Graph Transform Optimization with Application to Image Compression

TL;DR

This paper introduces a novel graph-based transform optimized for signal compression, demonstrating improved performance over classical methods in image and depth map coding through a convex optimization framework.

Contribution

It presents a new graph estimation algorithm and a convex optimization approach for graph transform coding, applicable to various signal types including images and depth maps.

Findings

Outperforms DCT in natural and piecewise smooth image coding.

Achieves results comparable to state-of-the-art depth map coding methods.

Provides a flexible framework for graph-based signal compression.

Abstract

In this paper, we propose a new graph-based transform and illustrate its potential application to signal compression. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance through an effective graph-based transform. We introduce a novel graph estimation algorithm, which uncovers the connectivities between the graph signal values by taking into consideration the coding of both the signal and the graph topology in rate-distortion terms. In particular, we introduce a novel coding solution for the graph by treating the edge weights as another graph signal that lies on the dual graph. Then, the cost of the graph description is introduced in the optimization problem by minimizing the sparsity of the coefficients of its graph Fourier transform (GFT) on the dual graph. In this way, we obtain a convex optimization problem whose solution defines an efficient transform coding strategy. The proposed technique is a general framework that can be applied to different types of signals, and we show two possible application fields, namely natural image coding and piecewise smooth image coding. The experimental results show that the proposed graph-based transform outperforms classical fixed transforms such as DCT for both natural and piecewise smooth images. In the case of depth map coding, the obtained results are even comparable to the state-of-the-art graph-based coding method, that are specifically designed for depth map images.