Natural Gradient Approach to Multichannel Blind Deconvolution

In this paper we study the geometrical structures of PIR filters and their application to multichannel blind deconvolution. First we introduce a Lie group structure and a Riemannian structure on the manifolds of the FIR filters. Then we derive the natural gradients on the manifolds using the isometry of the Riemannian metric. Using the natural gradient, we present a novel learning algorithm for blind deconvolution based on the minimization of mutual information. Some properties of the learning algorithm, such as equivariance and stability are also studied. Finally, the simulations are given to illustrate the effectiveness and validity of the proposed algorithm.