OPTIMALLY SPARSE IMAGE REPRESENTATION BY THE EASY PATH WAVELET TRANSFORM

摘要

The Easy Path Wavelet Transform (EPWT), 20 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. It works along pathways through the array of function values and it exploits the local correlations of the given data in a simple appropriate manner. In this paper, we show that the EPWT leads, for a suitable choice of the pathways, to optimal N-term approximations for piecewise Holder continuous functions with singularities along curves.