Related papers: Phase Retrieval via Structured Modulations in Pale…
In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…
A fundamental task in phase retrieval is to recover an unknown signal $\vx\in \Rn$ from a set of magnitude-only measurements $y_i=\abs{\nj{\va_i,\vx}}, \; i=1,\ldots,m$. In this paper, we propose two novel perturbed amplitude models (PAMs)…
Recovering a signal from its Fourier magnitude is referred to as phase retrieval, which occurs in different fields of engineering and applied physics. This paper gives a new characterization of the phase retrieval problem. Particularly…
Phase retrieval deals with the recovery of complex- or real-valued signals from magnitude measurements. As shown recently, the method PhaseMax enables phase retrieval via convex optimization and without lifting the problem to a higher…
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 studies several aspects of signal reconstruction of sampled data in spaces of bandlimited functions. In the first part, signal spaces are characterized in which the classical sampling series uniformly converge, and we investigate…
We consider the recovery of signals from their observations, which are samples of a transform of the signals rather than the signals themselves, by using machine learning (ML). We will develop a theoretical framework to characterize the…
We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…
A computationally quick and conceptually simple method to recover time delay of the chaotic system from scalar time series is developed in this paper. We show that the orbits in the incomplete two-dimensional reconstructed phase-space will…
The aim of sparse phase retrieval is to recover a $k$-sparse signal $\mathbf{x}_0\in \mathbb{C}^{d}$ from quadratic measurements $|\langle \mathbf{a}_i,\mathbf{x}_0\rangle|^2$ where $\mathbf{a}_i\in \mathbb{C}^d, i=1,\ldots,m$. Noting…
The phase retrieval problem has garnered significant attention since the development of the PhaseLift algorithm, which is a convex program that operates in a lifted space of matrices. Because of the substantial computational cost due to…
Periodic nonuniform sampling is a known method to sample spectrally sparse signals below the Nyquist rate. This strategy relies on the implicit assumption that the individual samplers are exposed to the entire frequency range. This…
We consider the recovery of square-integrable signals from discrete, equidistant samples of their Gabor transform magnitude and show that, in general, signals can not be recovered from such samples. In particular, we show that for any…
The problem of recovering a signal $\mathbf{x}\in \mathbb{R}^n$ from a set of magnitude measurements $y_i=|\langle \mathbf{a}_i, \mathbf{x} \rangle |, \; i=1,\ldots,m$ is referred as phase retrieval, which has many applications in fields of…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…
Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a…
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 studies the phase-only reconstruction problem of recovering a complex-valued signal $\textbf{x}$ in $\mathbb{C}^d$ from the phase of $\textbf{Ax}$ where $\textbf{A}$ is a given measurement matrix in $\mathbb{C}^{m\times d}$. The…
Fourier phase retrieval is the problem of reconstructing a signal given only the magnitude of its Fourier transformation. Optimization-based approaches, like the well-established Gerchberg-Saxton or the hybrid input output algorithm,…
"Phase retrieval" refers to the recovery of signals from the magnitudes (and not the phases) of linear measurements. While there has been a recent explosion in development of phase retrieval methods, the lack of a common interface has made…