Design of block wavelet filters generating unitary transform matrices

In this thesis several methods and algorithms for wavelet filter banks which generate unitary transform matrices are developed. It is aimed to find the filter bank which gives the best compression by using Karhunen?Loéve transform matrix since Karhunen?Loéve transform is the transform coding method which gives the best coding gain for a class of signals with known correlation structures. For this purpose, some numerical and analytical methods are studied and the successes of the methods are presented with the experimental results. It is shown that the coefficients of the aimed quadrature mirror filter banks can be computed by the new lattice parameterization based method which is named as Block Wavelet Transform Inversion.