Adaptive wavelet transform possessing the properties of translation and scale invariance
Huilin Xiong, Tianxu Zhang · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1998
In this paper, we propose a new approach to deal with the translation-invariant problem of wavelet transform. We first adaptively renormalize the original signal by a orthonomal scale function and first order and second order moments of the signal. This procedure can be fulfilled by a changeable filter, of which the coefficients are selected from a 'mother mask' prepared before. Then, we decompose the renormalized signal using Mallat's algorithm, and prove that the coefficients of this adaptive wavelet transform, called adaptive wavelet invariant moments, are translation- invariant and scale-invariant. Finally, experiment result for 2D digital signals are given.