A theory of wavelet packets is developed for nonlinear operators consisting of a composition, generalizing a sigmoidal operation, followed by convolutions with filter pairs H0 and H1. The pyramidal wavelet packet structure is defined by bit reversal trees. The reconstruction theorem, from which the original signal is obtained from frequency localized data at other nodes of the three, requires fixed point theory as well as conditions on H0 and H1 resembling those defining quadrature mirror filter pairs. Applications will be to biological systems and neural networks where such nonlinearities occur
Subband coding for sigmoidal nonlinear operations
SALIANI, Sandra
1994-01-01
Abstract
A theory of wavelet packets is developed for nonlinear operators consisting of a composition, generalizing a sigmoidal operation, followed by convolutions with filter pairs H0 and H1. The pyramidal wavelet packet structure is defined by bit reversal trees. The reconstruction theorem, from which the original signal is obtained from frequency localized data at other nodes of the three, requires fixed point theory as well as conditions on H0 and H1 resembling those defining quadrature mirror filter pairs. Applications will be to biological systems and neural networks where such nonlinearities occurFile in questo prodotto:
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