Related papers: Lower Lipschitz Bounds for Phase Retrieval from Lo…
In ultrasound nondestructive testing, a widespread approach is to take synthetic aperture measurements from the surface of a specimen to detect and locate defects within it. Based on these measurements, imaging is usually performed using…
We consider the phase retrieval problem of reconstructing a $n$-dimensional real or complex signal $\mathbf{X}^{\star}$ from $m$ (possibly noisy) observations $Y_\mu = | \sum_{i=1}^n \Phi_{\mu i} X^{\star}_i/\sqrt{n}|$, for a large class of…
The mutual intensity and its equivalent phase-space representations quantify an optical field's state of coherence and are important tools in the study of light propagation and dynamics, but they can only be estimated indirectly from…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…
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)…
A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…
In this paper we study a realistic setup for phase retrieval, where the signal of interest is modulated or masked and then for each modulation or mask a diffraction pattern is collected, producing a coded diffraction pattern (CDP) [CLM13].…
Phase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in the deterministic setting phase retrieval from frame…
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 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…
An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…
We investigate stable recovery guarantees for phase retrieval under two realistic and challenging noise models: the Poisson model and the heavy-tailed model. Our analysis covers both nonconvex least squares (NCVX-LS) and convex least…
Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase.…
The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in…
Robustness to noise and outliers is a desirable trait in phase retrieval algorithms for many applications in imaging and signal processing. In this paper, we develop novel robust phase retrieval algorithms based on the minimization of…
The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex…
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…
Phase retrieval is the problem of reconstructing images from magnitude-only measurements. In many real-world applications the problem is underdetermined. When training data is available, generative models allow optimization in a…
The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science. Fourier phase retrieval poses fundamental theoretical and…
In this paper, we consider the problem of phase retrieval, which consists of recovering an $n$-dimensional real vector from the magnitude of its $m$ linear measurements. We propose a mirror descent (or Bregman gradient descent) algorithm…