Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
A study of compactly supported scaling functions and wavelets
An international conference on curves and surfaces on Wavelets, images, and surface fitting
Decomposition and reconstruction algorithms for bivariate spline wavelets on the unit square
An international conference on curves and surfaces on Wavelets, images, and surface fitting
Wavelets for computer graphics: theory and applications
Wavelets for computer graphics: theory and applications
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
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We construct biorthogonal spline wavelets for periodic splines which extend the notion of ''lazy'' wavelets for linear functions (where the wavelets are simply a subset of the scaling functions) to splines of higher degree. We then use the lifting scheme in order to improve the approximation properties with respect to a norm induced by a weighted inner product with a piecewise constant weight function. Using the lifted wavelets we define a multiresolution analysis of tensor-product spline functions and apply it to image compression of black-and-white images. By performing-as a model problem-image compression with black-and-white images, we demonstrate that the use of a weight function allows to adapt the norm to the specific problem.