# A Region Based Easy Path Wavelet Transform For Sparse Image Representation

## TL;DR

This paper introduces a region-based variation of the Easy Path Wavelet Transform that improves sparse image representation and compression by reducing storage needs and enabling region-specific quality encoding.

## Contribution

The proposed method segments the image domain into regions and finds deterministic paths within each, eliminating the need to store paths at each level while maintaining compression quality.

## Key findings

- Effective in encoding regions of interest with different quality levels
- Reduces storage requirements compared to original method
- Achieves good quality lossy compression

## Abstract

The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. 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 one dimensional 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 two dimensional 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. [1] Gerlind Plonka. The easy path wavelet transform: A new adaptive wavelet transform for sparse representation of two-dimensional data. Multiscale Modeling & Simulation, 7(3):1474$-$1496, 2008.