Related papers: Characterization of (weak) phase retrieval dual fr…
Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the…
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…
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…
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 the recovery of the phase information of a signal from…
Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from…
Fourier phasing is the problem of retrieving Fourier phase information from Fourier intensity data. The standard Fourier phase retrieval (without a mask) is known to have many solutions which cause the standard phasing algorithms to…
We develop a novel and unifying setting for phase retrieval problems that works in Banach spaces and for continuous frames and consider the questions of uniqueness and stability of the reconstruction from phaseless measurements. Our main…
Wavefront sensing involves estimating the phase and intensity of light, enabling a wide range of imaging applications, from adaptive optics and astronomy to biomedical imaging. Since conventional image sensors can only measure the spatial…
Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. In this paper, we study the notion of excess for woven…
Wavelet frames for $L^2({\mathbb R})$ can be characterized by means of spectral techniques. This work uses spectral formulas to determine all the tight wavelet frames for $L^2({\mathbb R})$ with a fixed finite number of generators of…
The available probes of the large scale structure in the Universe have distinct properties: galaxies are a high resolution but biased tracer of mass, while weak lensing avoids such biases but, due to low signal-to-noise ratio, has poor…
We present a general method for determining the phase diagram of systems of a finite number of one dimensional Hubbard--like systems coupled by single--particle hopping with weak interactions. The technique is illustrated by detailed…
Weak measurements offer the possibility of tuning the information acquired on a system, hence the imposed disturbance. This suggests that it could be a useful tool for multi-parameter estimation, when two parameters can not be measured…
In many applications we seek to recover signals from linear measurements far fewer than the ambient dimension, given the signals have exploitable structures such as sparse vectors or low rank matrices. In this paper we work in a general…
An important yet challenging problem in understanding indoor scene is recovering indoor frame structure from a monocular image. It is more difficult when occlusions and illumination vary, and object boundaries are weak. To overcome these…
Phase-sensitive coherent imaging exploits changes in the phases of backscattered light to observe tiny alterations of scattering structures or variations of the refractive index. But moving scatterers or a fluctuating refractive index…
As a main research area in applied and computational harmonic analysis, the theory and applications of framelets have been extensively investigated. Most existing literature is devoted to framelet systems that only use one dilation matrix…
Characterizing the phase space distribution of particle beams in accelerators is a central part of accelerator understanding and performance optimization. However, conventional reconstruction-based techniques either use simplifying…
This paper develops uniqueness theory for 3D phase retrieval with finite, discrete measurement data for strong phase objects and weak phase objects, including: (i) {\em Unique determination of (phase) projections from diffraction patterns}…
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 $.…