Abstract

Classical decision theory allows the user to decide optimally between two alternative signatures, H_1i or H_2i, given data R_i, i = 1,…, N. The probability for making a correct decision turns out to depend solely on the forms of H_1i (and H_2i, and the type of noise present. Here regard H_1i as an unknown object that it is desired to restore or reconstruct from incomplete data R_i. Let H_2i be a known template object that the user wants to bias an estimate of H_1i toward. In the absence of data, H_1i should equal H_2i, and with any data present H_1i should be minimally distinguishable from H_2i. Thus H_2i represents prior information about the shape of H_1i and provides a medium for inserting such information. The precise sense by which H_1i and H_2i is to be minimally distinguishable is as follows: Even if the data were combined optimally by classical decision theory, the decision should still be minimally probable to be correct. On this basis, different estimators for H_1i may be formed, depending on the statistics of the noise in the data. As examples, with additive Gaussian noise the estimator is least squares; with Poisson noise, the estimator is maximum cross-entropy.

© 1987 Optical Society of America