A region-based easy-path wavelet transform for sparse image representation

Abstract

The Easy-Path Wavelet Transform (EPWT) is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in G. Plonka, The easy path wavelet: A new adaptive wavelet transform for sparse representation of two-dimensional data, Multiscale Model. Simul. 7(3) (2009) 1474–1496.13 It provides a sparse representation by finding a path in the domain of the function leveraging the local correlations of the function values. It then applies a 1-dimensional (ID) wavelet transform to the obtained vector, decimates the points and iterates the procedure. The main drawback of such method is the need to store, for each level of the transform, the path which vectorizes the 2-dimensional (2D) data. Here, we propose a variation on the method which consists of firstly applying a segmentation procedure to the function domain, partitioning it into regions where the variation in the function values is low; in a second step, inside each such region, a path is found in some deterministic way, i.e. not data-dependent. This circumvents the need to store the paths at each level, while still obtaining good quality lossy compression. This method is particularly well suited to encode a region of interest in the image with different quality than the rest of the image.