Optimization in the construction of cardinal and symmetric wavelets on the line

We present an optimization approach to wavelet architecture that hinges on the Zak transform to formulate the construction as a minimization problem. The transform warrants parametrization of the quadrature mirror filter in terms of the possible integer sample values of the scaling function and the associated wavelet. The parameters are predicated to satisfy constraints derived from the conditions of regularity, compact support and orthonormality. This approach allows for the construction of nearly cardinal scaling functions when an objective function that measures deviation from cardinality is minimized. A similar objective function based on a measure of symmetry is also proposed to facilitate the construction of nearly symmetric scaling functions on the line.

Multi-Rate Filter Banks

This chapter presents the theoretical description and the principle of the operation of analysis and synthesis filter banks. This is essential material for understanding the modern design of transceivers that are based on discrete-time signal processing. The structure of a quadrature mirror filter bank is presented and the operation of the analysis and synthesis component filters is explained. The condition for a perfect reconstruction of a two-channel filter bank is derived. Based on a two-channel quadrature mirror filter bank, the procedure of making a multichannel quadrature mirror filter bank is presented. A brief description of multilevel filter banks with equal or unequal passband widths is given.

POTENTIALITY OF USING DIGITAL WAVELET/QMF PYRAMIDS IN REMOTELY SENSED SATELLITES’ IMAGES CLASSIFICATION

Wavelet or quadrature mirror filter (QMF) satellites’ images are not commonly used in classification because of the modification in spectral responses that may confuse any classifier. Boundary pixels are hardly classified correctly in pixel-based classification especially in medium and coarse resolution. In such case, the sudden change in landcover is not measurable by the classifiers because the pixel may contain mor than one class. This research work is a trial to investigate the proper enhancement in accuracy that may occur by using wavelet/QMF bands’ pyramids are in classification instead of the original image bands. The reference map is prepared traditionally to measure the performance of the new system. The Wavelet/QMF image is constructed for each band of the satellite image. Then the classification is carried out for both the Wavelet/QMF image pyramid and the original satellite image using competitive learning neural networks (CLNN) method. The evaluation is carried out by comparing the classified Wavelet/QMF image with the classified original image. A statistical test is carried out to study the significance of using the classified Wavelet/ QMF image in classification.