Wavelet transforms for vector fields using omnidirectionally balanced multiwavelets

被引:41
作者
Fowler, JE [1 ]
Hua, L [1 ]
机构
[1] Mississippi State Univ, Dept Elect Comp Engn, Engn Res Ctr, Starkville, MS 39762 USA
基金
美国国家科学基金会;
关键词
balanced multiwavelets; vector wavelet transforms; vector-valued signal processing;
D O I
10.1109/TSP.2002.805488
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
Vector wavelet transforms for vector-valued fields can be implemented directly from multiwavelets; however, existing multiwavelets offer surprisingly poor performance for transforms in vector-valued signal-processing applications. In this paper, the reason for this performance failure is identified, and a remedy is proposed. A multiwavelet design criterion known as omnidirectional balancing is introduced to extend to vector transforms the balancing philosophy previously proposed for multiwavelet-based scalar-signal expansion. It is shown that the straightforward implementation of a vector wavelet transform, namely, the application of a scalar transform to each vector component independently, is a special case of an omnidirectionally balanced vector wavelet transform in which filter-coefficient matrices are constrained to be diagonal. Additionally, a family of symmetric-antisymmetric multiwavelets is designed according to the omnidirectional-balancing criterion. In empirical results for a vector-field compression system, it is observed that the performance of vector wavelet transforms derived from these omnidirectionally-balanced symmetric-antisymmetric multiwavelets is far superior to that of transforms implemented via other multiwavelets and can exceed that of diagonal transforms derived from popular scalar wavelets.
引用
收藏
页码:3018 / 3027
页数:10
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