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Average sampling and reconstruction for signals in shift‐invariant subspaces of weighted mixed Lebesgue spaces
Author(s) -
Wang Suping,
Zhang Jiaxing
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7374
Subject(s) - mathematics , linear subspace , invariant (physics) , lebesgue integration , lp space , nonuniform sampling , subspace topology , sampling (signal processing) , invariant subspace , standard probability space , pure mathematics , mathematical analysis , banach space , algorithm , filter (signal processing) , quantization (signal processing) , computer science , mathematical physics , computer vision
In this paper, we mainly study the average sampling problem for signals in a shift‐invariant subspace of weighted mixed Lebesgue space. First, the sampling stability for two kinds of average sampling functionals is established. Then, two iterative reconstruction algorithms with exponential convergence are presented for recovering the shift‐invariant signals from the corresponding average samples.