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• W2029656520 abstract "In recent years there have been various attempts at the representations of {mbox multivariate} signals such as images, which outperform wavelets. As is well known, wavelets are not optimal in that they do not take full advantage of the geometrical regularities and singularities of the images. Thus these approaches have been based on tracing curves of singularities and applying bandlets, curvelets, ridgelets, etc., or allocating some weights to curves of singularities like the Mumford–Shah functional and its modifications. In the latter approach a function is approximated on subdomains where it is smoother but there is a penalty in the form of the total length (or other measurement) of the partitioning curves. We introduce a combined measure of smoothness of the function in several dimensions by augmenting its smoothness on subdomains by the smoothness of the partitioning curves. Also, it is known that classical smoothness spaces fail to characterize approximation spaces corresponding to multivariate piecewise polynomial nonlinear approximation. We show how the proposed notion of smoothness can almost characterize these spaces. The question whether the characterization proposed in this work can be further “simplified” remains open." @default.
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• W2029656520 date "2003-10-10" @default.
• W2029656520 modified "2023-09-27" @default.
• W2029656520 title "On Bivariate Smoothness Spaces Associated with Nonlinear Approximation" @default.
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• W2029656520 doi "https://doi.org/10.1007/s00365-003-0549-y" @default.
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