Related papers: Sampling Density for Gabor Phase Retrieval
This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…
We consider the problem of finding a low rank symmetric matrix satisfying a system of linear equations, as appears in phase retrieval. In particular, we solve the gauge dual formulation, but use a fast approximation of the spectral…
A variational approach to reconstruction of phase and amplitude of a complex-valued object from Poissonian intensity observations is developed. The observation model corresponds to the typical optical setups with a phase modulation of…
Variance-reduced stochastic gradient methods have gained popularity in recent times. Several variants exist with different strategies for the storing and sampling of gradients and this work concerns the interactions between these two…
The recovery of an unknown signal from its linear measurements is a fundamental problem spanning numerous scientific and engineering disciplines. Commonly, prior knowledge suggests that the underlying signal resides within a known algebraic…
In this paper, we study phase retrievable sequences and give a characterization of phase retrievability of a sequence of bounded linear operators on a Hilbert space $H$; in particular, for $H=\ell_2^d(\Bbb{C})$. We also give several…
We present a perfect sampling algorithm for Gibbs point processes, based on the partial rejection sampling of Guo et al. (2017). Our particular focus is on pairwise interaction processes, penetrable spheres mixture models and…
The aim of this chapter is to give an overview of the recent advances related to sampling and recovery of signals defined over graphs. First, we illustrate the conditions for perfect recovery of bandlimited graph signals from samples…
In this paper we consider the nonlinear inverse problem of phase retrieval in the context of dynamical sampling. Where phase retrieval deals with the recovery of signals & images from phaseless measurements, dynamical sampling was…
Conventional optical coherent receivers capture the full electrical field, including amplitude and phase, of a signal waveform by measuring its interference against a stable continuous-wave local oscillator (LO). In optical coherent…
We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions, a simple subgradient method converges linearly when initialized within a constant relative distance of an…
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…
We study convex relaxation algorithms for phase retrieval on imaging problems. We show that structural assumptions on the signal and the observations, such as sparsity, smoothness or positivity, can be exploited to both speed-up convergence…
Highly multiplexed microscopy enables rich spatial characterization of tissues at single-cell resolution, yet most analyses rely on two-dimensional sections despite inherently three-dimensional tissue organization. Acquiring dense…
In this paper, we study the generalized phase retrieval problem: to recover a signal $\bm{x}\in\mathbb{C}^n$ from the measurements $y_r=\lvert \langle\bm{a}_r,\bm{x}\rangle\rvert^2$, $r=1,2,\ldots,m$. The problem can be reformulated as a…
We generalize three main concepts of Gabor analysis for lattices to the setting of model sets: Fundamental Identity of Gabor Analysis, Janssen's representation of the frame operator and Wexler-Raz biorthogonality relations. Utilizing the…
In this paper, we study the affine phase retrieval problem, which aims to recover signals from the magnitudes of affine measurements. We develop second-order optimization methods based on Newton and Gauss-Newton iterations and establish…
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…
This paper shows how data-driven deep generative models can be utilized to solve challenging phase retrieval problems, in which one wants to reconstruct a signal from only few intensity measurements. Classical iterative algorithms are known…
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…