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 optimization 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 resolution 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 optimization 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 optimization techniques.