Wavelet interpolation networks for hierarchical approximation

Christophe P. Bernard; Stephane G. Mallat; Jean-Jeacques E. Slotine

doi:10.1117/12.366782

26 October 1999 Wavelet interpolation networks for hierarchical approximation

Christophe P. Bernard, Stephane G. Mallat, Jean-Jeacques E. Slotine

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366782
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

In this paper, we motivate and describe a scattered data interpolation scheme based on a hierarchical wavelet subfamily selection process named allocation. This interpolation method applies in any dimension, where it compares well to regularization techniques, especially in terms of stability, of adaptivity and of sparsity of the learned function representation. Adaptive convergence theorems are stated, and their proofs are outlined. We also describe a variant of this approach that can be incremental, and thus works as an online learning process.

Citation Download Citation

Christophe P. Bernard, Stephane G. Mallat, and Jean-Jeacques E. Slotine "Wavelet interpolation networks for hierarchical approximation", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366782

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