Maximum Likelihood Deconvolution: a New Perspective

Jerry M. Mendel

Maximum-likelihood deconvolution can be presented from at least two very different points of view. Unfortunately, in most journal articles, it is couched in the mystique of state-variable models and estimation theory, both of which, are generally quite foreign to geophysical signal processors. This paper explains maximum-likelihood deconvolution using the well-known convolutional model and some relatively simple ideas from optimization theory. Both of these areas should be well known to geophysical signal processors. Although it is straightforward to develop the theory of maximum-likelihood deconvolution using the convolutional model and optimization theory, this approach does not lead to practical computational algorithms. Recursive algorithms must be used; they are orders of magnitude faster than the batch algorithms that are associated with the convolutional model.

AAPG Search and Discovery Article #91035©1988 AAPG-SEPM-SEG Pacific Sections and SPWLA Annual Convention, Santa Barbara, California, 17-19 April 1988.