Signal denoising on graphs via graph filtering

Signal recovery from noisy measurements is an important task that arises in many areas of signal processing. In this paper, we consider this problem for signals represented with graphs using a recently developed framework of discrete signal processing on graphs. We formulate graph signal denoising as an optimization problem and derive an exact closed-form solution expressed by an inverse graph filter, as well as an approximate iterative solution expressed by a standard graph filter. We evaluate the obtained algorithms by applying them to measurement denoising for temperature sensors and opinion combination for multiple experts.