Phaseless reconstruction from space–time samples
Author ORCID Identifier
Ilya Krishtal:https://orcid.org/0000-0001-7171-2177
Publication Title
Applied and Computational Harmonic Analysis
ISSN
10635203
E-ISSN
43831
Document Type
Article
Abstract
Phaseless reconstruction from space–time samples is a nonlinear problem of recovering a function x in a Hilbert space H from the modulus of linear measurements {|〈x,ϕi〉|, …, |〈ALix,ϕi〉|:i∈I}, where {ϕi;i∈I}⊂H is a set of functionals on H, and A is a bounded operator on H that acts as an evolution operator. In this paper, we provide various sufficient or necessary conditions for solving this problem, which has connections to X-ray crystallography, the scattering transform, and deep learning.
First Page
395
Last Page
414
Publication Date
1-1-2020
DOI
10.1016/j.acha.2018.06.002
Keywords
Frames, Müntz–Szász Theorem, Reconstruction, Sampling theory, Sub-sampling
Recommended Citation
Aldroubi, A.; Krishtal, Ilya; and Tang, S., "Phaseless reconstruction from space–time samples" (2020). NIU Bibliography. 492.
https://huskiecommons.lib.niu.edu/niubib/492
Department
Department of Mathematical Sciences
