On the Application of the Generalized Means to Construct Multiresolution Schemes Satisfying Certain Inequalities Proving Stability

Multiresolution representations of data are known to be powerful tools in analysis and processing, they particularly interesting for compression. In order obtain a proper definition the edges, good option is use nonlinear reconstructions. These reconstruction heart prediction processes which appear subdivision multiresolution schemes. We define study some reconstructions based on means, more concrete so-called Generalized means. means have two properties that will allow us get associated operators adapted presence discontinuities, having maximum possible approximation smooth areas. Once we these defined, can build related schemes prove accurate inequalities regarding contractivity scheme first differences turn results about stability. this paper, also new two-dimensional as non-separable, i.e., not tensor product. then present stability issues numerical experiments reinforcing proven theoretical showing usefulness algorithm.