Generalized Lifting for Sparse Image Representation and Coding

This paper investigates the use of generalized lifting to increase the sparseness of wavelet decompositions with application to image representation and coding. As in the bandelet approach, the strategy consists in applying first a separable wavelet decomposition and then in processing the details subbands to further decorrelate the signal representation. For this second step, we use a generalized lifting [13] which allows nonlinear processing of the details subbands. In this paper, the generalized lifting design is based on the pdf of the details coefficients after the separable wavelet decomposition and its goal is to minimize the coefficients energy. Both separable and non separable approaches are investigated. The generalized lifting is shown to reduce significantly the energy and the entropy of the representation. Furthermore, a simple quantification and entropy coding strategy is used to compare the rate-distortion characteristics of wavelet, bandelet and the proposed approach based on generalized lifting. Promising results are demonstrated.