A Framework for Feature-Centric Filter Design

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 visualization of large scientific data sets. However, it is important that 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. We also demonstrate how the axioms can be used to design linear featurecentric filters that are optimal in the sense that they are closest in to the ideal low pass filter. Results are included that demonstrate the feature-preservation characteristics of each filter.