Title :
Convex multiresolution analysis
Author :
Combettes, P.L. ; Pesquet, J.-C.
Author_Institution :
Dept. of Electr. Eng., City Univ. of New York, NY, USA
Abstract :
A standard wavelet multiresolution analysis can be defined via a sequence of projection operators onto a monotone sequence of closed vector subspaces possessing suitable invariance properties. We propose an extension of this framework in which the linear projection operators are replaced by nonlinear retractions onto convex sets. These retractions are chosen so as to provide a recursive, monotone signal approximation scheme. Numerical simulations are also provided
Keywords :
invariance; signal processing; wavelet transforms; closed vector subspaces; convex multiresolution analysis; convex sets; invariance properties; linear projection operators; monotone sequence; monotone signal approximation scheme; nonlinear retractions; numerical simulations; projection operators sequence; standard wavelet multiresolution analysis; Filtering; Multiresolution analysis; Nonlinear filters; Partial differential equations; Signal processing; Signal resolution;
Conference_Titel :
Time-Frequency and Time-Scale Analysis, 1996., Proceedings of the IEEE-SP International Symposium on
Conference_Location :
Paris
Print_ISBN :
0-7803-3512-0
DOI :
10.1109/TFSA.1996.547473
