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Adaptive integer-to-integer wavelet transforms using update lifting

A class of adaptive wavelet transforms that map integers to integers based on the adaptive update lifting scheme is presented. The main feature in the adaptive update lifting scheme is that the update lifting step, which is considered as an averaging operator and is performed prior to the prediction step, is adapted to the underlying signal content and the adaptivity decisions can be recovered at the synthesis transform without bookkeeping of the adaptivity decisions. The perfect reconstruction criterion for the integer realisation of such transforms are presented in this paper. These adaptive integer-to-integer wavelet transforms can be used in scalable lossless image coding applications. The lossless image coding and spatially scalable decoding performances are demonstrated.