Related papers: Phase-Retrieval as a Regularization Problem
Image deconvolution is still to be a challenging ill-posed problem for recovering a clear image from a given blurry image, when the point spread function is known. Although competitive deconvolution methods are numerically impressive and…
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 $.…
Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors…
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase.…
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…
Phase retrieval is the nonlinear inverse problem of recovering a true signal from its Fourier magnitude measurements. It arises in many applications such as astronomical imaging, X-Ray crystallography, microscopy, and more. The problem is…
In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be…
In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…
Phase retrieval is to recover the signals from phaseless measurements which is raised in many areas. A fundamental problem in phase retrieval is to determine the minimal measurement number $m$ so that one can recover $d$-dimensional signals…
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…
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,…
X-ray ptychography is one of the versatile techniques for nanometer resolution imaging. The magnitude of the diffraction patterns is recorded on a detector and the phase of the diffraction patterns is estimated using phase retrieval…
Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect to a dynamical frame, i.e. a sequence of sampling vectors constructed by the…
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…
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…
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.…
Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and a single real parameter $\beta$. For the standard application in optics, where the two projections…
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…
A recently proposed convex formulation of the phase retrieval problem estimates the unknown signal by solving a simple linear program. This new scheme, known as PhaseMax, is computationally efficient compared to standard convex relaxation…