We introduce a new approach in order to construct a wavelets with arbitrary support on the interval. This result allows us to adapt on the interval some important classes of wavelets (coiflets, symlets, Lemarié's wavelets). In addition, we show how to obtain multiresolution analysis on the interval with better approximation rate in some neighborhood of the interval.

We improve Wang's characterization for a pair of biorthogonal wavelets to be associated with biorthogonal multiresolution analyses (MRA's). We show that one of the two conditions in his characterization is redundant, and, along the way, show that for a pair of biorthogonal wavelets to be associated with biorthogonal MRA's it is necessary and suÆcient that one of the wavelets is associated with ...

Abstract. We propose the application of hyperbolic interpolatory wavelets for large-scale -dimensional data fitting. In particular, we show how wavelets can be used as a highly efficient tool for multidimensional smoothing. The grid underlying these wavelets is a sparse grid. The hyperbolic interpolatory wavelet space of level uses basis functions and it is shown that under sufficient smoothnes...

Properties determining optimal behavior of continuous analytic wavelet functions are investigated, and wavelet functions nearly obtaining such behavior are identified. This is accomplished through detailed investigation of the generalized Morse wavelets, a highly flexible family of exactly analytic continuous wavelets. The degree of time/frequency localization, the existence of a unique interpr...

In this work we investigate new feature extraction algorithms on the T-ray response of normal human bone cells and human osteosarcoma cells. One of the most promising feature extraction methods is the Discrete Wavelet Transform (DWT). However, the classification accuracy is dependant on the specific wavelet base chosen. Adaptive wavelets circumvent this problem by gradually adapting to the sign...

Wavelets and multiresolution analysis are instrumental for developing ee-cient methods for representing, storing and manipulating functions at various levels of detail. Although alternative methods such as hierarchical quadtrees or pyramidal models have been used to that eeect as well, wavelets have picked up increasing popularity in recent years due to their energy compactness, ee-ciency, and ...