Paper
3 April 1997 Invariant multiresolution analysis: theory and applications
C. W. Kok, Y. Hui, Truong Q. Nguyen
Author Affiliations +
Abstract
The characterization and construction of translation invariant multiresolution system is discussed. Multiresolution basis that provides optimal performance in approximating functions with different translation is considered. Translation variance is defined to be the variance of the energy when projecting input signal under different translation to the vector space constructed by multiresolution basis. It is proved that the translation variant property of all the multiresolution basis onto themselves is a complete representation of the translation variant property of the multiresolution system. By considering scale limited signal expansion in multiresolution analysis, optimal signal adapted multiresolution basis function is defined. The results are used to design optimal signal adapted translation invariant multiresolution basis. Simulation results on the signal adapted translation invariant multiresolution basis in detection problems are presented. The constructed system outperforms tradition multiresolution system that uses translation variant basis.
© (1997) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
C. W. Kok, Y. Hui, and Truong Q. Nguyen "Invariant multiresolution analysis: theory and applications", Proc. SPIE 3078, Wavelet Applications IV, (3 April 1997); https://doi.org/10.1117/12.271752
Advertisement
Advertisement
RIGHTS & PERMISSIONS
Get copyright permission  Get copyright permission on Copyright Marketplace
KEYWORDS
Wavelets

Signal detection

Vector spaces

Sensors

Detection theory

Electronic filtering

Signal analyzers

Back to Top