|Title:||IMAGE RECONSTRUCTION FROM NOISY FOURIER MAGNITUDE WITH PARTIAL PHASE INFORMATION
|Authors:||Eliyahu Osherovich, Michael Zibulevsky, and Irad Yavneh
|Abstract:||We present a convex optimization framework to the classical problem of image reconstruction from the modulus of its Fourier transform. Unlike the original problem, we consider the case where the phase information is not lost completely; instead, it can be roughly estimated to lie within a certain interval. Provided that the interval of uncertainty is less than $\pi$ radians, our algorithm demonstrates significantly faster convergence than the classical algorithms. Moreover, in contrast to these algorithms, our approach gives a great deal of flexibility in incorporating prior knowledge into the computational scheme. By including priors like smoothness of the sought image or known statistical distribution of the noise in measurements we manage to obtain a much better reconstruction in the case of noisy data.|
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