Graph transform learning for image compression

In this paper, we propose a new graph-based compression scheme for image coding. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance. In particular, we model the pixels as nodes of a graph and we treat the pixel intensities as a signal living on an unknown graph topology. We then introduce a novel graph learning algorithm targeted for image compression that uncovers the connectivities between the pixels, by taking into consideration the coding of the image signal and the graph topology in rate-distortion terms. The cost of the graph description is introduced in the optimization problem by treating the edge weights as another graph signal that lies on the dual graph, and minimizing the sparsity of its graph Fourier coefficients (GFT). In this way, we obtain a convex optimization problem whose solution defines the transform of the image signal. The experimental results show that the proposed method outperforms classical fixed transforms such as DCT, and confirm the potential of graph-based methods for adaptive image coding solutions.