Craciun Gheorghe, Jiang Ming, Thompson David, Machiraju Raghu
Mathematical Biosciences Institute, The Ohio State University, 231 W. 18th Ave., Columbus, OH 43210, USA.
IEEE Trans Vis Comput Graph. 2005 Mar-Apr;11(2):149-59. doi: 10.1109/TVCG.2005.35.
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.
高保真小波变换有助于对大型科学数据集进行可视化和分析。然而，重要的是原始特征的显著特性在变换下得以保留。我们在空间域提出了一组滤波器设计公理，这些公理确保某些特征特性在不同尺度间得以保留，并且所得滤波器对应于允许原地实现的小波变换。我们展示了这些公理如何用于设计线性特征保留滤波器，这些滤波器在L2范数意义上最接近理想低通滤波器，因而具有最优性。我们特别关注由计算流体动力学模拟生成的大型数据集的线性小波变换。我们的工作不同于仅专注于频域性能的经典滤波器设计方法。文中给出的结果展示了我们滤波器的特征保留特性。
