Spatial domain wavelet design for feature preservation in computational data sets

High-fidelity wavelet transforms can facilitate visualization and analysis of large scientific data sets. However, it is important that salient characteristics of the original features be preserved under the transformation. We present a set of filter design axioms in the spatial domain which ensure that certain feature characteristics are preserved from scale to scale and that the resulting filters correspond to wavelet transforms admitting in-place implementation. We demonstrate how the axioms can be used to design linear feature-preserving filters that are optimal in the sense that they are closest in L2 to the ideal low pass filter. We are particularly interested in linear wavelet transforms for large data sets generated by computational fluid dynamics simulations. Our effort is different from classical filter design approaches which focus solely on performance in the frequency domain. Results are included that demonstrate the feature-preservation characteristics of our filters.