Related papers: One-Dimensional Phase Retrieval: Regularization, B…
Phase retrieval aims at recovering a complex-valued signal from magnitude-only measurements, which attracts much attention since it has numerous applications in many disciplines. However, phase recovery involves solving a system of…
The recovery of an unknown signal from its linear measurements is a fundamental problem spanning numerous scientific and engineering disciplines. Commonly, prior knowledge suggests that the underlying signal resides within a known algebraic…
The phase retrieval problem has a long history and is an important problem in many areas of optics. Theoretical understanding of phase retrieval is still limited and fundamental questions such as uniqueness and stability of the recovered…
Fourier phase retrieval is a classical problem of restoring a signal only from the measured magnitude of its Fourier transform. Although Fienup-type algorithms, which use prior knowledge in both spatial and Fourier domains, have been widely…
Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function.…
The classical phase retrieval problem involves estimating a signal from its Fourier magnitudes (power spectrum) by leveraging prior information about the desired signal. This paper extends the problem to compact groups, addressing the…
This paper considers the phase retrieval problem in which measurements consist of only the magnitude of several linear measurements of the unknown, e.g., spectral components of a time sequence. We develop low-complexity algorithms with…
In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction…
We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows…
In this paper, we consider the phase retrieval problem in which one aims to recover a signal from the magnitudes of affine measurements. Let $\{{\mathbf a}_j\}_{j=1}^m \subset {\mathbb H}^d$ and ${\mathbf b}=(b_1, \ldots,…
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…
We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows…
This work studies phase retrieval for wave fields, aiming to recover the phase of an incoming wave from multi-plane intensity measurements behind different types of linear and nonlinear media. We show that unique phase retrieval can be…
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…
We consider the problem of phase retrieval from magnitudes of short-time Fourier transform (STFT) measurements. It is well-known that signals are uniquely determined (up to global phase) by their STFT magnitude when the underlying window…
Real-valued Phase retrieval is a non-convex continuous inference problem, where a high-dimensional signal is to be reconstructed from a dataset of signless linear measurements. Focusing on the noiseless case, we aim to disentangle the two…
We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…
Signal recovery from nonlinear measurements involves solving an iterative optimization problem. In this paper, we present a framework to optimize the sensing parameters to improve the quality of the signal recovered by the given iterative…
The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…
In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex…