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Average sampling and reconstruction in a reproducing kernel subspace of homogeneous type space
Author(s) -
Xian Jun
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200203
Subject(s) - mathematics , subspace topology , kernel (algebra) , projection (relational algebra) , variable kernel density estimation , kernel method , linear subspace , convergence (economics) , kernel principal component analysis , homogeneous , space (punctuation) , sampling (signal processing) , kernel embedding of distributions , type (biology) , algorithm , mathematical analysis , artificial intelligence , combinatorics , pure mathematics , computer science , computer vision , support vector machine , filter (signal processing) , economics , economic growth , ecology , biology , operating system
In this paper, we first introduce a reproducing kernel subspace ofL p ( X , ρ , μ ) , where ( X , ρ , μ ) is a homogeneous type space. Then we consider average sampling and reconstruction of signals in the reproducing kernel subspace ofL p ( X , ρ , μ ) , 1 ≤ p ≤ ∞ . We show that signals in the reproducing kernel subspace ofL p ( X , ρ , μ )could be stably reconstructed from its average samples taken on a relatively‐separated set with small gap. Exponential convergence is established for the iterative approximation‐projection reconstruction algorithm.