Related papers: Phase Retrieval: An Overview of Recent Development…
Measuring the phase of light is fundamental to optical imaging, sensing, and signal processing applications. Conventional optical phase measurements rely on multipath configurations, bulky interferometric setups, and computationally…
In this paper, we introduce two symmetric directed graphs depending on supports of signals and windows, and we show that the connectivity of those graphs provides either necessary and sufficient conditions to phase retrieval of a signal…
The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…
In phase retrieval we want to recover an unknown signal $\boldsymbol x\in\mathbb C^d$ from $n$ quadratic measurements of the form $y_i = |\langle{\boldsymbol a}_i,{\boldsymbol x}\rangle|^2+w_i$ where $\boldsymbol a_i\in \mathbb C^d$ are…
Measurements achieved with ptychographic imaging are a special case of diffraction measurements. They are generated by illuminating small parts of a sample with, e.g., a focused X-ray beam. By shifting the sample, a set of far-field…
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…
This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements…
In the context of the phase retrieval problem, it is known that certain natural classes of measurements, such as Fourier measurements and random Bernoulli measurements, do not lead to the unique reconstruction of all possible signals, even…
We develop a fast phase retrieval method which can utilize a large class of local phaseless correlation-based measurements in order to recover a given signal ${\bf x} \in \mathbb{C}^d$ (up to an unknown global phase) in near-linear…
Diffusion models have demonstrated their utility as learned priors for solving various inverse problems. However, most existing approaches are limited to linear inverse problems. This paper exploits the efficient and unsupervised posterior…
The problem of phase retrieval has been intriguing researchers for decades due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phase-less measurements.…
Phase retrieval aims to recover a signal $x \in \mathbb{C}^{n}$ from its amplitude measurements $|<x, a_i > |^2$, $i=1,2,...,m$, where $a_i$'s are over-complete basis vectors, with $m$ at least $3n -2$ to ensure a unique solution up to a…
This work studies phase retrieval for wave fields, aiming to recover the phase of an incoming wave from multi-plane intensity measurements behind different types of linear and nonlinear media. We show that unique phase retrieval can be…
The Fourier inversion of phased coherent diffraction patterns offers images without the resolution and depth-of-focus limitations of lens-based tomographic systems. We report on our recent experimental images inverted using recent…
In this paper, we propose a new non-convex algorithm for solving the phase retrieval problem, i.e., the reconstruction of a signal $ \vx\in\H^n $ ($\H=\R$ or $\C$) from phaseless samples $ b_j=\abs{\langle \va_j, \vx\rangle } $, $…
This paper considers the phase retrieval problem in which measurements consist of only the magnitude of several linear measurements of the unknown, e.g., spectral components of a time sequence. We develop low-complexity algorithms with…
Electronic wave functions of planar molecules can be reconstructed via inverse Fourier transform of angle-resolved photoelectron spectroscopy (ARPES) data, provided the phase of the electron wave in the detector plane is known. Since the…
I show that the power iteration method applied to the phase retrieval problem converges under special conditions. One is given the relative phases between small non-overlapping groups of pixels of a recorded intensity pattern, but no…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
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…