Proceedings ArticleDOI
Spherical wavelets: efficiently representing functions on the sphere
Peter Schröder,Wim Sweldens +1 more
- pp 161-172
TLDR
This paper shows how biorthogonal wavelets with custom properties can be constructed with the lifting scheme, and gives examples of functions defined on the sphere, and shows how they can be efficiently represented with spherical wavelets.Abstract:
Wavelets have proven to be powerful bases for use in numerical analysis and signal processing. Their power lies in the fact that they only require a small number of coefficients to represent general functions and large data sets accurately. This allows compression and efficient computations. Classical constructions have been limited to simple domains such as intervals and rectangles. In this paper we present a wavelet construction for scalar functions defined on the sphere. We show how biorthogonal wavelets with custom properties can be constructed with the lifting scheme. The bases are extremely easy to implement and allow fully adaptive subdivisions. We give examples of functions defined on the sphere, such as topographic data, bidirectional reflection distribution functions, and illumination, and show how they can be efficiently represented with spherical wavelets. CRread more
Citations
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Factoring wavelet transforms into lifting steps
Ingrid Daubechies,Wim Sweldens +1 more
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Journal ArticleDOI
The Lifting Scheme: A Custom-Design Construction of Biorthogonal Wavelets
TL;DR: In this paper, a lifting scheme is proposed for constructing compactly supported wavelets with compactly support duals, which can also speed up the fast wavelet transform and is shown to be useful in the construction of wavelets using interpolating scaling functions.
References
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Journal ArticleDOI
Ten Lectures on Wavelets
TL;DR: In this article, the regularity of compactly supported wavelets and symmetry of wavelet bases are discussed. But the authors focus on the orthonormal bases of wavelets, rather than the continuous wavelet transform.
Journal ArticleDOI
Orthonormal bases of compactly supported wavelets
TL;DR: This work construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity, by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction.
Journal ArticleDOI
Biorthogonal bases of compactly supported wavelets
TL;DR: In this paper, it was shown 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.
Journal ArticleDOI
The Lifting Scheme: A Custom-Design Construction of Biorthogonal Wavelets
TL;DR: In this paper, a lifting scheme is proposed for constructing compactly supported wavelets with compactly support duals, which can also speed up the fast wavelet transform and is shown to be useful in the construction of wavelets using interpolating scaling functions.
The lifting scheme: A construction of second generation wavelets
TL;DR: The lifting scheme is presented, a simple construction of second generation wavelets; these are wavelets that are not necessarily translates and dilates of one fixed function, and can be adapted to intervals, domains, surfaces, weights, and irregular samples.