Recent results have underlined the importance of incoherence in redundant dictionaries for a good behavior of decomposition algorithms like Matching and Basis Pursuit. However, appropriate dictionaries for a given application may not be able to meet the incoherence condition. In such case, decomposition algorithms may completely fail in the retrieval of the sparsest approximation. This paper studies the effect of introducing a priori knowledge when recovering sparse approximations over redundant dictionaries. Theoretical results show how the use of reliable a priori information (which in this work appears under the form of weights) can improve the performances of standard approaches such as greedy algorithms and relaxation methods. Our results reduce to the classical case when no prior information is available. Examples validate and illustrate our theoretical statements.

This paper presents a new scalable and highly flexible color image coder based on a Matching Pursuit expansion. The Matching Pursuit algorithm provides an intrinsically progressive stream and the proposed coder allows us to reconstruct color information from the first bit received. In order to efficiently capture edges in natural images, the dictionary of atoms is built by translation, rotation and anisotropic refinement of a wavelet-like mother function. This dictionary is moreover invariant under shifts and isotropic scaling, thus leading to very simple spatial resizing operations. This flexibility and adaptivity of the MP coder makes it appropriate for asymmetric applications with heterogeneous end user terminals. 1.

To be efficient, data protection algorithms should generally exploit the properties of the media information in the transform domain. In this paper, we will advocate the use of non-linear image approximations using highly redundant dictionaries, for security algorithms. We show that a flexible image representation based on a multidimensional and geometry-based coding scheme, has precious attributes for security information embedding. Redundant expansions provide very good approximation properties, as well as an increased resiliency to coding noise, and a simple stream structure enables easy manipulations. This paper describes simple examples of image scrambling and watermarking applications, based on a Matching Pursuit image coder. It illustrates the very interesting potential of redundant decompositions for data protection and security applications.

This paper presents a new scalable and highly flexible color image coder based on a Matching Pursuit expansion. The Matching Pursuit algorithm provides an intrinsically progressive stream and the proposed coder allows us to reconstruct color information from the first bit received. In order to