#### Technical Report USC-SIPI-122

“Heuristically Constrained Estimation for Intelligent Signal Processing”

by Robert F. Popoli and Jerry M. Mendel

February 1988

The solution of many estimation problems can be greatly enhanced by the incorporation of inexact knowledge or vague human reasoning. For such estimation problems, two distinct forms of problem knowledge can be identified: statistical (objective) knowledge and heuristic (subjective) knowledge. This chapter discusses a systematic way of expressing and integrating these two forms of knowledge into the estimation processes. This work can be interpreted as a fuzzification of standard constrained optimization. Fuzzy set theory is used to form a fuzzy constraint which represents the domain-specific knowledge of human experts. This work may also be interpreted as a systematization of the use of subjective priors by Bayesians. Although our work is of general applicability, we demonstrate the use of heuristically constrained estimation to the particular problem of seismic deconvolution. These results show that the incorporation of heuristic knowledge (albeit vague) yields better results than if such knowledge is ignored.

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