A Graph Signal Denoising Method Using Eigenvector Associated with Minimum Eigenvalue

Graph signal denoising is a crucial technique for mitigating noise in irregular data collected from various sensor networks. When developing a graph signal denoising algorithm, two key measures must be considered: the proximity between the denoised signal and the observed signal, and the signal's total variation (TV), which measures its smoothness. Traditional denoising methods use a weighted sum of these two measures to construct a cost function, which is then minimized through matrix inversion to obtain the denoised signal. In this article, we propose a new cost function that incorporates signal energy to improve the signal-to-noise ratio (SNR). The optimal denoised signal corresponds to the eigenvector associated with the minimum eigenvalue of a specific matrix. Consequently, the well-known iterative power method can be used to efficiently obtain the solution. We evaluate the performance of the proposed method against the conventional method by comparing the SNR improvements using temperature data collected from the Taiwan sensor network.