Bandlimited graph signal reconstruction by diffusion operator

Signal processing on graphs extends signal processing concepts and methodologies from the classical signal processing theory to data indexed by general graphs. For a bandlimited graph signal, the unknown data associated with unsampled vertices can be reconstructed from the sampled data by exploiting the spatial relationship of graph signal. In this paper, we propose a generalized analytical framework of unsampled graph signal and introduce a concept of diffusion operator which consists of local-mean and global-bias diffusion operator. Then, a diffusion operator-based iterative algorithm is proposed to reconstruct bandlimited graph signal from sampled data. In each iteration, the reconstructed residuals associated with the sampled vertices are diffused to all the unsampled vertices for accelerating the convergence. We then prove that the proposed reconstruction strategy converges to the original graph signal. The simulation results demonstrate the effectiveness of the proposed reconstruction strategy with various downsampling patterns, fluctuation of graph cut-off frequency, robustness on the classic graph structures, and noisy scenarios.