Performance analysis on a class of inverse filter criteria for blind deconvolution

Blind deconvolution is to estimate the input signal of an unknown linear time-invariant (LTI) system from the noisy observation. A popular way is to use an inverse filter to compensate for the distortion introduced by the LTI system. This paper analyzes the performance of a class of criteria used for the construction of inverse filter. (2s)th and (l + s)th order of cumulant are involved in these criteria, and a gradient type optimization method is usually used to find the desirable inverse filter. Several existent criteria are included in this class of criteria as special cases. It is proved that with a gradient type optimization method, algorithms maximizing these criteria are guaranteed to converge to the global optimum. The convergence rate near the point of global optimum is also found to be of (2s - 1)st order. These two valuable properties make this class of criteria very attractive in blind deconvolution. Computer simulation shows the effectiveness of these inverse filter criteria.