TY - JOUR
T1 - Best bases for signal spaces
AU - Aflalo, Yonathan
AU - Brezis, Haïm
AU - Bruckstein, Alfred
AU - Kimmel, Ron
AU - Sochen, Nir
N1 - Publisher Copyright:
© 2016 Académie des sciences
PY - 2016/12/1
Y1 - 2016/12/1
N2 - We discuss the topic of selecting optimal orthonormal bases for representing classes of signals defined either through statistics or via some deterministic characterizations, or combinations of the two. In all cases, the best bases result from spectral analysis of a Hermitian matrix that summarizes the prior information we have on the signals we want to represent, achieving optimal progressive approximations. We also provide uniqueness proofs for the discrete cases.
AB - We discuss the topic of selecting optimal orthonormal bases for representing classes of signals defined either through statistics or via some deterministic characterizations, or combinations of the two. In all cases, the best bases result from spectral analysis of a Hermitian matrix that summarizes the prior information we have on the signals we want to represent, achieving optimal progressive approximations. We also provide uniqueness proofs for the discrete cases.
UR - http://www.scopus.com/inward/record.url?scp=84996598866&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2016.10.002
DO - 10.1016/j.crma.2016.10.002
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84996598866
SN - 1631-073X
VL - 354
SP - 1155
EP - 1167
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 12
ER -