Maximum likelihood image reconstruction from Fourier-offset data using the expectation-maximization algorithm

A maximum likelihood (ML) estimate of the magnitude of a complex-valued image from measurements of its Fourier transform in a limited region offset from the origin is derived under the assumption of independent, uniformly distributed image phase samples. The expectation-maximization (EM) algorithm is employed to solve the resulting nonlinear maximum likelihood equation, and it yields a computationally efficient iterative estimator. Reconstructions from this algorithm contain significantly more energy than conventional reconstructions, but with only slightly improved reconstruction quality.<
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