A large number of deconvolution procedures have appeared in the literature during the last three decades, including a number of maximum-likelihood deconvolution (MLD) procedures. The major advantages of the MLD procedures are (1) no assumption is required about the phase of the wavelet (most of the classical deconvolution techniques assume a minimum-phase wavelet, an assumption that may not be appropriate for many data sets); (2) MLD procedures can resolve closely spaced events (i.e., they are high-resolution techniques); and (3) they can efficiently handle modeling and measurement errors, as well as backscatter effects (i.e., reflections from small features).A comparative study of six different MLD procedures for estimating the input of a linear, time-invariant system from measurements, which have been corrupted by additive noise, was made by using a common framework developed from fundamental optimization theory arguments. To date, only the Kormylo and the Chi-t algorithms can be recommended.

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