Temperature Data Denoising Based on Directed Laplacian Matrix and Heat Kernel Smoothing

Abstract

In this paper, a temperature data denoising method using directed Laplacian matrix (DLM) and heat kernel smoothing (HKS) is presented. First, the temperature data collected from sensor network is represented as the directed graph signal. Then, the adjacency matrix and degree matrix of directed graph is used to define the DLM. And, directed graph Fourier transform is defined by the eigen-decomposition of DLM. Next, the HKS filter is employed to reduce the noise superimposed on the temperature data. Using the Taylor series expansion, the HKS filter can be approximated by a polynomial digraph filter to get a distributed implementation in vertex domain. Finally, the performance of proposed denoising method is evaluated by the real-word temperature data to show its effectiveness.