Phase retrieval for imaging problems

Abstract

ABSTRACT. We study convex relaxation algorithms for phase retrieval on imaging problems. We show that exploiting structural assumptions on the signal and the observations, such as sparsity, smoothness or positivity, can significantly speed-up convergence and improve recovery performance. We detail numerical results in molecular imaging experiments simulated using data from the Protein Data Bank (PDB).

Excitation Retrieval of Microwave Linear Arrays From Phaseless Far-Field Data

“…However, these methods are not known to converge in general and they can stall in a local minima. Recently, phase retrieval problems have been treated using semidefinite relaxation and low-rank matrix recovery ideas [12]- [16]. To date, these convex approaches are the only ones providing guarantees on the recovery performances under some specific conditions (given in Section IV).…”

Coherent diffractive imaging using randomly coded masks

“…It is based on recent convex relaxation algorithms [12][13][14][15] that have been shown to provide stable convergence to the global, unique solution and are robust to noise, while also removing the need for phase and support constraints. It is an extension to CDI that utilizes a series of known, randomly coded masks to encode additional information into the measured diffraction patterns to guarantee uniqueness of the retrieved image, 16 and that builds on recent ptychography work which showed that randomized illumination improves reconstruction quality.…”

“…3(a). This reconstruction was performed using the "PhaseCut" algorithm, 13 refined by Fienup's input-output algorithm. 25 PhaseCut is an algorithm solving a convex relaxation of the phase retrieval problem.…”

“…Specifically, this approach consists of minimizing a quantity based on the estimate for the diffraction phases. For implementation details see Fogel et al 13 The The laser is first spatially filtered using a 25 lm diameter aperture and collimated with a 10 cm focal length lens. The resulting beam illuminates the object, which is followed immediately by the randomly coded mask.…”

“…Further, this indicates that the achieved resolution is that imposed by the NA of 15 lm. While the required number of masks may vary based on the particular sample as well as the signal to noise ratio of the measurement, 13 the PRTF can be used to judge how many are necessary for a given experiment. In order to make an object-space error calculation, the lens-based image is first registered to the 15-mask reconstruction shown in Fig.…”