Related papers: Robust Wrapping-free Phase Retrieval Method Based …
In this paper, we propose an optimization-based method for robust phase retrieval problem where the goal is to estimate an unknown signal from a quadratic measurement corrupted by outliers. To enhance the robustness of existing optimization…
Interferometry can measure the shape or the material density of a system that could not be measured otherwise by recording the difference between the phase change of a signal and a reference phase. This difference is always between $-\pi$…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
The phase retrieval problem in the presence of noise aims to recover the signal vector of interest from a set of quadratic measurements with infrequent but arbitrary corruptions, and it plays an important role in many scientific…
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…
Phase retrieval problems involve solving linear equations, but with missing sign (or phase, for complex numbers) information. More than four decades after it was first proposed, the seminal error reduction algorithm of (Gerchberg and Saxton…
Ptychography has risen as a reference X-ray imaging technique: it achieves resolutions of one billionth of a meter, macroscopic field of view, or the capability to retrieve chemical or magnetic contrast, among other features. A…
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…
Signal recovery from nonlinear measurements involves solving an iterative optimization problem. In this paper, we present a framework to optimize the sensing parameters to improve the quality of the signal recovered by the given iterative…
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 from phaseless short-time Fourier transform (STFT) measurements is known to be inherently unstable when measurements are taken with respect to a single window. While an explicit inversion formula exists, it is useless in…
In terms of 3D imaging speed and system cost, the single-camera system projecting single-frequency patterns is the ideal option among all proposed Fringe Projection Profilometry (FPP) systems. This system necessitates a robust spatial phase…
The number of phase wraps in 2D wrapped phase map can be completely eliminated, or greatly reduced by frequency shifting. But the wraps usually cannot be optimally reduced using the conventional fast Fourier transform (FFT) because the…
We develop procedures, based on minimization of the composition $f(x) = h(c(x))$ of a convex function $h$ and smooth function $c$, for solving random collections of quadratic equalities, applying our methodology to phase retrieval problems.…
This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements…
Companion paper [118] developed a powerful \emph{Random duality theory} (RDT) based analytical program to statistically characterize performance of \emph{descending} phase retrieval algorithms (dPR) (these include all variants of gradient…
We study the phase retrieval problem, which solves quadratic system of equations, i.e., recovers a vector $\boldsymbol{x}\in \mathbb{R}^n$ from its magnitude measurements $y_i=|\langle \boldsymbol{a}_i, \boldsymbol{x}\rangle|, i=1,..., m$.…
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.…
This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…
The phase retrieval problem is a fundamental problem in many fields, which is appealing for investigation. It is to recover the signal vector $\tilde{x}\in\mathbb{C}^d$ from a set of $N$ measurements $b_n=|f^*_n\tilde{x}|^2,\ n=1,\cdots,…