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Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…
We propose a method for constructing the time-dependent phase space distribution function (DF) of a collisionless system from an isolated kinematic snapshot. In general, the problem of mapping a single snapshot to a time-dependent function…
Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single…
Successive differences on a sequence of data help to discover some smoothness features of this data. This was one of the main reasons for rewriting the classical interpolation formula in terms of such data differences. The aim of this paper…
Gaussian mixture models are universal approximators in the sense that any smooth density can be approximated arbitrarily well with a Gaussian mixture model with enough components. Due to their broad expressive power, Gaussian mixture models…
The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…
In recent work [P. Grohs and M. Rathmair. Stable Gabor Phase Retrieval and Spectral Clustering. Communications on Pure and Applied Mathematics (2018)] the instabilities of the Gabor phase retrieval problem, i.e., the problem of…
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…
We study the geometric action of some modular conjugations in two dimensional (2D) conformal field theories. We investigate the bipartition given by an interval when the system is in the ground state, either on the line or on the circle,…
A method for revealing the covariance matrix of an unknown two-mode Gaussian state is given based on the interference with a reference twin beam whose covariance matrix is known. In the method, first- and second-order cross-correlation…
Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches…
We present the first phase retrieval algorithm guaranteed to solve the multidimensional phase retrieval problem in polynomial arithmetic complexity without prior information. The method successfully terminates in O(N log(N)) operations for…
Phase imaging techniques extract the optical path-length information of a scene, whereas wavefront sensors provide the shape of an optical wavefront. Since these two applications have different technical requirements, they have developed…
A non-iterative method for the construction of the Short-Time Fourier Transform (STFT) phase from the magnitude is presented. The method is based on the direct relationship between the partial derivatives of the phase and the logarithm of…
This article aims at discovering the unknown variables in the system through data analysis. The main idea is to use the time of data collection as a surrogate variable and try to identify the unknown variables by modeling gradual and sudden…
The realm of classical phase retrieval concerns itself with the arduous task of recovering a signal from its Fourier magnitude measurements, which are fraught with inherent ambiguities. A single-exposure intensity measurement is commonly…
The problem of phase retrieval is a classic one in optics and arises when one is interested in recovering an unknown signal from the magnitude (intensity) of its Fourier transform. While there have existed quite a few approaches to phase…
The classical phase retrieval refers to the recovery of an unknown signal from its Fourier magnitudes, which is widely used in fields such as quantum mechanics, signal processing, optics, etc. The offset linear canonical transform (OLCT),…
The generalized phase retrieval problem over compact groups aims to recover a set of matrices -- representing an unknown signal -- from their associated Gram matrices. This framework generalizes the classical phase retrieval problem, which…
This paper investigates the properties of continuous frames, with a particular focus on phase retrieval and norm retrieval in the context of Hilbert spaces. We introduce the concept of continuous near-Riesz bases and prove their invariance…