New orthonormal basis of eigenfunctions for the Vladimirov operator of p–adic fractional derivation is constructed. The map of p–adic numbers onto real numbers (p–adic change of variable) is considered. p–Adic change of variable (for p = 2) provides an equivalence between the constructed basis of eigenfunctions of the Vladimirov operator and the wavelet basis in L 2 (R +) generated from the Haa...

Wavelet analysis as a p–adic spectral analysis Abstract New orthonormal basis of eigenfunctions for the Vladimirov operator of p–adic fractional derivation is constructed. The map of p–adic numbers onto real numbers (p–adic change of variable) is considered. p–Adic change of variable maps the Haar measure on p–adic numbers onto the Lebesgue measure on the positive semiline. p–Adic change of var...

The Wavelet Element Method (WEM) provides a construction of multiresolution systems and biorthogonal wavelets on fairly general domains. These are split into subdomains that are mapped to a single reference hypercube. Tensor products of scaling functions and wavelets defined on the unit interval are used on the reference domain. By introducing appropriate matching conditions across the interele...

Unlike Fourier basis which constitutes fixed sine and cosine waves; the Wavelet Transform has infinite basis functions. The choice of good basis is application dependent. Statistical parameters of the image are dynamic and differ from image to image. A moment vector of natural image will be different from the moment vector of synthetic image. Similarly the edges in natural image have structural...

To use wavelet packets for lossy data compression, the following issues must be addressed: quantization of the wavelet subbands, allocation of bits to each subband, and best-basis selection. We present an algorithm for wavelet packets that systematically identifies all bit allocations/best-basis selections on the lower convex hull of the rate-distortion curve. We demonstrate the algorithm on tr...

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...

In this paper, we revisit wavelet theory starting from the representation of a scaling function as the convolution of a B-spline (the regular part of it) and a distribution (the irregular or residual part). This formulation leads to some new insights on wavelets and makes it possible to rederive the main results of the classical theory—including some new extensions for fractional orders—in a se...

The orthonormal basis generated by a wavelet of L(R) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis of L(R) is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized...

A novel descriptor for pattern recognition is proposed by using dual-tree complex wavelet features and SVM. The approximate shiftinvariant property of the dual-tree complex wavelet and its good directional selectivity in 2D make it a very appealing choice for pattern recognition. Recently, SVM has been shown to be very successful in pattern recognition. By combining these two tools we find that...

Conventional signal processing typically involves frequency selective techniques which are highly inadequate for nonstationary signals. In this paper, we present an approach to perform time-frequency selective processing using the Wavelet Transform. The approach is motivated by the excellent localization, in both time and frequency, aaorded by the wavelet basis functions. Suitably chosen wavele...