Related papers: Phase Retrieval Without Small-Ball Probability Ass…
In this paper, we develop a framework of generalized phase retrieval in which one aims to reconstruct a vector ${\mathbf x}$ in ${\mathbb R}^d$ or ${\mathbb C}^d$ through quadratic samples ${\mathbf x}^*A_1{\mathbf x}, \dots, {\mathbf…
The recovery of a signal from the intensity measurements with some entries being known in advance is termed as {\em affine phase retrieval}. In this paper, we prove that a natural least squares formulation for the affine phase retrieval is…
This paper provides novel results for the recovery of signals from undersampled measurements based on analysis $\ell_1$-minimization, when the analysis operator is given by a frame. We both provide so-called uniform and nonuniform recovery…
We address the problem of signal reconstruction from intensity measurements with respect to a measurement frame. This non-convex inverse problem is known as phase retrieval. The case considered in this paper concerns phaseless measurements…
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…
We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of the Fourier phase information, this problem is ill-posed. Therefore,…
Irreversible aggregation is revisited in view of recent work on renormalization of complex networks. Its scaling laws and phase transitions are related to percolation transitions seen in the latter. We illustrate our points by giving the…
Donoho and Stark have shown that a precise deterministic recovery of missing information contained in a time interval shorter than the time-frequency uncertainty limit is possible. We analyze this signal recovery mechanism from a physics…
We present a method and software for ballot-polling risk-limiting audits (RLAs) based on Bernoulli sampling: ballots are included in the sample with probability $p$, independently. Bernoulli sampling has several advantages: (1) it does not…
The phase retrieval from multi-frequency intensity (power) observations is considered. The object to be reconstructed is complex-valued. A novel algorithm is presented that accomplishes both the object phase (absolute phase) retrieval and…
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 identification of sampling sets that enable unique signal recovery is fundamental to many applications in signal processing and remains a central problem in mathematical analysis. Recent studies in the mathematical literature,…
This paper determines to within a single measurement the minimum number of measurements required to successfully reconstruct a signal drawn from a Gaussian mixture model in the low-noise regime. The method is to develop upper and lower…
Low-rank matrix recovery addresses the problem of recovering an unknown low-rank matrix from few linear measurements. Nuclear-norm minimization is a tractible approach with a recent surge of strong theoretical backing. Analagous to the…
We study the problem of recovering a function from the magnitude of its Gabor transform sampled on a discrete set. While it is known that uniqueness fails for general square integrable functions, we show that phase retrieval is possible for…
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…
In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames.…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
We address the problem of recovering signals from samples taken at their rate of innovation. Our only assumption is that the sampling system is such that the parameters defining the signal can be stably determined from the samples, a…
Phase retrieval refers to algorithmic methods for recovering a signal from its phaseless measurements. Local search algorithms that work directly on the non-convex formulation of the problem have been very popular recently. Due to the…