TY - GEN
T1 - New operators for fixed-point theory
T2 - 2013 21st European Signal Processing Conference, EUSIPCO 2013
AU - Slavakis, Konstantinos
AU - Kopsinis, Yannis
AU - Theodoridis, Sergios
PY - 2013/1/1
Y1 - 2013/1/1
N2 - The present paper offers a link between fixed point theory and thresholding; one of the key enablers in sparsity-promoting algorithms, associated mostly with non-convex penalizing functions. A novel family of operators, the partially quasi-nonexpansive mappings, is introduced to provide the necessary theoretical foundations. Based on such fixed point theoretical ground, and motivated by hard thresholding, the generalized thresholding (GT) mapping is proposed that encompasses hard, soft, as well as recent advances of thresholding rules. GT is incorporated into an online/time-adaptive algorithm of linear complexity that demonstrates competitive performance with respect to computationally thirstier, state-of-the-art, RLS- and proportionate-type sparsity-aware methods.
AB - The present paper offers a link between fixed point theory and thresholding; one of the key enablers in sparsity-promoting algorithms, associated mostly with non-convex penalizing functions. A novel family of operators, the partially quasi-nonexpansive mappings, is introduced to provide the necessary theoretical foundations. Based on such fixed point theoretical ground, and motivated by hard thresholding, the generalized thresholding (GT) mapping is proposed that encompasses hard, soft, as well as recent advances of thresholding rules. GT is incorporated into an online/time-adaptive algorithm of linear complexity that demonstrates competitive performance with respect to computationally thirstier, state-of-the-art, RLS- and proportionate-type sparsity-aware methods.
KW - Thresholding
KW - adaptive filtering
KW - fixed point theory
KW - sparsity
UR - http://www.scopus.com/inward/record.url?scp=84901358887&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84901358887&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84901358887
SN - 9780992862602
T3 - European Signal Processing Conference
BT - 2013 Proceedings of the 21st European Signal Processing Conference, EUSIPCO 2013
PB - European Signal Processing Conference, EUSIPCO
Y2 - 9 September 2013 through 13 September 2013
ER -