Related papers: On the Injectivity of STFT Phase Retrieval with su…
In this paper, we analyze the non-convex framework of Wirtinger Flow (WF) for phase retrieval and identify a novel sufficient condition for universal exact recovery through the lens of low rank matrix recovery theory. Via a perspective in…
Motivated by the X-ray crystallography technology to determine the atomic structure of biological molecules, we study the crystallographic phase retrieval problem, arguably the leading and hardest phase retrieval setup. This problem entails…
We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…
A phase retrieval technique using a spatial light modulator (SLM) and a phase diffuser for a fast reconstruction of smooth wave fronts is demonstrated experimentally. Diffuse illumination of a smooth test object with the aid of a phase…
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…
In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts the recovery of the phase information of a signal from…
We consider the well-studied Sparse Fourier transform problem, where one aims to quickly recover an approximately Fourier $k$-sparse vector $\widehat{x} \in \mathbb{C}^{n^d}$ from observing its time domain representation $x$. In the exact…
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…
We present a new approach for constructing optical phase-space-time-frequency tomography (OPSTFT) of an optical wave field. This tomography can be measured by using a novel four-window optical imaging system based on two local oscillator…
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…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
In this paper, we propose a differentiable version of the short-time Fourier transform (STFT) that allows for gradient-based optimization of the hop length or the frame temporal position by making these parameters continuous. Our approach…
Phase-retrieval techniques aim to recover the original signal from just the modulus of its Fourier transform, which is usually much easier to measure than its phase, but the standard iterative techniques tend to fail if only part of the…
Recovering a signal up to a unimodular constant from the magnitudes of linear measurements has been popular and well studied in recent years. However, numerous unsolved problems regarding phase retrieval still exist. Given a phase retrieval…
The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can…
Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by…
Sampled Gabor phase retrieval - the problem of recovering a square-integrable signal from the magnitude of its Gabor transform sampled on a lattice - is a fundamental problem in signal processing, with important applications in areas such…
We develop an alternative approach to the study of Fourier series, based on the Short-Time-Fourier Transform (STFT) acting on $L_{\nu }^{2}(0,1)$, the space of measurable functions $f$ in ${R}$, square-integrable in $ (0,1)$, and…
The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those used in practice. Designing flexible stationary covariance…
Sampling theory in fractional Fourier Transform (FrFT) domain has been studied extensively in the last decades. This interest stems from the ability of the FrFT to generalize the traditional Fourier Transform, broadening the traditional…