Title :
On the least squares signal approximation model for overdecimated rational nonuniform filter banks and applications
Author :
Tkacenko, Andre ; Vaidyanathan, P.P.
Author_Institution :
Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA
Abstract :
With the advent of wavelets for lossy data compression came the notion of representing signals in a certain vector space by their projections in well chosen subspaces of the original space. In this paper, we consider the subspace of signals generated by an overdecimated rational nonuniform filter bank and find the optimal conditions under which the mean-squared error between a given deterministic signal and its representation in this subspace is minimized for a fixed set of synthesis filters. Under these optimal conditions, it is shown that choosing the synthesis filters to further minimize this error is simply an energy compaction problem. With this, we introduce the notion of deterministic energy compaction filters for classes of signals. Simulation results are presented showing the merit of our proposed method for optimizing the synthesis filters.
Keywords :
channel bank filters; data compression; filtering theory; least squares approximations; mean square error methods; optimisation; wavelet transforms; deterministic signal; least squares signal approximation; lossy data compression; mean-squared error; overdecimated rational nonuniform filter banks; synthesis filters; Channel bank filters; Compaction; Data compression; Filter bank; Least squares approximation; Least squares methods; Signal generators; Signal processing; Signal synthesis; Space technology;
Conference_Titel :
Multimedia and Expo, 2003. ICME '03. Proceedings. 2003 International Conference on
Print_ISBN :
0-7803-7965-9
DOI :
10.1109/ICME.2003.1221053
