Signal inpainting on graphs via total variation minimization

We propose a novel recovery algorithm for signals with complex, irregular structure that is commonly represented by graphs. Our approach is a generalization of the signal inpainting technique from classical signal processing. We formulate corresponding minimization problems and demonstrate that in many cases they have closed-form solutions. We discuss a relation of the proposed approach to regression, provide an upper bound on the error for our algorithm and compare the proposed technique with other existing algorithms on real-world datasets.