Abstract

A probabilistic approach is proposed for the problem of estimating a function from the modulus of its Fourier transform. In this approach, the statistics of the measurement noise and prior knowledge about the function itself (for example, support and positivity) can be incorporated in an optimal fashion. The procedure is iterative and is based on a succession of linear estimation steps involving higher and higher spatial-frequency cutoffs. A series of numerical experiments was performed to test the ability of the algorithm to reconstruct two-dimensional test images under various circumstances. For these particular experiments, the inversion was performed on the assumption that the statistical ensemble of possible images corresponds to a Gaussian random process with no positivity constraint.

© 1988 Optical Society of America

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