Related papers: Phase retrieval with complexity guidance
Compressive phase retrieval refers to the problem of recovering a structured $n$-dimensional complex-valued vector from its phase-less under-determined linear measurements. The non-linearity of measurements makes designing…
Phase retrieval seeks to reconstruct a signal from phaseless intensity measurements and, in applications where measurements contain errors, demands stable reconstruction. We study local stability of phase retrieval in reproducing kernel…
This paper proposes a new framework to regularize the highly ill-posed and non-linear phase retrieval problem through deep generative priors using simple gradient descent algorithm. We experimentally show effectiveness of proposed algorithm…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…
Retrieval-Augmented Generation (RAG) prevails in Large Language Models. It mainly consists of retrieval and generation. The retrieval modules (a.k.a. retrievers) aim to find useful information used to facilitate the generation modules…
One of the most prominent challenges in the field of diffractive imaging is the phase retrieval (PR) problem: In order to reconstruct an object from its diffraction pattern, the inverse Fourier transform must be computed. This is only…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…
Phase retrieval has been an attractive but difficult problem rising from physical science, and there has been a gap between state-of-the-art theoretical convergence analyses and the corresponding efficient retrieval methods. Firstly, these…
Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…
Phase retrieval (PR), a long-established challenge for recovering a complex-valued signal from its Fourier intensity-only measurements, has attracted considerable attention due to its widespread applications in digital imaging. Recently,…
We consider the problem of phase retrieval, i.e. that of solving systems of quadratic equations. A simple variant of the randomized Kaczmarz method was recently proposed for phase retrieval, and it was shown numerically to have a…
The phase retrieval problem in the presence of noise aims to recover the signal vector of interest from a set of quadratic measurements with infrequent but arbitrary corruptions, and it plays an important role in many scientific…
Phase retrieval is concerned with recovering a function $f$ from the absolute value of its Fourier transform $|\widehat{f}|$. We study the stability properties of this problem in Lebesgue spaces. Our main results shows that $$ \|…
The recovery of a signal from the magnitude of its Fourier transform, also known as phase retrieval, is of fundamental importance in many scientific fields. It is well known that due to the loss of Fourier phase the problem in 1D is…
Phase retrieval is a problem encountered not only in speech and audio processing, but in many other fields such as optics. Iterative algorithms based on non-convex set projections are effective and frequently used for retrieving the phase…
The re-ranking approach leverages high-confidence retrieved samples to refine retrieval results, which have been widely adopted as a post-processing tool for image retrieval tasks. However, we notice one main flaw of re-ranking, i.e., high…
The problem of phase retrieval (PR) involves recovering an unknown image from limited amplitude measurement data and is a challenge nonlinear inverse problem in computational imaging and image processing. However, many of the PR methods are…
Phase retrieval with prior information can be cast as a nonsmooth and nonconvex optimization problem. We solve the problem by graph projection splitting (GPS), where the two proximity subproblems and the graph projection step can be solved…
Detecting multiple change points in functional data sequences has been increasingly popular and critical in various scientific fields. In this article, we propose a novel two-stage framework for detecting multiple change points in…