Related papers: Phase retrieval for wide-band signals
Graph signal processing extends spectral analysis to data supported on irregular domains. Existing fractional transforms for two-dimensional graph signals, including the two-dimensional graph fractional Fourier transform (GFRFT), typically…
Phase retrieval, i.e. the reconstruction of phase information from intensity information, is a central problem in many optical systems. Here, we demonstrate that a deep residual neural net is able to quickly and accurately perform this task…
Phase retrieval is the numerical procedure of recovering a complex-valued signal from knowledge about its amplitude and some additional information. Here, an indirect registration procedure, based on the large deformation diffeomorphic…
We consider the channel acquisition problem for a wideband terahertz (THz) communication system, where an extremely large-scale array is deployed to mitigate severe path attenuation. In channel modeling, we account for both the near-field…
Suppose we wish to recover a signal x in C^n from m intensity measurements of the form |<x,z_i>|^2, i = 1, 2,..., m; that is, from data in which phase information is missing. We prove that if the vectors z_i are sampled independently and…
We study the inverse problem of recovery a compactly supported non-linearity in the semilinear wave equation $u_{tt}-\Delta u+ \alpha(x) |u|^2u=0$, in two and three dimensions. We probe the medium with complex-valued harmonic waves of…
The problem of recovering a signal from its Fourier magnitude is of paramount importance in various fields of engineering and applied physics. Due to the absence of Fourier phase information, some form of additional information is required…
We prove weighted $L^2$ and refined $L^p$ decoupling estimates for functions whose Fourier transforms are supported in a small neighborhood of the unit sphere or the truncated paraboloid with an additional lower-dimensional frequency…
Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from…
We develop procedures, based on minimization of the composition $f(x) = h(c(x))$ of a convex function $h$ and smooth function $c$, for solving random collections of quadratic equalities, applying our methodology to phase retrieval problems.…
Time-frequency analysis, such as the Gabor transform, plays an important role in many signal processing applications. The redundancy of such representations is often directly related to the computational load of any algorithm operating in…
Continuous wavefront sensing benefits space observatories in on-orbit optical performance maintenance. To measure the phase of a wavefront, phase retrieval is an attractive technique as it uses multiple point spread function (PSF) images…
We revisit the classical problem of Fourier-sparse signal reconstruction -- a variant of the \emph{Set Query} problem -- which asks to efficiently reconstruct (a subset of) a $d$-dimensional Fourier-sparse signal ($\|\hat{x}(t)\|_0 \leq…
The problem of signal recovery from its Fourier transform magnitude is of paramount importance in various fields of engineering and has been around for over 100 years. Due to the absence of phase information, some form of additional…
In this paper, we present an assortment of both standard and advanced Fourier techniques that are useful in the analysis of astrophysical time series of very long duration -- where the observation time is much greater than the time…
Phase retrieval (PR) concerns the recovery of complex phases from complex magnitudes. We identify the connection between the difficulty level and the number and variety of symmetries in PR problems. We focus on the most difficult far-field…
Polarized synchrotron emission from multiple Faraday depths can be separated by calculating the complex Fourier transform of the Stokes' parameters as a function of the wavelength squared, known as Faraday Synthesis. As commonly…
Recovering a sparse signal from its low-pass projections in the Fourier domain is a problem of broad interest in science and engineering and is commonly referred to as super-resolution. In many cases, however, Fourier domain may not be the…
Phase retrieval is the nonlinear inverse problem of recovering a true signal from its Fourier magnitude measurements. It arises in many applications such as astronomical imaging, X-Ray crystallography, microscopy, and more. The problem is…
In this paper, we present a new algorithm, called MagnitudeCut, for recovering a signal from the phase of its Fourier transform. We casted our recovering problem into a new convex optimization problem, and then solved it by the block…