Related papers: Phase Retrieval Problem. Application to VLBI Mappi…
We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…
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…
Many important techniques for investigating the properties of extragalactic radio sources, such as spectral-index and rotation-measure mapping, involve the comparison of images at two or more frequencies. In the case of radio…
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…
Recovering images from optical interferometric observations is one of the major challenges in the field. Unlike the case of observations at radio wavelengths, in the optical the atmospheric turbulence changes the phases on a very short time…
Fraunhofer diffraction is a well-known phenomenon achieved with most wavelength even without lens. A single-shot intensity measurement of diffraction is generally considered inadequate to reconstruct the original light field, because the…
Very long baseline interferometry (VLBI) is a technique for imaging celestial radio emissions by simultaneously observing a source from telescopes distributed across Earth. The challenges in reconstructing images from fine angular…
One of the aims of next generation optical interferometric instrumentation is to be able to make use of information contained in the visibility phase to construct high dynamic range images. Radio and optical interferometry are at the two…
In this paper we tackle the problem of recovering the phase of complex linear measurements when only magnitude information is available and we control the input. We are motivated by the recent development of dedicated optics-based hardware…
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 introduce a generalized version of phase retrieval called multiplexed phase retrieval. We want to recover the phase of amplitude-only measurements from linear combinations of them. This corresponds to the case in which multiple…
Phase retrieval in inline holography is a fundamental yet ill-posed inverse problem due to the nonlinear coupling between amplitude and phase in coherent imaging. We present a novel off-the-shelf solution that leverages a diffusion model…
We present simulated images of Supernova 1993J at 8.4 GHz using Very Long Baseline Interferometry (VLBI) techniques. A spherically symmetric source model is convolved with realistic uv-plane distributions, together with standard imaging…
In this paper we prove two results regarding reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem"). First we show that phase retrievability as an algebraic property implies that nonlinear maps are…
Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and a single real parameter $\beta$. For the standard application in optics, where the two projections…
Differential phase observations with a near-IR interferometer offer a way to obtain spectra of extrasolar planets. The method makes use of the wavelength dependence of the interferometer phase of the planet/star system, which depends both…
The 2D phase unwrapping problem seeks to recover a phase image from its observation modulo 2$\pi$, and is a crucial step in a variety of imaging applications. In particular, it is one of the most time-consuming steps in the interferometric…
Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random,…
Traditional phase-shifting interferometry technique cannot be used to measure time-varying phase distributions. But single shot techniques could resolve the problem. Many efforts have been made on the phase retrieval methods from a single…
We consider the problem of reconstructing a function $f\in L^2(\mathbb{R})$ given phase-less samples of its Gabor transform, which is defined by $$\mathcal{G} f(x,\omega) := 2^{\frac14} \int_{\mathbb{R}} f(t) e^{-\pi (t-x)^2} e^{-2\pi i y…