The Easy Path Wavelet Transform: A New Adaptive Wavelet Transform for Sparse Representation of Two-Dimensional Data

Abstract

We introduce a new locally adaptive wavelet transform, called easy path wavelet transform (EPWT), that works along pathways through the array of function values and exploits the local correlations of the data in a simple appropriate manner. The usual discrete orthogonal and biorthogonal wavelet transform can be formulated in this approach. The EPWT can be incorporated into a multiresolution analysis structure and generates data dependent scaling spaces and wavelet spaces. Numerical results show the enormous efficiency of the EPWT for representation of two-dimensional data.