Wavelet transforms for vector fields using omnidirectionally balanced multiwavelets

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 signalprocessing applications. In this paper, the reason for this performance failure is identified, and a remedy is proposed. A multiwavelet design criterion, omnidirectional balancing, is introduced to extend to vector transforms the balancing philosophy previously proposed for multiwavelet-based scalarsignal 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 symmetricantisymmetric multiwavelets is designed according to the omnidirectionalbalancing 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. Keywords— Vector wavelet transforms, balanced multiwavelets, vectorvalued signal processing