G. Craciun, D. Thompson, R. Machiraju, and M. Jiang, "A Framework for Filter Design Emphasizing Multiscale Feature Preservation," Proceedings of the AHPCRC and CASC/LLNL Third Workshop on Mining Scientific Datasets, Chicago, IL, pp. 105-111, April 5-7, 2001.
In this paper we develop a filter design framework emphasizing feature preservation. We are particularly interested in multiscale filters that can be used in wavelet transforms for large datasets generated by computational fluid dynamics simulations. High-fidelity wavelet transforms can facilitate the accurate mining of scientific data. However, it is important that the salient characteristics of the original features be preserved under the transformation. Our effort is different from classical filter design approaches which focus solely on performance in the frequency domain. In particular, we present a set of filter design axioms that ensure certain feature characteristics are preserved and that the resulting filter corresponds to a wavelet transform admitting in-place implementation. Three standard filters, corresponding to the Haar, linear, and cubic lifting wavelets, are shown to violate at least one of the criteria related to feature preservation. We also demonstrate how the axioms can be used to design a simple feature-centric filter. Results are included that demonstrate the feature-preservation characteristics of each filter.
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