2017/02/10 by Weng-Tai Su, Su, Weng-Tai, Gene Cheung +3
Computer Science · Physics and Astronomy · #Advanced Graph Neural Networks #Complex Network Analysis Techniques #Computer Vision and Pattern Recognition (cs.CV) #Error Correcting Code Techniques #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.1702.03105
openalex publication_date 2017/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recent advent in graph signal processing (GSP) has led to the development of new graph-based transforms and wavelets for image / video coding, where the underlying graph describes inter-pixel correlations. In this paper, we develop a new transform called signed graph Fourier transform (SGFT), where the underlying graph G contains negative edges that describe anti-correlations between pixel pairs. Specifically, we first construct a one-state Markov process that models both inter-pixel correlations and anti-correlations. We then derive the corresponding precision matrix, and show that the loopy graph Laplacian matrix Q of a graph G with a negative edge and two self-loops at its end nodes is approximately equivalent. This proves that the eigenvectors of Q - called SGFT - approximates the optimal Karhunen-Lo`eve Transform (KLT). We show the importance of the self-loops in G to ensure Q is positive semi-definite. We prove that the first eigenvector of Q is piecewise constant (PWC), and thus can well approximate a piecewise smooth (PWS) signal like a depth image. Experimental results show that a block-based coding scheme based on SGFT outperforms a previous scheme using graph transforms with only positive edges for several depth images.