Adaptive 2-D wavelet transform based on the lifting scheme with preserved vanishing moments
IEEE Transactions on Image Processing
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An efficient realization of a two-channel wavelet filter bank that maps integers to integers with an adaptive number of zero moments is presented. Filters with more zero moments result in a better representation of the smooth parts of the analyzed signal, while fewer zero moments are better for transients and singularities. The proposed realization is based on the lifting scheme that enables mapping integer signals to integer wavelet coefficients, preserving the perfect reconstruction property. The realization is derived from a method of fixed wavelet filter bank design, using Lagrange interpolation of samples in the time domain. The adaptation criterion is computed from integer wavelet coefficients, which is, under some restrictions, reproducible on the reconstruction side. Quantization introduces non-predictable components of the wavelet coefficients thus influencing the behavior of the adaptation algorithm. Adaptation on the interval is used to reduce the variance of the filter parameters.