Piecewise constant wavelets on triangulations obtained by 1-3 splitting
(2008) Workshop on Multiscale Methods, Sparse Decompositions and Parsimonious Statistics — Location: Neuherberg(Germany) (11.September.2006)
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- Abstract
- We construct piecewise constant wavelets on a bounded planar triangulation, the refinement process consisting of dividing each triangle into three triangles having the same area. Thus, the wavelets depend on two parameters linked by a certain relation. We perform a compression and try to compare different norms of the compression error, when one wavelet coefficient is canceled. Finally, we show how this construction can be moved on to the two-dimensional sphere and sphere-like surfaces, avoiding the distortions around the poles, which occur in other approaches. As numerical example, we perform a compression of some spherical data and calculate some norms of the compression error for different compression rates. The main advantage is the orthogonality and sparsity of the decomposition and reconstruction matrices.
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Citations
Rosca, D.-D. (2008). Piecewise constant wavelets on triangulations obtained by 1-3 splitting. International Journal of Wavelets, Multiresolution and Information Processing, 6(2), 209-222. https://doi.org/10.1142/S0219691308002318 (Original work published 2008)