Related papers: Phaseless Rcovery using Gauss-Newton Method
We present an analytic method, based on the Bohmian equations for quantum mechanics, for approaching the phase-retrieval problem in the following formulation: By knowing the probability density $\left\vert…
Phase-retrieval techniques aim to recover the original signal from just the modulus of its Fourier transform, which is usually much easier to measure than its phase, but the standard iterative techniques tend to fail if only part of 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…
A standardized phase retrieval algorithm is presented and applied to an industry-grade high-energy ultrashort pulsed laser to uncover its spatial phase distribution. We describe in detail how to modify the well-known algorithm in order to…
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.…
A variational approach to reconstruction of phase and amplitude of a complex-valued object from Poissonian intensity observations is developed. The observation model corresponds to the typical optical setups with a phase modulation of…
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…
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…
We prove by means of elementary methods that phase retrieval of complex polynomials p of degree less than N is possible with 4N-4 phaseless Fourier measurements of p and p'. In addition, we provide an associated algorithm and prove that it…
We consider a least absolute deviation (LAD) approach to the robust phase retrieval problem that aims to recover a signal from its absolute measurements corrupted with sparse noise. To solve the resulting non-convex optimization problem, we…
To estimate accurate voltage phasors from inaccurate voltage magnitude and complex power measurements, the standard approach is to iteratively refine a good initial guess using the Gauss--Newton method. But the nonconvexity of the…
This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations…
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.…
A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations $|Ax|^2=y$. The algorithms are developed by exploiting the inherent low rank structure of the problem based on the…
We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the…
We study the Kaczmarz methods for solving systems of quadratic equations, i.e., the generalized phase retrieval problem. The methods extend the Kaczmarz methods for solving systems of linear equations by integrating a phase selection…
Iterative phase retrieval algorithms are widely used in digital optics for their efficiency and simplicity. Conventionally, these algorithms do not consider aberrations as they assume an ideal, aberration-free optical system. Here, we…
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 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…
Exploring the idea of phase retrieval has been intriguing researchers for decades, due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phaseless…