Graph Signal Recovery via Primal-Dual Algorithms for Total Variation Minimization

Abstract

We consider the problem of recovering a smooth graph signal from noisy samples taken on a subset of graph nodes. The smoothness of the graph signal is quantified in terms of total variation. We formulate the signal recovery task as a convex optimization problem that minimizes the total variation of the graph signal while controlling its global or node-wise empirical error. We propose a first-order primal-dual algorithm to solve these total variation minimization problems. A distributed implementation of the algorithm is devised to handle large-dimensional applications efficiently. We use synthetic and real-world data to extensively compare the performance of our approach with state-of-the-art methods.