ADAPTIVE LIFTING SCHEMES WITH A GLOBAL ℓ1 MINIMIZATION TECHNIQUE FOR IMAGE CODING

Many existing works related to lossy-to-lossless image compression are based on the lifting concept. In this paper, we present a sparse op-timization technique based on recent convex algorithms and applied to the prediction filters of a two-dimensional non separable lifting structure. The idea consists of designing these filters, at each resolu-tion level, by minimizing the sum of the ℓ1-norm of the three detail subbands. Extending this optimization method in order to perform a global minimization over all resolution levels leads to a new opti-mization criterion taking into account linear dependencies between the generated coefficients. Simulations carried out on still images show the benefits which can be drawn from the proposed optimiza-tion techniques. Index Terms — adaptive lifting scheme, image coding, opti-mization, ℓ1 minimization techniques, sparse representations. 1