Construction and application of hybrid wavelet and other parametric orthogonal transforms

We introduce new methods for construction and implementation of various parametric and hybrid orthogonal transforms, including generalized Haar-like, Daubechies, and Coiflet wavelet transforms. The corresponding fast algorithms of computations are briefly discussed and the variance properties of these transforms in analyzing 1-st order Markov processes are investigated. The designed hybrid transforms can be useful in various specific signal processing applications where combining properties of Hadamard and wavelet transforms may be of particular benefit. We also present some numerical results pertaining to image zonal and threshold coding using these hybrid transforms and compare their efficacy with those of traditional orthogonal transforms.