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We study the graph signal denoising problem by estimating a piecewiseconstant signal over an undirected graph. We propose a new Bayesian approachthat first converts a general graph to a chain graph via the depth-first searchalgorithm, and then imposes a heavy-tailed $t$-shrinkage prior on thedifferences between consecutive signals over the induced chain graph. We showthat the posterior computation can be conveniently conducted by fully exploringthe conjugacy structure in the model. We also derive the posterior contractionrate for the proposed estimator, and show that this rate is optimal up to alogarithmic factor, besides automatically adapting to the unknown edge sparsitylevel of the graph. We demonstrate the excellent empirical performance of theproposed method via extensive simulation studies and applications to stockmarket data.

Graph signal denoising using $t$-shrinkage priors