Graph Signal Denoising via Trilateral Filter on Graph Spectral Domain

This paper presents a graph signal denoising method with the trilateral filter defined in the graph spectral domain. The original trilateral filter (TF) is a data-dependent filter that is widely used as an edge-preserving smoothing method for image processing. However, because of the data-dependency, one cannot provide its frequency domain representation. To overcome this problem, we establish the graph spectral domain representation of the data-dependent filter, i.e., a spectral graph TF (SGTF). This representation enables us to design an effective graph signal denoising filter with a Tikhonov regularization. Moreover, for the proposed graph denoising filter, we provide a parameter optimization technique to search for a regularization parameter that approximately minimizes the mean squared error w.r.t. the unknown graph signal of interest. Comprehensive experimental results validate our graph signal processing-based approach for images and graph signals.