Related papers: Robust Phase Retrieval Algorithm for Time-Frequenc…
In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the…
This study presents a noise-robust framework for 1-bit diffraction tomography, a novel imaging approach that relies on intensity-only binary measurements obtained through coded apertures. The proposed reconstruction scheme leverages random…
A spatial signal is defined by its evaluations on the whole domain. In this paper, we consider stable reconstruction of real-valued signals with finite rate of innovations (FRI), up to a sign, from their magnitude measurements on the whole…
We study algorithms for solving quadratic systems of equations based on optimization methods over polytopes. Our work is inspired by a recently proposed convex formulation of the phase retrieval problem, which estimates the unknown signal…
Phase retrieval refers to algorithmic methods for recovering a signal from its phaseless measurements. Local search algorithms that work directly on the non-convex formulation of the problem have been very popular recently. Due to the…
This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of…
We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of the Fourier phase information, this problem is ill-posed. Therefore,…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…
Recovering an unknown but structured signal from its measurements is a challenging problem with significant applications in fields such as imaging restoration, wireless communications, and signal processing. In this paper, we consider the…
The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science. Fourier phase retrieval poses fundamental theoretical and…
Gabor phase retrieval for signals has attracted considerable attention in recent years. For the more general short-time linear canonical transform (STLCT), which arises naturally in optical systems and canonical time--frequency analysis,…
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…
Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…
In the undersampled phase retrieval problem, the goal is to recover an $N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce…
High-throughput computational imaging requires efficient processing algorithms to retrieve multi-dimensional and multi-scale information. In computational phase imaging, phase retrieval (PR) is required to reconstruct both amplitude and…
This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…
Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal…
Fourier ptychography is a new computational microscopy technique that provides gigapixel-scale intensity and phase images with both wide field-of-view and high resolution. By capturing a stack of low-resolution images under different…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequencies. It is well known that the non-uniqueness issue is a…