Principal component filter banks for optimal multiresolutionanalysis

Authors:
M.K. Tsatsanis;G.B. Giannakis
Affiliations:
Dept. of Electr. Eng., Virginia Univ., Charlottesville, VA;-
Venue:
IEEE Transactions on Signal Processing
Year:
1995

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Abstract

An important issue in multiresolution analysis is that of optimal basis selection. An optimal P-band perfect reconstruction filter bank (PRFB) is derived in this paper, which minimizes the approximation error (in the mean-square sense) between the original signal and its low-resolution version. The resulting PRFB decomposes the input signal into uncorrelated, low-resolution principal components with decreasing variance. Optimality issues are further analyzed in the special case of stationary and cyclostationary processes. By exploiting the connection between discrete-time filter banks and continuous wavelets, an optimal multiresolution decomposition of L2(R) is obtained. Analogous results are also derived for deterministic signals. Some illustrative examples and simulations are presented