,Performance Analysis on a Class of Inverse Filter Criteria for Blind Deconvolution

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Blind deconvolution is to estimate theinput signal of an unknown linear time-invariant (LTI)system from the noisy observation. A popular way isto 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 forthe construction of inverse filter. (2s)th and (l + s)thorder of cumulant are involved in these criteria, anda gradient type optimization method is usually usedto find the desirable inverse filter. Several existentcriteria are included in this class of criteria as specialcases. It is proved that with a gradient type optimization method, algorithms maximizing these criteria areguaranteed to converge to the global optimum. Theconvergence rate near the point of global optimum isalso found to be of (2s-1)st order. These two valuableproperties make this class of criteria very attractive inblind deconvolution. Computer simulation shows theeffectiveness of these inverse filter criteria.
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