Related papers: Phaseless Reconstruction from Space-Time Samples
We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…
The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…
We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
We consider the problem of reconstruction of planar domains from their moments. Specifically, we consider domains with boundary which can be represented by a union of a finite number of pieces whose graphs are solutions of a linear…
Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…
Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time-ordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are…
We consider the problem of spatiotemporal sampling in a discrete infinite dimensional spatially invariant evolutionary process $x^{(n)}=A^nx$ to recover an unknown convolution operator $A$ given by a filter $a \in \ell^1(\mathbb{Z})$ and an…
Phaseless super-resolution is the problem of recovering an unknown signal from measurements of the magnitudes of the low frequency Fourier transform of the signal. This problem arises in applications where measuring the phase, and making…
This work takes the first steps towards solving the "phaseless subspace tracking" (PST) problem. PST involves recovering a time sequence of signals (or images) from phaseless linear projections of each signal under the following structural…
This paper introduces a novel technique for reconstructing the phase of modified spectrograms of audio signals. From the analysis of mixtures of sinusoids we obtain relationships between phases of successive time frames in the…
We analyze signal recovery when samples are taken concomitantly from a signal and its Fourier transform. This two-sided sampling framework extends classical one-sided reconstruction and is particularly useful when measurements in either…
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…
We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its…
The problem of phase retrieval is to determine a signal $f\in \mathcal{H}$, with $\mathcal{H}$ a Hilbert space, from intensity measurements $|F(\omega)|$, where $F(\omega):=\langle f , \varphi_\omega\rangle$ are measurements of $f$ with…
A linear and thus convex phase retrieval algorithm for the application in phaseless near-field far-field transformations is presented. The formulation exploits locally known phase relations among sets of measurement samples, which can in…
One of the challenges in phase measuring deflectometry is to retrieve the wavefront from objects that present discontinuities or non-differentiable gradient fields. Here, we propose the integration of such gradients fields based on an…
Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be…
Machine learning is attracting surging interest across nearly all scientific areas by enabling the analysis of large datasets and the extraction of scientific information from incomplete data. Data-driven science is rapidly growing,…
Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…