Image approximation by a hybrid method based on the Easy Path Wavelet Transform

The Easy Path Wavelet Transform (EPWT) has recently been proposed by one of the authors as a tool for sparse representations of bivariate functions from discrete data, in particular from image data. The EPWT is a locally adaptive wavelet transform that works along pathways through the array of function values exploiting the local correlations of the given data. However, the EPWT suffers from its adaptivity costs that arise from the storage of path vectors. In this paper, we propose a new hybrid method for image approximation that exploits the advantages of the usual tensor product wavelet transform for representing smooth images and uses the EPWT for an efficient representation of edges and texture. Numerical results show the efficiency of this procedure.