Compactly supported wavelet bases for Sobolev spaces is investigated. Steming from a pair of compactly supported refinale functions with multiscale dilation factor in space 2 3 ( ) L R meeting a very mild condition, we provide a general approach for constructing wavelet bases, which is the generalization of univariate wavelets in Hilbert space. The notion of orthogonal non-tensor product trivar...

Orthogonal, semiorthogonal and biorthogonal wavelet bases are special cases of oblique multiwavelet bases. One of the advantage of oblique multiwavelets is the flexibility they provide for constructing bases with certain desired shapes and/or properties. The decomposition of a signal in terms of oblique wavelet bases is still a perfect reconstruction filter bank. In this paper, we present sever...

Wavelet analysis has become a developing branch of mathematics for over twenty years. In this paper, the notion of orthogonal nonseparable bivariate wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is proposed by virtue of analogy method and iteration method. Their biorthogonality traits are researched by using time-frequency analysis approach and variable sepa...

Wavelet analysis has become a developing branch of mathematics for over twenty years. In this paper, the notion of orthogonal nonseparable bivariate wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is proposed by virtue of analogy method and iteration method. Their biorthogonality traits are researched by using time-frequency analysis approach and variable sepa...

In this paper, formulas relating the Radon transform and Radon transform inversion to various wavelet and multiscale transformations, including the continuous wavelet transform, the semi{continuous wavelet transform of Mallat, steerable multiscale lters of Freeman and Adelson, and separable orthogonal and non{orthogonal wavelet bases, are given. The use of wavelets as a valuable tool in the loc...

We introduce and study a fast implementation of Orthogonal Greedy Algorithm for wavelet frames. The results of numerical simulation for N -term approximations of standard images by tight wavelet frames showed that to provide the same PSNR the popular 9/7 biorthogonal wavelet bases require 30%–40% more terms of the expansion. This is equivalent to 2–4 dB advantage of the wavelet frames in PSNR o...

Orthogonal wavelet bases have recently been developed using multiple mother wavelet functions. Applying the discrete multiple wavelet transform requires the input data to be preprocessed to obtain a more economical decomposition. We discuss the properties of several prepro-cessing methods and their eeect on the thresholding results. We propose a multivariate thresholding method for multiwavelet...

The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar bases generated by multiresolution analysis. Bases consist of three piecewise constant wavelet functions with a support $[0,1] \times [0,1] $.

In this note, we announce a general method for the construction of nonseparable orthogonal wavelet bases of L2(Rn), where n ≥ 2. Hence, we prove the existence of such type of wavelet bases for any integer n ≥ 2. Moreover, we show that this construction method can be extended to the construction of n-D multiwavelet matrix filters.