Abstract

A new procedure for parametric blur identification and image reconstruction is developed. It is shown that it is possible to identify the parametric blur and to reconstruct the underlying image simultaneously because the blurred image effectively lives in different spaces for sufficiently different values of the blur parameters. Using this fact, we formulate the blur-identification problem as a generalized hypothesis-testing problem with unequal a priori probabilities. The a priori probabilities are determined in such a way as to minimize the probability of incorrectly identifying the blur. This formulation leads to a sequence of statistical hypothesis tests that involve the projections of the observed noisy image on the null space of the adjoint of the blurring operator representation of the imaging system. A truncated pseudoinverse type of restoration technique is used to reconstruct the original image. Both the projections and the truncated pseudoinverse solution are computed with the use of a multigrid iterative scheme. Furthermore, the statistical tests are done in an optimal order to minimize the total number of tests that have to be performed.

© 1991 Optical Society of America

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