Related papers: The Numerics of Phase Retrieval
Phase retrieval is a well known ill-posed inverse problem where one tries to recover images given only the magnitude values of their Fourier transform as input. In recent years, new algorithms based on deep learning have been proposed,…
We study the convolutional phase retrieval problem, of recovering an unknown signal $\mathbf x \in \mathbb C^n $ from $m$ measurements consisting of the magnitude of its cyclic convolution with a given kernel $\mathbf a \in \mathbb C^m $.…
The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless…
A novel phase retrieval method, motivated by ptychographic imaging, is proposed for the approximate recovery of a compactly supported specimen function $f:\mathbb{R}\rightarrow\mathbb{C}$ from its continuous short time Fourier transform…
We present a new method for real- and complex-valued image reconstruction from two intensity measurements made in the Fourier plane: the Fourier magnitude of the unknown image, and the intensity of the interference pattern arising from…
We consider the inverse source problem of determining an acoustic source from multi-frequency phaseless far-field data. By supplementing some reference point sources to the inverse source model, we develop a novel strategy for recovering…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In this paper, we provide a…
Light-matter interaction is exploited in spectroscopic techniques to access information about molecular, atomic or nuclear constituents of the sample of interest. While scattered light carries both amplitude and phase information of the…
In the phase retrieval problem, an unknown vector is to be recovered given quadratic measurements. This problem has received considerable attention in recent times. In this paper, we present an algorithm to solve a nonconvex formulation of…
Reconstructing a signal from squared linear (rank-one quadratic) measurements is a challenging problem with important applications in optics and imaging, where it is known as phase retrieval. This paper proposes two new phase retrieval…
Quaternionic signal processing provides powerful tools for efficiently managing color signals by preserving the intrinsic correlations among signal dimensions through quaternion algebra. In this paper, we address the quaternionic phase…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
This paper discusses the noisy phase retrieval problem: recovering a complex image signal with independent noise from quadratic measurements. Inspired by the dark fringes shown in the measured images of the array detector, a novel phase…
Signal inpainting is the task of restoring degraded or missing samples in a signal. In this paper we address signal inpainting when Fourier magnitudes are observed. We propose a mathematical formulation of the problem that highlights its…
Bit retrieval, the problem of determining a binary sequence from its cyclic autocorrelation, is a special case of the phase retrieval problem. Algorithms for phase retrieval are extensively used in several scientific disciplines, and yet,…
Phaseless super-resolution is the problem of recovering an unknown signal from measurements of the magnitudes of the low frequency Fourier transform of the signal. This problem arises in applications where measuring the phase, and making…
In this paper we consider the following real-valued and finite dimensional specific instance of the 1-D classical phase retrieval problem. Let ${\bf F}\in\mathbb{R}^N$ be an $N$-dimensional vector, whose discrete Fourier transform has a…
We introduce a generalized version of phase retrieval called multiplexed phase retrieval. We want to recover the phase of amplitude-only measurements from linear combinations of them. This corresponds to the case in which multiple…
In the last five decades, iterative phase retrieval methods draw large amount of interest across the research community as a non-interferometric approach to recover quantitative phase distributions from one (or more) intensity measurement.…
This work introduces a novel Fourier phase retrieval model, called polarimetric phase retrieval that enables a systematic use of polarization information in Fourier phase retrieval problems. We provide a complete characterization of…