In this letter, the two wavelet families, biorthogonal and Riesz bases are introduced. Biorthogonality for two possible decompositions in these bases, The Riesz stability implies that there exist such that Biorthogonal wavelet bases are related to multiresolution approximations. The direct consequence of the above derivation is tradeoff made between the support size of a wavelet and its number ...

An adaptive watermarking algorithm is presented which exploits a biorthogonal wavelets-based human visual system (HVS) and a Fuzzy Inference System (FIS) to protect the copyright of images in learning object repositories. Specifically, the HVS relies on the linear-phase property of biorthogonal wavelet filters (symmetric wavelets) in order to efficiently extract the masking information, while t...

We present a method for constructing discriminative biorthogonal bases for classification. In the proposed method we use idea of the lifting scheme a method for constructing biorthogonal wavelets and Support Vector Machines used for building classifiers. Combining those two ideas resulted in the construction of classifiers which are based on information selected form the available data and stil...

In the last decade, Daubechies’ wavelets have been successfully used in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. In this paper, orthogonal and Biorthogona...

The proposed contribution describes a method for the detection and classification of harmonic transients, as they occur in electrical networks. The method uses, as bases, a special class of wavelet-packets, i. e. smooth biorthogonal sine and cosine-packets in order to find the best ’’Shannon-basis“. The algorithm is based on the minimization of Shannon‘s function for the decomposed wanted signa...

Wave Cluster is a grid based clustering approach. Many researchers have applied wave cluster technique for segmenting images. Wave cluster uses wave transformation for clustering the data item. Normally it uses Haar, Daubechies and Cohen Daubechies Feauveau or Reverse Bi-orthogonal wavelets. Symlet, Biorthogonal and Meyer wavelet families have been used in this paper to compare its clustering c...

A new family of multidimensional dimensional (MD) perfect reconstruction (PR) two channel filter banks with finite impulse response (FIR) filters induced from systems of biorthogonal MD scaling functions and wavelets are introduced. One of the advantages of this construction is that the biorthogonal scaling functions and wavelets are easy to establish due to the interpolatory property of the sc...