Wavelet matrices: algorithms and applications
Zhen Zhong Lu, Victor C. Chen, Harry Wechsler · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
Filter bank and multiresolution analysis have been widely used for wavelets. However, for multi-dimensional signals, the convolution algorithm needed for filter bank and multiresolution analysis is too complicated. In this paper, we propose a basic wavelet matrix, which can have either perfect reconstruction or desired result according to the chosen filter properties. The basic wavelet matrix method can be applied to pyramid wavelet decomposition, visual-based wavelet decomposition, tensor product, wavelet packets and adaptive tree-structured decomposition. Edge effects, the choice of filters are also discussed.