RESTORATION OF OPTICAL PATTERNS
UTAH STATE UNIV LOGAN ELECTRO-DYNAMICS LAB
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This paper treats the problem of estimating the intensity distribution of an optical pattern which has been distorted by diffraction and noise. Under the assumption that the signal and noise are additive and that they have prescribed means and covariance matrices, the optimum linear estimate of the object distribution is obtained. This estimate is shown to be a linearly-filtered combination of the a priori mean and the observed image distribution, with the details of the filtering depending on the prior information, the noise statistics, and the optical imaging system. The performance of the optimum estimation procedure is evaluated for the important special case of large a priori uncertainty. Finally, the optimum procedure for processing multiple observations is discussed. It is shown that as the number of observations becomes large, the estimate approaches the true object.