title: Spatial domain wavelet design for feature preservation in computational data sets.
abstract: 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.
authors.affiliation: Mathematical Biosciences Institute, The Ohio State University, 231 W. 18th Ave., Columbus, OH 43210, USA. graciun@math.ohio-state.edu
authors.forename: Gheorghe
authors.initials: G
authors.lastname: Craciun
authors.forename: Ming
authors.initials: M
authors.lastname: Jiang
authors.forename: David
authors.initials: D
authors.lastname: Thompson
authors.forename: Raghu
authors.initials: R
authors.lastname: Machiraju
mesh_terms: D000465:Algorithms; D003196:Computer Graphics; D003198:Computer Simulation; D016208:Databases, Factual; D016247:Information Storage and Retrieval / Q000379:methods*; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D012212:Rheology / Q000379:methods*; D012815:Signal Processing, Computer-Assisted; D014584:User-Computer Interface