Geometrical Structures of FIR Manifold and Multichannel Blind Deconvolution

Abstract

In this paper we study geometrical structures of the manifold of Finite Impulse Response (FIR) filters, and develop a natural gradient learning algorithm for blind deconvolution. First, A Lie group structure is introduced to the FIR manifold and the Riemannian metric is then derived by using the isometric property of the Lie group. The natural gradient on the FIR manifold is obtained by introducing a nonholonomic transformation. The Kullback-Leibler divergence is introduced as the measure of mutual independence of the output signals of the demixing model and a feasible cost function is derived for blind deconvolution. An efficient learning algorithm is presented based on the natural gradient approach and its stability analysis is also provided. Finally, we give computer simulations to demonstrate the performance and effectiveness of the proposed natural gradient algorithm.