Related papers: Phase Retrieval Using Unitary 2-Designs
We propose and study a class of novel algorithms that aim at solving bilinear and quadratic inverse problems. Using a convex relaxation based on tensorial lifting, and applying first-order proximal algorithms, these problems could be solved…
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…
A new method for phase recovery from a single two-beam interferogram is presented. Conventional approaches, relying on trigonometric inversion followed by phase unfolding and unwrapping, are hindered by discontinuities typically addressed…
Phase retrieval is a prevalent problem in digital signal processing and experimental physics that consists of estimating a complex signal from magnitude measurements. This paper expands the classical phase retrieval framework to electric…
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)…
Phase retrieval is a well known ill-posed inverse problem where one tries to recover images given only the magnitude values of their Fourier transform as input. In recent years, new algorithms based on deep learning have been proposed,…
The 2-D phase unwrapping problem aims at retrieving a "phase" image from its modulo $2\pi$ observations. Many applications, such as interferometry or synthetic aperture radar imaging, are concerned by this problem since they proceed by…
We study the low-rank phase retrieval problem, where the objective is to recover a sequence of signals (typically images) given the magnitude of linear measurements of those signals. Existing solutions involve recovering a matrix…
Phase retrieval problems occur in a wide range of applications in physics and engineering. Usually, these problems consist in the recovery of an unknown signal from the magnitudes of its Fourier transform. In some applications, however, the…
Universal multiport interferometers (UMIs) have emerged as a key tool for performing arbitrary linear transformations on optical modes, enabling precise control over the state of light in essential applications of classical and quantum…
In this work we demonstrate the use of adapted classical phase retrieval algorithms to perform control-free quantum phase estimation. We eliminate the costly controlled time evolution and Hadamard test commonly required to access the…
X-ray phase contrast tomography (XPCT) is widely used for 3D imaging of objects with weak contrast in X-ray absorption index but strong contrast in refractive index decrement. To reconstruct an object imaged using XPCT, phase retrieval…
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…
We use differentiable programming and gradient descent to find unitary matrices that can be used in the period finding algorithm to extract period information from the state of a quantum computer post application of the oracle. The standard…
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…
Phase retrieval deals with the estimation of complex-valued signals solely from the magnitudes of linear measurements. While there has been a recent explosion in the development of phase retrieval algorithms, the lack of a common interface…
We study efficient generations of random diagonal-unitary matrices, an ensemble of unitary matrices diagonal in a given basis with randomly distributed phases for their eigenvalues. Despite the simple algebraic structure, they cannot be…
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…
The classical problem of phase retrieval has found a wide array of applications in optics, imaging and signal processing. In this paper, we consider the phase retrieval problem in a one-bit setting, where the signals are sampled using…
This work introduces a novel Fourier phase retrieval model, called polarimetric phase retrieval that enables a systematic use of polarization information in Fourier phase retrieval problems. We provide a complete characterization of…