The stereographic projection determines a bijection between the two-sphere, minus the North Pole, and the tangent plane at the South Pole. This correspondence induces a unitary map between the corresponding L2 spaces. This map in turn leads to equivalence between the continuous wavelet transform formalisms on the plane and on the sphere. More precisely, any plane wavelet may be lifted, by inver...

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...

Compression of speech from the TIMIT corpus was investigated for several transform domain methods coding near-best and best bases from cosine and wavelet packet transforms. Satisficing (suboptimizing) search algorithms for selecting near-best bases were compared with optimizing algorithms for best bases in these adaptive tree-structured transforms. Experiments were performed on several hundred ...

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...

Wavelet thresholding is a powerful tool for denoising images and other signals with sharp discontinuities. Using different wavelet bases gives different results, and since the wavelet transform is not time-invariant, thresholding various shifts of the signal is one way to use different wavelet bases. This paper describes several denoising methods that apply wavelet thresholding or variations on...

In this paper, we propose a new M-channel wavelet bases called the cosine-modulated wavelets. We first generalize the theory of two-channel biorthogonal compactly supported wavelet bases to the M-channel case. A sufficient condition for the M-channel perfect reconstruction filter banks to construct M-channel compactly supported wavelet bases is given. By using this condition, a family of orthog...

This paper is concerned with the construction of biorthogonal wavelet bases defined on a union of parametric images of the unit n-cube. These bases are to satisfy certain requirements imposed by applications to a class of operator equations acting on such domains. This covers also elliptic boundary value problems, although this study is primarily motivated by our previous analysis of wavelet me...

Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under fairly general conditions, exact reconstruction schemes with synthesis filters different from the analysis filters give rise: to two dual Riesz bases of compactly supported wavelets. We give necessary ...

In recent years, the wavelet-based image denoising techniques mainly focus on the case that uses a single wavelet base. In fact, different wavelet bases can often effectively represents different areas or features of an image. In this paper a new image denoising method using multiple wavelet bases is proposed. First, the noisy image is denoised by various wavelet bases and then a set of the den...

We show how a wavelet basis may be adapted to best represent natural images in terms of sparse coefficients. The wavelet basis, which may be either complete or overcomplete, is specified by a small number of spatial functions which are repeated across space and combined in a recursive fashion so as to be self-similar across scale. These functions are adapted to minimize the estimated code lengt...