Geometrical structures of FIR manifold and their application to multichannel blind deconvolution

We study geometrical structures on the manifold of FIR filters and their application to multichannel blind deconvolution. First we introduce the Lie group and Riemannian metric to the manifold of FIR filters. Then we derive the natural gradient on the manifold 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. We also study properties of the learning algorithm, such as equivariance and stability. Simulations are given to illustrate the effectiveness and validity of the proposed algorithm.