BLIND DECONVOLUTION

The ability to implement deconvolution in a numerically stable fashion is essential in many applications. In blind deconvolution it is required to identify the excitation of a linear system using observations made on the associated system response in which no knowledge of the linear system is presumed. A solution to the blind deconvolution problem is herein presented that is based on maximizing the magnitude of the excitation estimate's kurtosis. Conditions under which this excitation estimate is equal to a scaled and time-shifted version of the actual excitation are provided. Furthermore, an effective algorithm for achieving the kurtosis magnitude maximization is developed. This blind deconvolution algorithm is different from other kurtosis type algorithms in that it: (i) is applicable to a larger class of excitations, (ii) imposes no constraints on the linear system's dynamics, and, (iii) requires no nuisance parameters entailing preknowledge of the excitation's statistics. The utility of this algorithm is illustrated by a number of examples. (C) 1995 Academic Press, Inc.