Building nonredundant adaptive wavelets by update lifting |
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Authors: | Henk JAM Heijmans Batrice Pesquet-Popescu Gemma Piella |
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Institution: | aCWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands;bSignal and Image Processing Department, Ecole Nationale Supérieure des Télécommunications, 37-39, rue Dareau, 75014 Paris, France |
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Abstract: | In this paper, we propose a technique for building adaptive wavelets by means of an extension of the lifting scheme. Our scheme comprises an adaptive update lifting step and a fixed prediction lifting step. The adaptivity consists hereof that the system can choose between two different update filters, and that this choice is triggered by the local gradient of the original signal. If the gradient is large (in some seminorm sense) it chooses one filter, if it is small the other. We derive necessary and sufficient conditions for the invertibility of such an adaptive system for various scenarios. Furthermore, we present some examples to illustrate our theoretical results. |
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Keywords: | Adaptive wavelets Lifting scheme Perfect reconstruction filter bank Seminorm Weighted gradient seminorm |
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