An Iterative Deconvolution Algorithm with Exponential Convergence

Abstract

Iterative deconvolution is an established technique for recovering the input sequence of a linear shift-invariant system given the output sequence and some knowledge about the distorting system [1]. Since the standard approach to iterative deconvolution has a linear convergence rate, some authors have proposed techniques such as gradient search methods [2,3] and kernel splitting [4] to increase the rate of convergence. These methods, however, are either computationally expensive or do not achieve a substantial gain in convergence rate. In this paper we describe an accelerated iterative algorithm that requires slightly more computational time or memory storage than the standard approach while achieving a favorable exponential rate of convergence.