Related papers: Designing and using prior knowledge for phase retr…
Fourier phase retrieval is the problem of reconstructing a signal given only the magnitude of its Fourier transformation. Optimization-based approaches, like the well-established Gerchberg-Saxton or the hybrid input output algorithm,…
The generalized phase retrieval problem over compact groups aims to recover a set of matrices -- representing an unknown signal -- from their associated Gram matrices. This framework generalizes the classical phase retrieval problem, which…
A novel phase retrieval algorithm for broadband hyperspectral phase imaging from noisy intensity observations is proposed. It utilizes advantages of the Fourier Transform spectroscopy in the self-referencing optical setup and provides,…
One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the…
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…
Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches…
Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…
Consider a scenario in which an unknown signal is transformed by a known linear operator, and then the pointwise absolute value of the unknown output function is reported. This scenario appears in several applications, and the goal is to…
If the phase retrieval problem can be solved by a method similar to that of solving a system of linear equations under the context of FFT, the time complexity of computer based phase retrieval algorithm would be reduced. Here I present such…
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,…
We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature…
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 to recover the phase information of a signal from the…
The recovery of a signal from the magnitude of its Fourier transform, also known as phase retrieval, is of fundamental importance in many scientific fields. It is well known that due to the loss of Fourier phase the problem in 1D is…
Phase retrieval refers to recovering a signal from its Fourier magnitude. This problem arises naturally in many scientific applications, such as ultra-short laser pulse characterization and diffraction imaging. Unfortunately, phase…
This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations…
This paper considers the problem of recovering a $k$-sparse, $N$-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very…
The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless…
A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…
The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics and,…
Signal inpainting is the task of restoring degraded or missing samples in a signal. In this paper we address signal inpainting when Fourier magnitudes are observed. We propose a mathematical formulation of the problem that highlights its…