Complexity reduction of graph signal denoising based on fast graph fourier transform

Denoising is one of the most fundamental and important problems in signal processing, and graph signal denoising methods have been actively studied. Several graph signal denoising methods based on mathematical programming require solving linear equations involving Laplacian matrix, which creates problem with computational accuracy and running time. This study proposes a fast and accurate solution of linear equations for denoising based on the fast graph Fourier transform method. Moreover, the proposed method can perform denoising not only on graphs for which the fast graph Fourier transform can be performed, but also on a wide class of graphs with more relaxed conditions, without loss of accuracy. Experiments demonstrate the efficiency of the proposed method and confirm that denoising can be performed up to 167.3 times faster without loss of accuracy.