Related papers: Measurement Matrix Design for Phase Retrieval Base…
Calibration is nowadays one of the most important processes involved in the extraction of valuable data from measurements. The current availability of an optimum data cube measured from a heterogeneous set of instruments and surveys relies…
The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy…
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…
Previous work regarding low-rank matrix recovery has concentrated on the scenarios in which the matrix is noise-free and the measurements are corrupted by noise. However, in practical application, the matrix itself is usually perturbed by…
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…
We address the problem of signal reconstruction from intensity measurements with respect to a measurement frame. This non-convex inverse problem is known as phase retrieval. The case considered in this paper concerns phaseless measurements…
In this study, we propose a generalized turbo signal recovery algorithm to estimate a signal from quantized measurements, in which the sensing matrix is a row-orthogonal matrix, such as the partial discrete Fourier transform matrix. The…
We consider the question of estimating a real low-complexity signal (such as a sparse vector or a low-rank matrix) from the phase of complex random measurements. We show that in this "phase-only compressive sensing" (PO-CS) scenario, we can…
We study the problem of recovering a structured signal from independently and identically drawn linear measurements. A convex penalty function $f(\cdot)$ is considered which penalizes deviations from the desired structure, and signal…
This paper investigates experimental means of measuring the transmission matrix (TM) of a highly scattering medium, with the simplest optical setup. Spatial light modulation is performed by a digital micromirror device (DMD), allowing high…
Phase retrieval deals with the recovery of complex- or real-valued signals from magnitude measurements. As shown recently, the method PhaseMax enables phase retrieval via convex optimization and without lifting the problem to a higher…
We consider the problem of finding a low rank symmetric matrix satisfying a system of linear equations, as appears in phase retrieval. In particular, we solve the gauge dual formulation, but use a fast approximation of the spectral…
Phase retrieval is the problem of reconstructing images from magnitude-only measurements. In many real-world applications the problem is underdetermined. When training data is available, generative models allow optimization in a…
In this paper, we introduce two symmetric directed graphs depending on supports of signals and windows, and we show that the connectivity of those graphs provides either necessary and sufficient conditions to phase retrieval of a signal…
Phase retrieval is an important problem with significant physical and industrial applications. In this paper, we consider the case where the magnitude of the measurement of an underlying signal is corrupted by Gaussian noise. We introduce a…
Recent advances in convex optimization have led to new strides in the phase retrieval problem over finite-dimensional vector spaces. However, certain fundamental questions remain: What sorts of measurement vectors uniquely determine every…
This paper considers phase retrieval from the magnitude of 1D over-sampled Fourier measurements, a classical problem that has challenged researchers in various fields of science and engineering. We show that an optimal vector in a…
Recent development in compressed sensing (CS) has revealed that the use of a special design of measurement matrix, namely the spatially-coupled matrix, can achieve the information-theoretic limit of CS. In this paper, we consider the…
We study information theoretic limits of recovering an unknown $n$ dimensional, complex signal vector $\mathbf{x}_\star$ with unit norm from $m$ magnitude-only measurements of the form $y_i = |(\mathbf{A} \mathbf{x}_\star)_i|^2, \; i = 1,2…
We study lower bounds on adaptive sensing algorithms for recovering low rank matrices using linear measurements. Given an $n \times n$ matrix $A$, a general linear measurement $S(A)$, for an $n \times n$ matrix $S$, is just the inner…