Open AccessOn the Building Blocks of Sparsity Measures
Author(s) -
Arian Eamaz,
Farhang Yeganegi,
Mojtaba Soltanalian
Publication year - 2022
Publication title -
ieee signal processing letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.815
H-Index - 138
eISSN - 1558-2361
pISSN - 1070-9908
DOI - 10.1109/lsp.2022.3233000
Subject(s) - signal processing and analysis , computing and processing , communication, networking and broadcast technologies
Understanding the mathematics and the innate machinery of sparsity measures is instrumental in the proper usage of such information measures in various application arenas, ranging from information collection and sensing, to communications and signal processing. In this letter, the structure of sparsity measures is investigated. Specifically, it is shown that sparsity measures satisfying proper sparsity axioms may only be constructed by vector norms. Moreover, the asymptotic behavior of sparsity measures is studied. Owing to their mathematical structure, our numerical results illustrate a convergence of sparsity measures, as the number of input samples grows large.