Francesc Aràndiga

Nonlinear multiscale decompositions: The approach of A. Harten

Data‐dependent interpolatory techniques can be used in the reconstruction step of a multiresolution scheme designed “à la Harten”. In this paper we carefully analyze the class of Essentially Non‐Oscillatory (ENO) interpolatory techniques described in [11] and their potential to improve the compression capabilities of multiresolution schemes. When dealing with nonlinear multiresolution schemes the issue of stability also needs to be carefully considered.

Tensor product multiresolution analysis with error control for compact image representation

A class of multiresolution representations based on nonlinear prediction is studied in the multivariate context based on tensor product strategies. In contrast to standard linear wavelet transforms, these representations cannot be thought of as a change of basis, and the error induced by thresholding or quantizing the coefficients requires a different analysis. We propose specific error control algorithms which ensure a prescribed accuracy in various norms when performing such operations on the coefficients. These algorithms are compared with standard thresholding, for synthetic and real images.

Analysis of WENO Schemes for Full and Global Accuracy

Liu, Osher, and Chan introduced weighted essentially nonoscillatory (WENO) reconstructions in [X.-D. Liu, S. Osher, and T. Chan, J. Comput. Phys., 115 (1994), pp. 200-212] to improve the order of accuracy of essentially nonoscillatory (ENO) reconstructions [A. Harten et al., J. Comput. Phys., 71 (1987), pp. 231-303]. In [G.-S. Jiang and C.-W. Shu, J. Comput. Phys., 126 (1996), pp. 202-228], the authors proposed smoothness indicators to obtain a WENO fifth order reconstruction from third order ENO reconstructions. With these smoothness indicators, Balsara and Shu [J. Comput. Phys., 160 (2000), pp. 405-452] and, later, [G. A. Gerolymos, D. Senechal, and I. Vallet, J. Comput. Phys., 228 (2009), pp. 8481-8524] obtained

Interpolation and Approximation of Piecewise Smooth Functions

(2r-1)

Morse description and geometric encoding of digital elevation maps

th order WENO reconstructions from

Multiresolution Based on Weighted Averages of the Hat Function I: Linear Reconstruction Techniques

r

Multiresolution Based on Weighted Averages of the Hat Function II: Nonlinear Reconstruction Techniques

th order ENO reconstructions for

Adaptive interpolation of images

4\leq r\leq 6

Discrete multiresolution based on hermite interpolation: computing derivatives

, resp.,

Weighted ENO interpolation and applications

7\leq r\leq 9