We study wavelet packets in the setting of a multiresolution analysis of L2(Rd) generated by an arbitrary dilation matrix A satisfying |det A| = 2. In particular, we consider the wavelet packets associated with a multiresolution analysis with a scaling function given by the characteristic function of some set (called a tile) in Rd. The functions in this class of wavelet packets are called gener...

{ It has been demonstrated that wavelets compete well against DCT based image compression techniques 1]. However the advantages of nonseparable wavelet transforms for image and video coding have not yet been adequately explored. In this paper we discuss nonseparable wavelet transforms on the quincunx lattice and show that they have certain properties which make them an attractive choice for ima...

We construct orthonormal wavelet bases of L2(IR) with compact support for dilation matrices of determinant 2. The key idea is to describe the set H2 of all two-dimensional (2D) scaling coefficients satisfying the orthogonality condition as an implicit function. This set includes the scaling coefficients for induced 1D wavelets. We compute the tangent space of H2 at HN , the scaling coefficients...

We construct smooth nonseparable compactly supported refinable functions that generate multiresolution analyses on L2(R), d > 1. Using these refinable functions we construct smooth nonseparable compactly supported orthonormal wavelet systems. These systems are nonseparable, in the sense that none of its constituent functions can be expressed as the product of two functions defined on lower dime...

In this paper, we present the realization of an adaptive shift invariant wavelet transform defined on the quincunx grid. The wavelet transform relies on the lifting scheme which enables us to easily introduce the adaptation by splitting the predict stage into two parts. The first part of the predict stage is fixed and guarantees the number of vanishing moments of the wavelet filter bank while t...

The Paper Adaptive Nonseparable Wavelet Transform via Lifting and its Application to Content-Based Image Retrieval. Adapt a multidimensional wavelet filter bank, based on the nonseparable lifting scheme framework. The lifting scheme there are two linear filter denoted P (prediction) and U ( update) are defined as Neville filters of order N and N ~ , respectively. We are applying the Haar wavele...

This paper presents a new approach to face recognition by using a nonseparable bivariate wavelets. A new nonseparable bivariate wavelet filter banks with linear phase are constructed from the centrally symmetric matrices. Our investigations demonstrate that these filter banks have a matrix factorization and they are capable of describing the features of face image. The implementations of our al...

Tensor product (separable) multivariate (bi)orthogonal wavelets have been widely used in many applications. On the other hand, non-tensor product (nonseparable) wavelets have been extensively argued in the literature to have many advantages over separable wavelets, for example, more freedom in design of nonseparable wavelets (such design is typically much more complicated and di±cult than the a...

For nonseparable bidimensional wavelet transforms, the choice of the dilation matrix is all–important, since it governs the downsampling and upsampling steps, determines the cosets that give the positions of the filters, and defines the elementary set that gives a tesselation of the plane. We introduce nonseparable bidimensional wavelets, and give formulae for the analysis and synthesis of imag...

We demonstrate that many multivariate wavelets are projectable wavelets; that is, they essentially carry the tensor product (separable) structure though themselves may be non-tensor product (nonseparable) wavelets. We show that a projectable wavelet can be replaced by a tensor product wavelet without loss of desirable properties such as spatial localization, smoothness and vanishing moments.