Multiresolution representation of data: A general framework

In this paper we present a general framework for a multiresolution representation of data which is obtained by the discretization of mappings. This framework which can be viewed as a generalization of the theory of wavelets, includes discretizations corresponding to unstructured grids in several space dimensions, and thus is general enough to enable us to embed most numerical problems in a multiresolution setting. Furthermore, this framework allows for nonlinear (data-dependent) multiresolution representation schemes and thus enables us to design adaptive data-compression algorithms. In this paper we also study the stability of Linear schemes fora multiresolution representation and derive sufficient conditions for existence of a multiresolution basis.