Accelerated Matrix Inversion Approximation-Based Graph Signal Reconstruction

Graph signal processing (GSP) is an emerging field which studies signals lived on graphs, like collected signals in a sensor network. One important research point in this area is graph signal reconstruction, i.e., recovering the original graph signal from its partial collections. Matrix inverse approximation (MIA)-based reconstruction has been proven more robust to large noise than the conventional least square recovery. However, this strategy requires the K-th eigenvalue of Laplacian operator \(\varvec{\mathcal {L}}\). In this paper, we propose an efficient strategy for approximating the K-th eigenvalue in this GSP filed. After that, the MIA reconstruction method is modified by this proposed substitution, and thereby accelerated. Consequently, we apply this modified strategy into artificial graph signal recovery and real-world semi-supervised learning field. Experimental results demonstrate that the proposed strategy outperforms some existed graph reconstruction methods and is comparable to the MIA reconstruction with lower numerical complexity.