ABOUT THE SYSTEMS WITH FULL SPARK


Cite item

Abstract

Frames of a finite-dimensional Euclidean and unitary spaces composed of discrete Fourier transform matrices are considered. The relationship of phaseless reconstruction systems with the alternative completeness property is presented. In the complex case, alternative completeness is only a necessary condition for phaseless reconstruction. A system of vectors is constructed such that each of its subsystems with a volume equal to the dimension of space is linearly independent. These systems are called systems with full spark. In particular, such systems are optimal for phase retrieval.

About the authors

D. A. Rogach

Samara National Research University, 34, Moskovskoye shosse, 443086, Russian
Federation.

Author for correspondence.
Email: morenov.sv@ssau.ru
ORCID iD: 0000-0001-8857-9325

third year post-graduate student of the Department of Functional Analysis and Function Theory

Russian Federation

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Copyright (c) 2020 Д. А. Рогач

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