Related papers: On the Phase Retrievable Sequences
In this paper, we develop a novel phase retrieval approach to reconstruct x-ray differential phase shift induced by an object. A primary advantage of our approach is a higher-order accuracy over that with the conventional linear…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
The conjugate phase retrieval problem concerns the determination of a complex-valued function, up to a unimodular constant and conjugation, from its magnitude observations. It can also be considered as a conjugate phaseless sampling and…
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…
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…
Loosely speaking, a semi-frame is a generalized frame for which one of the frame bounds is absent. More precisely, given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower)…
It was recently shown that the phase retrieval imaging of a sample can be modeled as a simple convolution process. Sometimes, such a convolution depends on physical parameters of the sample which are difficult to estimate a priori. In this…
We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that…
Frames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded…
Phase retrievability of a quantum channel asks whether pure states can be reconstructed from suitable measurements. In this paper, we study this problem from three complementary viewpoints: quantum information theory, operator-valued…
Phase retrieval is an inverse problem that, on one hand, is crucial in many applications across imaging and physics, and, on the other hand, leads to deep research questions in theoretical signal processing and applied harmonic analysis.…
In this paper, structural properties of lower semi-frames in separable Hilbert spaces are explored with a focus on transformations under linear operators (may be unbounded). Also, the direct sum of lower semi-frames, providing necessary and…
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,…
This paper studies phase and norm retrieval by subspaces. We first investigate norm retrieval by hyperplanes. We show that if $N$ hyperplanes $\{\varphi_i^\perp\}_{i=1}^N\subset \mathbb{R}^N$ allow norm retrieval and the vectors…
A standardized phase retrieval algorithm is presented and applied to an industry-grade high-energy ultrashort pulsed laser to uncover its spatial phase distribution. We describe in detail how to modify the well-known algorithm in order to…
The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science. Fourier phase retrieval poses fundamental theoretical and…
The main objective of this paper is to find algorithms accompanied by explicit error bounds for phase retrieval from noisy magnitudes of frame coefficients when the underlying frame has a low redundancy. We achieve these goals with frames…
The problem of phase retrieval has been intriguing researchers for decades due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phase-less measurements.…
Let $H$ be a reflexive, dense, separable, infinite dimensional complex Hilbert space and let $B(H)$ be the algebra of all bounded linear operators on $H$. In this paper, we carry out characterizations of norm-attainable operators in normed…
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…