm for the causal FIR filter based on the minimization of mutual information. Using information backpropagation, we derive a novel learning algorithm for the nonsausal FIR filter. Simulations are given to illustrate the validity and good learning performance of the proposed algorithms.