相关论文: Phase Retrieval from 4N-4 Measurements

Edidin [3] proved a fundamental result in phase retrieval: Theorem: A family of orthogonal projections $\{P_i\}_{i=1}^m$ does phase retrieval in $\mathbb{R}^n$ if and only if for every $0\not= x\in \mathbb{R}^n$, the family…

This paper addresses fundamental scaling issues that hinder phase retrieval (PR) in high dimensions. We show that, if the measurement matrix can be put into a generalized block-diagonal form, a large PR problem can be solved on separate…

The classical phase retrieval problem involves estimating a signal from its Fourier magnitudes (power spectrum) by leveraging prior information about the desired signal. This paper extends the problem to compact groups, addressing the…

Fraunhofer diffraction is a well-known phenomenon achieved with most wavelength even without lens. A single-shot intensity measurement of diffraction is generally considered inadequate to reconstruct the original light field, because the…

We study the phase retrieval property for orbits of general irreducible representations of nilpotent groups, for the classes of simply connected connected Lie groups, and for finite groups. We prove by induction that in the Lie group case,…

In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex…

Phase retrieval refers to recovering a signal from its Fourier magnitude. This problem arises naturally in many scientific applications, such as ultra-short laser pulse characterization and diffraction imaging. Unfortunately, phase…

This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup where one can…

Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…

I show that the power iteration method applied to the phase retrieval problem converges under special conditions. One is given the relative phases between small non-overlapping groups of pixels of a recorded intensity pattern, but no…

Phase retrieval, a long-established challenge for recovering a complex-valued signal from its Fourier intensity measurements, has attracted significant interest because of its far-flung applications in optical imaging. To enhance accuracy,…

Zernike's phase contrast microscopy (PCM) is among the most widely used techniques for observing phase objects, but it lacks quantitative nature, as it cannot directly provide phase information. Current methods for computationally…

A novel phase retrieval algorithm for broadband hyperspectral phase imaging from noisy intensity observations is proposed. It utilizes advantages of the Fourier Transform spectroscopy in the self-referencing optical setup and provides,…

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 $.…

In this paper, we consider the generalized phase retrieval from affine measurements. This problem aims to recover signals ${\mathbf x} \in {\mathbb F}^d$ from the affine measurements $y_j=\norm{M_j^*\vx +{\mathbb b}_j}^2,\; j=1,\ldots,m,$…

The recovery of a signal from the magnitude of its Fourier transform, also known as phase retrieval, is of fundamental importance in many scientific fields. It is well known that due to the loss of Fourier phase the problem in 1D is…

We study algorithms for solving quadratic systems of equations based on optimization methods over polytopes. Our work is inspired by a recently proposed convex formulation of the phase retrieval problem, which estimates the unknown signal…

The conjugate phase retrieval problem concerns the determination of a complex-valued function, up to a unimodular constant and conjugation, from its magnitude observations. It can also be considered as a conjugate phaseless sampling and…

The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics and,…

In this paper, we tackle the general compressive phase retrieval problem. The problem is to recover a K-sparse complex vector of length n, $x\in \mathbb{C}^n$, from the magnitudes of m linear measurements, $y=|Ax|$, where $A \in…