On the role of sampling and sparsity in phase retrieval for optical coherence tomography

This paper considers the problem of sparse phase retrieval for Frequency Domain Optical Coherence Tomography (FDOCT). Existing phase retrieval algorithms typically require larger number of measurements and the reconstruction is accurate only up to some ambiguities that are inherent in Fourier phase retrieval. In this paper, we overcome these drawbacks by developing a compressive differential FDOCT (dFDOCT) technique that uses li minimization for reconstructing the signal from a pair of differential phaseless measurements. Theoretical guarantees are developed which establish that the proposed method requires minimal number of measurements for sparse phase retrieval. Numerical results demonstrate the superior performance of this method for signals of large length and sparsity without any ambiguities.

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