Related papers: Blind Phaseless Short-Time Fourier Transform Recov…
This paper is concerned with the problem of recovering a structured signal from a relatively small number of corrupted random measurements. Sharp phase transitions have been numerically observed in practice when different convex programming…
In this paper we tackle the problem of recovering the phase of complex linear measurements when only magnitude information is available and we control the input. We are motivated by the recent development of dedicated optics-based hardware…
We study the recovery of square-integrable signals from the absolute values of their wavelet transforms, also called wavelet phase retrieval. We present a new uniqueness result for wavelet phase retrieval. To be precise, we show that any…
We consider the geometry associated to the ambiguities of the one-dimensional Fourier phase retrieval problem for vectors in ${\mathbb C}^{N+1}$. Our first result states that the space of signals has a finite covering (which we call 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…
We consider the problem of high-dimensional misspecified phase retrieval. This is where we have an $s$-sparse signal vector $\mathbf{x}_*$ in $\mathbb{R}^n$, which we wish to recover using sampling vectors…
The aim of this paper is to build up the theoretical framework for the recovery of sparse signals from the magnitude of the measurement. We first investigate the minimal number of measurements for the success of the recovery of sparse…
We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that…
Recovering a signal from auto-correlations or, equivalently, retrieving the phase linked to a given Fourier modulus, is a wide-spread problem in imaging. This problem has been tackled in a number of experimental situations, from optical…
We address the problem of recovering a signal (up to global phase) from its short-time Fourier transform (STFT) magnitude measurements. This problem arises in several applications, including optical imaging and speech processing. In this…
Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function.…
The classical shift retrieval problem considers two signals in vector form that are related by a shift. The problem is of great importance in many applications and is typically solved by maximizing the cross-correlation between the two…
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 $y_j=\norm{M_j^*\vx +{\mathbb b}_j}^2,\; j=1,\ldots,m,$…
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…
This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequencies. It is well known that the non-uniqueness issue is a…
In many applications in compressed sensing, the measurement matrix is a Fourier matrix, i.e., it measures the Fourier transform of the underlying signal at some specified `base' frequencies $\{u_i\}_{i=1}^M$, where $M$ is the number of…
Completely blind sensing is the problem of recovering bandlimited signals from measurements, without any spectral information beside an upper bound on the measure of the whole support set in the frequency domain. Determining the number of…
In this work we characterize all ambiguities of the linear (aperiodic) one-dimensional convolution on two fixed finite-dimensional complex vector spaces. It will be shown that the convolution ambiguities can be mapped one-to-one to…
We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input…
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…