Noise Reduction of Temperature Data Using Jacobi and Gauss-Seidel Iterations

When a sensor network is used to collect temperature data, the data may be corrupted by unwanted noise. Therefore, it is desirable to develop a graph signal processing (GSP) method to reduce noise when the sensor network is represented as a graph model. Traditionally, a smoothness-based method has been used to address this problem, assuming that temperature data is smooth over the network while noise exhibits high variation. This method requires solving a linear system using matrix inversion, which is impractical for large networks. In this article, we present the Jacobi and Gauss-Seidel iterations to solve the linear system of the smoothness-based method. These iterations generate a sequence of approximate solutions that only involve matrixvector multiplication of the sparse matrix. We derive the convergence conditions of these iterative methods to ensure that a solution can be obtained. Finally, we use temperature data collected by sensor network in Taiwan to study the convergence speed of the iterations. We also demonstrate the signal-to-noise ratio (SNR) improvement of the proposed method to show its effectiveness in noise reduction.