For a square integrable vector-valued process f on the Loeb product space, it is shown that vector orthogonality is almost equivalent to componentwise scalar orthogonality. Various characterizations of almost sure uncorrelatedness for f are presented. The process f is also related to multilinear forms on the target Hilbert space. Finally, a general structure result for f involving the biorthogo...

In applications, it is well known that high smoothness, small support and high vanishing moments are the three most important properties of a biorthogonal wavelet. In this paper, we shall investigate the mutual relations among these three properties. A characterization of Lp (1 ≤ p ≤ ∞) smoothness of multivariate refinable functions is presented. It is well known that there is a close relation ...

Starting from any two given multiresolution analyses of L2, fV 1 j gj 2Z, and fV 2 j gj 2Z, we construct biorthogonal wavelet bases that are associated with this chosen pair of multiresolutions. Thus, our construction method takes a point of view opposite to the one of Cohen–Daubechies–Feauveau (CDF), which starts from a well-chosen pair of biorthogonal discrete filters. In our construction, th...

In this paper, we analyze the design issues for the SPIHT (set partitioning in hierarchical trees) coding, one of the most prestigious embedded-wavelet-based algorithms in the literature. Equipped with the multiresolution decomposition, progressive scalar quantization and adaptive arithmetic coding, SPIHT generates highly compact scalable bitstreams suitable for real-time multimedia application...

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 ...