Phase Retrieval for Binary Signals: Box Relaxation and Uniqueness
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Recovering a signal from its Fourier magnitude is referred to as phase retrieval, which occurs in different fields of engineering and applied physics. This paper gives a new characterization of the phase retrieval problem. Particularly useful is the analysis revealing that the common gradient-based regularization does not contain more information other than the magnitude measurements for phase retrieval. Focusing on binary signals, we show that a box relaxation to the binary constraint is equivalent to the original problem. We further prove that binary signals can be recovered uniquely up to trivial ambiguities under certain conditions. Finally, we use the characterization theorem to develop an efficient denoising algorithm.
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