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Bicomplex signals with sparsity constraints
Author(s) -
Cerejeiras Paula,
Fu Yingxiong,
Gomes Narciso
Publication year - 2018
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.5059
Subject(s) - mathematics , idempotence , basis (linear algebra) , algebra over a field , representation (politics) , fourier transform , pure mathematics , algorithm , mathematical analysis , geometry , politics , political science , law
In this paper, we aim to prove the possibility to reconstruct a bicomplex sparse signal, with high probability, from a reduced number of bicomplex random samples. Due to the idempotent representation of the bicomplex algebra, this case is similar to the case of the standard Fourier basis, thus allowing us to adapt in a rather easy way the arguments from the recent works of Rauhut and Candés et al.