Bayesian Estimation of Graph Signals

We consider the problem of recovering random graph signals from nonlinear measurements. For this setting, closed-form Bayesian estimators are usually intractable and even numerical evaluation may be difficult to compute for large networks. In paper, we propose a signal processing (GSP) framework recovery that utilizes information on structure behind data. First, develop GSP-linear minimum mean-squared-error (GSP-LMMSE) estimator, which minimizes (MSE) among represented as an output filter. The GSP-LMMSE estimator is based diagonal covariance matrices in frequency domain, thus, has reduced complexity compared with LMMSE estimator. This property especially important when using sample-mean training dataset. then state conditions under low-complexity coincides optimal Next, approximate parametrization by filters. present three implementations parametric typical These filters more robust outliers network topology changes. our simulations, evaluate performance proposed estimation power systems, can interpreted task. show sample-GSP outperform sample-LMMSE limited dataset changes form adding/removing vertices/edges.