Well conditioned ptychograpic imaging via lost subspace completion

Abstract

Ptychography, a special case of the phase retrieval problem, is a popular method in modern imaging. Its measurements are based on the shifts of a locally supported window function. In general, direct recovery of an object from such measurements is known to be an ill-posed problem. Although for some windows the conditioning can be controlled, for a number of important cases it is not possible, for instance for Gaussian windows. In this paper we develop a subspace completion algorithm, which enables stable reconstruction for a much wider choice of windows, including Gaussian windows. The combination with a regularization technique leads to improved conditioning and better noise robustness.

arXiv comment21 pages, 4 figures

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Cited by in corpus (2)

• On recovery guarantees for angular synchronization
• Phase Retrieval for $L^2([-\pi ,\pi ])$ via the Provably Accurate and Noise Robust Numerical Inversion of Spectrogram Measurements