Stability for nonlinear 2-D multiresolution: The approach of A. Harten (Q2782153)

The authors consider the multiresolution framework introduced by \textit{A. Harten} [Appl. Numer. Math. 12, 153-192 (1993; Zbl 0777.65004); SIAM J. Numer. Anal. 33, 1205-1256 (1996; Zbl 0861.65130)]. The multiresolution of Harten has a similar form than the original wavelet representations. But the decomposition process which connects two scales can be nonlinear. This allows a better adapted treatment of singularities of the given function.NEWLINENEWLINENEWLINEIn this paper, a multiresolution representation based on nonlinear prediction in the two-dimensional case is presented. In this case, stability can be ensured by modifying the encoding algorithm. Some error-control algorithms in order to obtain stability are proposed.