Related papers: Uniqueness of phase retrieval from offset linear c…
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 a variant of the phase retrieval problem, where vectors are replaced by unitary matrices, i.e., the unknown signal is a unitary matrix U, and the measurements consist of squared inner products |Tr(C*U)|^2 with unitary matrices C…
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…
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,…
Generalized analytic signal associated with the linear canonical transform (LCT) was proposed recently by Fu and Li ["Generalized Analytic Signal Associated With Linear Canonical Transform," Opt. Commun., vol. 281, pp. 1468-1472, 2008].…
This work undertakes a twofold investigation. In the first part, we examine the inequalities and uncertainty principles in the framework of offset linear canonical transform (OLCT), with particular attention to its scaling and shifting…
Retrieving a signal from its triple correlation spectrum, also called bispectrum, arises in a wide range of signal processing problems. Conventional methods do not provide an accurate inversion of bispectrum to the underlying signal. In…
The identification of sampling sets that enable unique signal recovery is fundamental to many applications in signal processing and remains a central problem in mathematical analysis. Recent studies in the mathematical literature,…
Transmission optical coherence tomography (OCT) enables analysis of biological specimens in vitro through detection of forward scattered light. Up to now, transmission OCT was considered as a technique that cannot directly retrieve…
We give a large class of examples of non-uniqueness for the phase retrieval problem in multidimensions. Our constructions are based on "oblique tensorization", where one-dimensional results are strongly used, and its generalizations towards…
Exact reconstruction of an image from measurements of its Discrete Fourier Transform (DFT) typically requires all DFT coefficients to be available. However, incorporating the prior assumption that the image contains only integer values…
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…
Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…
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 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…
We study the problem of recovering a signal from magnitudes of its wavelet frame coefficients when the analyzing wavelet is real-valued. We show that every real-valued signal can be uniquely recovered, up to global sign, from its…
The main aim of this paper is to study quaternion phase retrieval (QPR), i.e., the recovery of quaternion signal from the magnitude of quaternion linear measurements. We show that all $d$-dimensional quaternion signals can be reconstructed…
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…
While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…