A multigrid approach to object support estimation from diffraction-limited images

A procedure for object support estimation from diffraction-limited images is developed under the assumptions that the (not necessarily spatially invariant) point spread function of the imaging system and the object location are known. The problem is formulated 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 object support. This formulation leads to a sequence of statistical hypothesis tests which involve projections of the observed noisy image on the null spaces of certain matrices derived from the point spread function of the imaging system. The projections are computed using a multigrid iterative scheme. The statistical tests are done in an optimal order to minimize the total number of tests that have to be performed