With the development of the theory of wavelet transform, biorthogonal wavelet filter banks with linear phase and compact support characteristics are widely used in signal and image processing. We study the multiscale edge detection using anti-symmetrical biorthogonal wavelet filter banks with the same even length based on the analysis of the properties of this wavelet filter banks. The steps of...

The selection of filter bank in wavelet compression is crucial, affecting image quality and system design. Recently, the biorthogonal coiflet (cooklet) family of wavelet filters has been constructed [2] [4], and explicit frequency domain formulae have been developed [2] in the Bernstein polynomial basis. In this paper we use the Bernstein basis for frequency domain design and construction of bi...

A new approach to the multiresolution time-domain (MRTD) algorithm is presented in this paper by introducing a field expansion in terms of biorthogonal scaling and wavelet functions. Particular focus is placed on the Cohen–Daubechies–Feauveau (CDF) biorthogonal-wavelet class, although the methodology is appropriate for general biorthogonal wavelets. The computational efficiency and numerical di...

In this paper we study the algebraic and geometric structure of the space of compactly supported biorthogonal wavelets. We prove that any biorthogonal wavelet matrix pair (which consists of the scaling lters and wavelet lters) can be factored as the product of primitive parau-nitary matrices, a pseudo identity matrix pair, an invertible matrix, and the canonical Haar matrix. Compared with the f...

Biorthogonal wavelet transform has been widely used in the fields of image denoising and image coding. It is usually realized by linear phase filters. All phase digital filter is a new type of linear phase digital filter which has been proposed in recent years and has frequency structure. On the basis of analyzing principle of biorthogonal wavelet transform and discrete cosine sequency filter (...

In this paper, we introduce the notion of biorthogonal wavelet packets associated with nonuniform multiresoltion analysis and study their characteristics by means of Fourier transform. Three biorthogonal formulas regarding these wavelet packets are established. Moreover, it is shown how to obtain several new Riesz bases of the space (R) by constructing a series of subspaces of these nonuniform ...

We construct oblique multi-wavelets bases which encompass the orthogonal multi-wavelets and the biorthogonal uni-wavelets of Cohen, Deaubechies and Feauveau. These oblique multi-wavelets preserve the advantages of orthogonal and biorthogonal wavelets and enhance the flexibility of wavelet theory to accommodate a wider variety of wavelet shapes and properties. Moreover, oblique multi-wavelets ca...

We show how it is possible to diagonalize a certain class of homogeneous linear operators in a biorthogonal wavelet basis. Given a linear operator and a biorthogonal wavelet basis we construct a new biorthog-onal wavelet basis such that by analyzing a function in the new basis and multiplying the wavelet coeecients by a scale dependent factor we get the wavelet coeecients of the transformed fun...

This work presents a framework for wavelet-based representation of a given deterministic signal. We propose a method for matched wavelet based representation of the signal. Our method requires a signalconditioning step at each stage of the wavelet decomposition. The wavelet system designed in this work is biorthogonal. Both the signal-conditioning step and the wavelet system depend on the given...

Efficient image watermarking techniques have been developed in the wavelet domain. Similar to other wavelet-based image processing, the choice of wavelet filters generally affects the performance of a wavelet-based watermarking system. In this paper, we evaluate the performance of a set of biorthogonal integer wavelets under a multiresolution-watermarking framework. Biorthogonal integer wavelet...