The Numerics of Phase Retrieval

04/13/2020
by   Albert Fannjiang, et al.
0

Phase retrieval, i.e., the problem of recovering a function from the squared magnitude of its Fourier transform, arises in many applications such as X-ray crystallography, diffraction imaging, optics, quantum mechanics, and astronomy. This problem has confounded engineers, physicists, and mathematicians for many decades. Recently, phase retrieval has seen a resurgence in research activity, ignited by new imaging modalities and novel mathematical concepts. As our scientific experiments produce larger and larger datasets and we aim for faster and faster throughput, it becomes increasingly important to study the involved numerical algorithms in a systematic and principled manner. Indeed, the last decade has witnessed a surge in the systematic study of computational algorithms for phase retrieval. In this paper we will review these recent advances from a numerical viewpoint.

READ FULL TEXT

Authors

page 11

page 15

page 34

page 39

page 40

04/18/2022

PR-DAD: Phase Retrieval Using Deep Auto-Decoders

Phase retrieval is a well known ill-posed inverse problem where one trie...
03/05/2022

Algebraic theory of phase retrieval

The purpose of this article is to discuss recent advances in the growing...
02/24/2020

Toward a mathematical theory of the crystallographic phase retrieval problem

Motivated by the X-ray crystallography technology to determine the atomi...
11/01/2020

Efficient Solutions for the Multidimensional Sparse Turnpike Problem

The turnpike problem of recovering a set of points in ℝ^D from the set o...
06/04/2021

Phase Retrieval for L^2([-π,π]) via the Provably Accurate and Noise Robust Numerical Inversion of Spectrogram Measurements

In this paper, we focus on the approximation of smooth functions f: [-π,...
08/06/2018

Super Resolution Phase Retrieval for Sparse Signals

In a variety of fields, in particular those involving imaging and optics...
12/14/2020

Phase Retrieval with Holography and Untrained Priors: Tackling the Challenges of Low-Photon Nanoscale Imaging

Phase retrieval is the inverse problem of recovering a signal from magni...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.