Estimation of Bandlimited Signals on Graphs From Single Bit Recordings of Noisy Samples

Recently, there has been interest in graph signal processing. We consider the problem of a bandlimited graph signal estimation (denoising) from single-bit samples obtained at each graph node. The samples before quantization are affected by zero-mean additive white Gaussian noise of known variance. Using Banach's contraction mapping theorem on complete metric spaces, we develop a recursive algorithm for bandlimited graph signal estimation. For our recursive algorithm, we show that the expected mean-squared error between the graph signal and its estimate is proportional to the bandwidth of the signal and inversely proportional to the size of the graph. We also consider the problem of choosing the nodes to sample based on the properties of graph Laplacian eigenvectors to minimize the mean-squared error of the estimate. Numerical tests with synthetic signals demonstrate the effectiveness of our estimation algorithm for Erdös-Rényi (ER) graphs, Barabäsi-Albert (BA) graphs, and Minnesota road-network graph.