Bayesian Formulations for Graph Spectral Denoising

We consider noisy signals which are defined on the vertices of a graph and present smoothing algorithms for the cases of Gaussian, dropout, and uniformly distributed noise. The signals are assumed to follow a prior distribution defined in the frequency domain which favors signals which are smooth across the edges of the graph. By pairing this prior distribution with our three models of noise generation, we propose \textit{Maximum A Posteriori} (M.A.P.) estimates of the true signal in the presence of noisy data and provide algorithms for computing the M.A.P. Finally, we demonstrate the algorithms' ability to effectively restore white noise on image data, and from severe dropout in toy \& EHR data.