ABSTRACT. A multiresolution analysis of a curve is normal if each wavelet detail vector with respect to a certain subdivision scheme lies in the local normal direction. In this paper we study properties such as regularity, convergence, and stability of a normal multiresolution analysis. In particular we show that these properties critically depend on the underlying subdivision scheme and that i...

We identify multiresolution subspaces giving rise via Hankel transforms to Bessel functions. They emerge as orthogonal systems derived from geometric Hilbert-space considerations, the same way the wavelet functions from a multiresolution scaling wavelet construction arise from a scale of Hilbert spaces. We study the theory of representations of the C ∗-algebra Oν+1 arising from this multiresolu...

Wavelet packet functions provide a new class of orthogonal expansions in L(R) and comprise a rich family of building block functions, localized in time and offer more flexibility than wavelets in representing different types of signals. It is a simple, but very powerful extension of wavelets and multiresolution analysis (MRA). The power of wavelet packet lies in the fact that we have much more ...

In this paper we investigate Isotropic Multiresolution Analysis(IMRA), isotropic refinable functions, and wavelets. The main results are the characterization of IMRAs in terms of the Lax-Wiener Theorem, and the characterization of isotropic refinable functions in terms of the support of their Fourier transform. As an immediate consequence of these results, there are no compactly supported (in t...

The huge amount of data made available by the technologies for sequencing the human genome calls for sophisticated and automated analysis techniques. In this direction, the GOLAM framework has been developed within the scope of the GenData 2020 Project to enable multiresolution analysis and mining of matches between genomic regions. In this paper we show how the GOLAM framework can be used for ...

We present an effective construction of divergence-free wavelets on the square, with suitable boundary conditions. Since 2D divergence-free vector functions are the curl of scalar stream-functions, we simply derive divergence-free multiresolution spaces and wavelets by considering the curl of standard biorthogonal multiresolution analyses (BMRAs) on the square. The key point of the theory is th...

The objective of this study is to propose multiresolution data fusion scheme using multiresolution analysis (MRA). Three techniques compared, respectively based on Haar wavelet basis (HWB), Daubechies wavelet basis (DWB), and IHS transform. Daubechies Wavelet Basis (DWB) is far more efficient than the HWB and IHS transform, thus establishing the advantages for data fusion of formally multiresol...