| The multiwavelet concept, that is considered in this thesis, uses two scaling functions and two wavelet functions to generate a multichannel multiresolution pyramid decomposition for finite energy signals. The scaling functions are used to extract the lowpass information of the input data and the wavelets to extract the highpass information. When the lowpass filters associated with the scaling functions are cascaded, a multiresolution pyramid decomposition/reconstruction system is formed with each convolution operator having two inputs and two outputs. However, there is only one dataset available to initialize this process. This thesis addresses the question of how to best modify the dataset using different FIR filters so that the decomposition of the dataset contains the most useful information for the given problem. The "best" filters are determined by the minimization of the energy of preselected decomposition component outputs. The resulting decomposition is therefore signal adaptive and, under appropriate conditions, orthogonal with perfect reconstruction. Implementations of this adaptive decomposition scheme are given for both one and two dimensional datasets. Performance comparisons are made among several different multiwavelet optimization methods and traditional wavelet methods. |
