Fractal functions and wavelet expansions based on several scaling functions
Journal of Approximation Theory
A study of orthonormal multi-wavelets
Applied Numerical Mathematics - Special issue on selected keynote papers presented at 14th IMACS World Congress, Atlanta, NJ, July 1994
New biorthogonal multiwavelets for image compression
Signal Processing
Short wavelets and matrix dilation equations
IEEE Transactions on Signal Processing
Balanced multiwavelet bases based on symmetric FIR filters
IEEE Transactions on Signal Processing
Vector-valued wavelets and vector filter banks
IEEE Transactions on Signal Processing
Balanced multiwavelets theory and design
IEEE Transactions on Signal Processing
Super high definition image coding using wavelet vector quantization
IEEE Transactions on Circuits and Systems for Video Technology
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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, omnidirectional balancing, is introduced to extend to vector transforms the balancing philosophy previously proposed for multiwavelet-based scalar-signal expansion. 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.