Adaptive lifting schemes combining seminorms for lossless image compression

We present a new class of adaptive wavelet decompositions that can capture the directional nature of picture information. Our method exploits the properties of seminorms to build lifting structures able to choose between different update filters, the choice being triggered by a local gradient of the input. In order to discriminate between different geometrical information, the system makes use of multiple criteria, giving rise to multiple choice of update filters. We establish the conditions under which these decisions can be recovered at synthesis, without the need for transmitting overhead information.