Interpolation and Denoising of Graph Signals Using Plug-and-play Admm

Signals defined on a network or a graph are often prone to errors due to missing data and noise. In order to restore the graph signal, interpolation and denoising are two necessary steps along with other graph signal processing procedures. However, existing graph signal interpolation and denoising methods are largely decoupled due to the opposite objectives of the two tasks and the inherent high computational complexity. The goal of this paper is to integrate graph interpolation and denoising using the Plug-and-Play (PnP) ADMM, a recently developed technique in image processing. When using the subsampling process as the forward model and graph filter as the denoiser, we show that PnP ADMM is equivalent to interpolating a bandlimited signal. Preliminary results are demonstrated via experiments, where the proposed method shows significantly better performance over existing methods.