A Generalized Heat Kernel Smoothing Filter for Signal Denoising over Graph

Heat kernel smoothing (HKS) is a prominent method in graph signal processing (GSP) tailored for handling irregular data from complex networks. This paper introduces a generalized HKS filter designed for enhanced signal denoising over graphs. Initially, we generalize the graph Laplacian matrix (GLM) in HKS method to the p-power GLM. This allows modification of the spectral response of the HKS filter, enabling a flatter passband and a steeper transient band through adjustments to the value of positive integer p. Subsequently, two methods are presented to implement the generalized HKS filter. One is the centralized implementation method that is based on eigen-decomposition of GLM; the other is the distributed implementation method that is based on Bernstein polynomial approximation. As a case study, we apply the HKS filter to temperature data from sensor networks, demonstrating its efficacy. Experimental results show that the proposed HKS filter can provides higher signal to noise ratio (SNR) than original HKS filter.