The anisotropic wavelet packet transform is an extension of the conventional wavelet (packet) transform where the basis can have di erent scales in di erent dimensions. As there are certain kinds of images with di erent behaviour in horizontal and vertical direction, anisotropic wavelet packet bases can be adapted more precisely to these images. Zero-tree image compression has already proved it...

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...

The construction of wavelet bases and frames on the Vilenkin group Gp is studied. Wavelet systems consisting functions that are compactly supported band-limited at same time our interest. A complete description all refinable providing such given.

In this paper the wavelet-based image compression technique is applied to PIV processing for reducing the physical storage. To determine the effect of the choice of the wavelet bases, the standard PIV images are compressed by some known wavelet families, Daubechies, Coifman and baylkin families. It was found that high order wavelet bases provides good compression performance for compressing PIV...

Calculations based on high-resolution quantizations prove that the distortion rate D( R) of an image transform coding is proportional to 2 2 R when R is large enough. In wavelet and block cosine bases, we show that if R < 1 bit/pixel, then D( R) varies like R1 2 , where remains of the order of 1 for most natural images. The improved performance of embedded codings in wavelet bases is analyzed. ...

This paper presents an algebraic approach to construct M-band orthonormal wavelet bases with perfect reconstruction. We first derive the system of constraint equations of M-band filter banks, and then an algebraic solution based on matrix decomposition is developed. The structure of the solutions is presented, and practical construction procedures are given. By using this algebraic approach, so...

Calculations based on high-resolution quantizations prove that the distortion rate D( R) of an image transform coding is proportional to 2 2 R when R is large enough. In wavelet and block cosine bases, we show that if R < 1 bit/pixel, then D( R) varies like R1 2 , where remains of the order of 1 for most natural images. The improved performance of embedded codings in wavelet bases is analyzed. ...

Two multiresolution analyses (MRA) intended to be used in scientiic visualization, and that are both based on a non-nested set of approximating spaces, are presented. The notion of approximated reenement is introduced to deal with non nested spaces. The rst MRA scheme, referred to as BLaC (Blending of Linear and Constant) wavelets is based on a one parameter family of wavelet bases that realize...

Various results on constructing wavelets, multiwavelets and wavelet frames for periodic functions are reviewed. The orthonormal and Riesz bases as well as frames are constructed from sequences of subspaces called multiresolution analyses. These studies employ general frequency-based approaches facilitated by functions known as orthogonal splines and polyphase splines. While the focus is on the ...

This paper presents an image fusion method suitable for pan-sharpening of multispectral (MS) bands, based on nonseparable multiresolution analysis (MRA). The low-resolution MS bands are resampled to the fine scale of the panchromatic (Pan) image and sharpened by injecting highpass directional details extracted from the high-resolution Pan image by means of the curvelet transform (CT). CT is a n...