  Sparse data models, where data is assumed to be well represented as a linear
combination of a few elements from a dictionary, have gained considerable
attention in recent years, and their use has led to state-of-the-art results in
many signal and image processing tasks. It is now well understood that the
choice of the sparsity regularization term is critical in the success of such
models. Based on a codelength minimization interpretation of sparse coding, and
using tools from universal coding theory, we propose a framework for designing
sparsity regularization terms which have theoretical and practical advantages
when compared to the more standard l0 or l1 ones. The presentation of the
framework and theoretical foundations is complemented with examples that show
its practical advantages in image denoising, zooming and classification.
