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A multiresolution analysis for tensor-product splines using weighted spline wavelets. (English) Zbl 1169.65129

Summary: 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.

MSC:

65T60 Numerical methods for wavelets
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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