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The phase retrieval problem is a fundamental problem in many fields, which is appealing for investigation. It is to recover the signal vector $\tilde{x}\in\mathbb{C}^d$ from a set of $N$ measurements $b_n=|f^*_n\tilde{x}|^2,\ n=1,\cdots,…

Optimization and Control · Mathematics 2017-08-30 Jian-Feng Cai , Haixia Liu , Yang Wang

Lensless in-line holography is a simple, portable, and cost-effective method of imaging especially for the biomedical microscopy applications. We propose a multiplicative gradient descent optimization based method to obtain multi-depth…

Image and Video Processing · Electrical Eng. & Systems 2020-04-20 Sanjeev Kumar , Manjunatha Mahadevappa , Pranab Kumar Dutta

A fundamental task in phase retrieval is to recover an unknown signal $\vx\in \Rn$ from a set of magnitude-only measurements $y_i=\abs{\nj{\va_i,\vx}}, \; i=1,\ldots,m$. In this paper, we propose two novel perturbed amplitude models (PAMs)…

Numerical Analysis · Mathematics 2021-12-16 Jian-Feng Cai , Meng Huang , Dong Li , Yang Wang

The Levenberg-Marquardt algorithm is one of the most popular algorithms for finding the solution of nonlinear least squares problems. Across different modified variations of the basic procedure, the algorithm enjoys global convergence, a…

Optimization and Control · Mathematics 2020-04-08 E. Bergou , Y. Diouane , V. Kungurtsev

Phase retrieval is the numerical procedure of recovering a complex-valued signal from knowledge about its amplitude and some additional information. Here, an indirect registration procedure, based on the large deformation diffeomorphic…

Image and Video Processing · Electrical Eng. & Systems 2023-06-29 Erik Malm

We study an approach to solving the phase retrieval problem as it arises in a phase-less imaging modality known as ptychography. In ptychography, small overlapping sections of an unknown sample (or signal, say $x_0\in \mathbb{C}^d$) are…

Numerical Analysis · Mathematics 2019-10-09 Brian Preskitt , Rayan Saab

Recent advances in neural-network architecture allow for seamless integration of convex optimization problems as differentiable layers in an end-to-end trainable neural network. Integrating medium and large scale quadratic programs into a…

Optimization and Control · Mathematics 2021-12-15 Andrew Butler , Roy Kwon

We present a convex relaxation-based algorithm for large-scale general phase retrieval problems. General phase retrieval problems include i.a. the estimation of the phase of the optical field in the pupil plane based on intensity…

Optimization and Control · Mathematics 2018-08-15 Reinier Doelman , H. Thao Nguyen , Michel Verhaegen

We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…

Numerical Analysis · Mathematics 2024-07-11 Robert Beinert , Michael Quellmalz

Phase retrieval aims at recovering a complex-valued signal from magnitude-only measurements, which attracts much attention since it has numerous applications in many disciplines. However, phase recovery involves solving a system of…

Information Theory · Computer Science 2017-06-13 Wen-Jun Zeng , H. C. So

In nanoscale imaging technique and ultrafast laser, the reconstruction procedure is normally formulated as a blind phase retrieval (BPR) problem, where one has to recover both the sample and the probe (pupil) jointly from phaseless data.…

Optimization and Control · Mathematics 2022-11-15 Huibin Chang , Li Yang , Stefano Marchesini

Planes are generally used in 3D reconstruction for depth sensors, such as RGB-D cameras and LiDARs. This paper focuses on the problem of estimating the optimal planes and sensor poses to minimize the point-to-plane distance. The resulting…

Computer Vision and Pattern Recognition · Computer Science 2022-11-22 Lipu Zhou

This paper shows how data-driven deep generative models can be utilized to solve challenging phase retrieval problems, in which one wants to reconstruct a signal from only few intensity measurements. Classical iterative algorithms are known…

Image and Video Processing · Electrical Eng. & Systems 2020-07-17 Martin Reiche , Peter Jung

The successes of deep learning, variational inference, and many other fields have been aided by specialized implementations of reverse-mode automatic differentiation (AD) to compute gradients of mega-dimensional objectives. The AD…

Machine Learning · Computer Science 2021-03-16 Deniz Oktay , Nick McGreivy , Joshua Aduol , Alex Beatson , Ryan P. Adams

In this paper, we focus on Stochastic Amplitude Flow (SAF) for phase retrieval, a stochastic gradient descent for the amplitude-based squared loss. While the convergence to a critical point of (nonstochastic) Amplitude Flow is…

Numerical Analysis · Mathematics 2022-12-12 Oleh Melnyk

The null vector method, based on a simple linear algebraic concept, is proposed as a solution to the phase retrieval problem. In the case with complex Gaussian random measurement matrices, a non-asymptotic error bound is derived, yielding…

Information Theory · Computer Science 2016-07-27 P. Chen , A. Fannjiang , G. Liu

This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations…

Information Theory · Computer Science 2011-09-21 Emmanuel J. Candes , Yonina Eldar , Thomas Strohmer , Vlad Voroninski

An outlier-resistance phase retrieval algorithm based on alternating direction method of multipliers (ADMM) is devised in this letter. Instead of the widely used least squares criterion that is only optimal for Gaussian noise environment,…

Information Theory · Computer Science 2017-02-22 Xue Jiang , H. C. So , X. Liu

We study nonconvex optimization for phase retrieval and the more general problem of semidefinite low-rank matrix sensing; in particular, we focus on the global nonconvex landscape of overparametrized versions of the nonsmooth amplitude…

Optimization and Control · Mathematics 2025-11-25 Andrew D. McRae

Phase retrieval (PR) is an inverse problem about recovering a signal from phaseless linear measurements. This problem can be effectively solved by minimizing a nonconvex amplitude-based loss function. However, this loss function is…

Signal Processing · Electrical Eng. & Systems 2020-07-24 Q. Luo , H. Wang