We study the multivariate approximation by certain partial sums (hyperbolic wavelet sums) of wavelet bases formed by tensor products of univariate wavelets. We characterize spaces of functions which have a prescribed approximation error by hyperbolic wavelet sums in terms of a K -functional and interpolation spaces. The results parallel those for hyperbolic trigonometric cross approximation of ...

Explicit solutions are given for the rational function P (z) for two classes of IIR orthogonal 2-band wavelet bases, for which the scaling lter is maximally at. P (z) denotes the rational transfer function H(z)H(1=z) where H(z) is the (lowpass) scaling lter. The rst is the class of solutions that are intermediate , between the Daubechies and the Butterworth wavelets. It is found that the Daubec...

Explicit solutions are given for the rational function P (z) for two classes of IIR orthogonal two-band wavelet bases, for which the scaling filter is maximally flat. P (z) denotes the rational transfer function H(z)H(1=z), where H(z) is the (lowpass) scaling filter. The first is the class of solutions that are intermediate between the Daubechies and the Butterworth wavelets. It is found that t...

Two elementary algorithms are introduced for image compression each of which is based on efficient, lossless encoding of quantized bi-orthogonal wavelet coefficients. Application of this type of algorithm is applied to several standard test images using regular and hyperbolic wavelet bases, and comparisons are given to Shapiro’s EZW algorithm. Peak signal to noise ratio improvements typically o...

In this study wavelet based high-order Taylor Galerkin methods is introduced. Additional time layers are used to obtain high-order temporal accuracy unattainable within a two-step strategy. Two explicit model schemes are constructed and asymptotic stability of schemes are verified. The compactly supported orthogonal wavelet bases developed by Daubechies are used in Galerkin scheme. The behavior...

We discuss the use of orthogonal wavelet transforms in multivariate data analysis methods such as clustering and dimensionality reduction. Wavelet transforms allow us to introduce multiresolution approximation, and multiscale nonparametric regression or smoothing, in a natural and integrated way into the data analysis. Applications illustrate the powerfulness of this new perspective on data ana...

Wavelet transforms using matrix-valued wavelets (MVWs) can process the components of vector-valued signals jointly, and thus offer potential advantages over scalar wavelets. For every matrix-valued scaling filter, there are infinitely many matrix-valued wavelet filters corresponding to rotated bases. We show how the arbitrary orthogonal factor in the choice of wavelet filter can be selected ada...

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Top-down tree search algorithms with non-additive information cost comparisons as decision criteria have recently been proposed by Taswell for the selection of near-best bases in wavelet packet transforms. Advantages of top-down non-additive near-best bases include faster computation speed, smaller memory requirement, and extensibility to biorthogonal wavelets in addition to orthogonal wavelets...