A family of stable nonlinear nonseparable multiresolution schemes in 2D
Journal of Computational and Applied Mathematics
Weighted-powerp nonlinear subdivision schemes
Proceedings of the 7th international conference on Curves and Surfaces
Lossless and near-lossless image compression based on multiresolution analysis
Journal of Computational and Applied Mathematics
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Nonlinear analogues of classical wavelet transformations have been designed within spatially oriented multiresolution frameworks such as Harten’s framework [J. Appl. Numer. Math., 12 (1993), pp. 153-193] and the lifting framework [R. L. Claypoole &etal;, IEEE Trans. Image Process., 12 (2003), pp. 1449-1459]. In designing and using nonlinear multiscale transformations for data compression purposes, the main issue is that of ensuring stability. In [J. Appl. Numer. Math., 12 (1993), pp. 153-193], Harten ensures stability by designing a special error-control mechanism that provides estimates for the compression error. In [R. L. Claypoole &etal;, IEEE Trans. Image Process., 12 (2003), pp. 1449-1459] no theoretical results are provided, but the authors argue that stability is a consequence of synchronization between the nonlinear decisions made by the prediction operators in the direct and inverse transformations. By interpreting the nonlinear multiscale transformation of R. L. Claypoole &etal; within Harten’s cell-average framework, we are able to provide stability bounds for the scheme of R. L. Claypoole &etal; and establish a theoretical basis for comparison between both nonlinear multiresolution schemes.