Related papers: Gabor phase retrieval via semidefinite programming
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex…
This study investigates the phase retrieval problem for wide-band signals. We solve the following problem: given f $\in$ L 2 (R) with Fourier transform in L 2 (R, e^{2c|x|} dx), we find all functions g $\in$ L 2 (R) with Fourier transform…
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…
Short-time Fourier transform (STFT) phase retrieval refers to the reconstruction of a function $f$ from its spectrogram, i.e., the magnitudes of its short-time Fourier transform $V_gf$ with window function $g$. While it is known that for…
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…
We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature…
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…
The well-known phase problem which means image reconstruction from only spectrum magnitude without using any spectrum phase information is considered basically in application to VLBI mapping of compact extragalactic radio sources (active…
Phaseless reconstruction from space-time samples is a nonlinear problem of recovering a function $x$ in a Hilbert space $\mathcal{H}$ from the modulus of linear measurements $\{\lvert \langle x, \phi_i\rangle \rvert$, $ \ldots$, $\lvert…
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…
In this note we prove that reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem") can be performed using Lipschitz continuous maps. Specifically we show that when the nonlinear analysis map…
In the data analysis of oscillatory systems, methods based on phase reconstruction are widely used to characterize phase-locking properties and inferring the phase dynamics. The main component in these studies is an extraction of the phase…
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…
We consider the phase retrieval problem of reconstructing a $n$-dimensional real or complex signal $\mathbf{X}^{\star}$ from $m$ (possibly noisy) observations $Y_\mu = | \sum_{i=1}^n \Phi_{\mu i} X^{\star}_i/\sqrt{n}|$, for a large class of…
Recovery of signals with elements defined on the nodes of a graph, from compressive measurements is an important problem, which can arise in various domains such as sensor networks, image reconstruction and group testing. In some scenarios,…
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…
In this paper, we introduce a computational framework for recovering a high-resolution approximation of an unknown function from its low-resolution indirect measurements as well as high-resolution training observations by merging the…
Phase retrieval (PR), also sometimes referred to as quadratic sensing, is a problem that occurs in numerous signal and image acquisition domains ranging from optics, X-ray crystallography, Fourier ptychography, sub-diffraction imaging, and…
The phase retrieval problem has garnered significant attention since the development of the PhaseLift algorithm, which is a convex program that operates in a lifted space of matrices. Because of the substantial computational cost due to…