A Graph Signal Denoising Method Using Total Variation Regularization and Fractional Graph Fourier Transform

In the research area of graph signal processing (GSP), total variation (TV) regularization has been effectively utilized to develop a graph signal denoising method in the vertex domain. This paper aims to enhance the performance of the traditional TV-based denoising method by first providing the spectral-domain interpretation of the total variation regularization method. Then, the graph Fourier transform (GFT) is extended to the fractional graph Fourier transform (FrGFT) to obtain a more generalized TV regularization method based on FrGFT. The conventional TV regularization is merely a special case of the proposed TV regularization using FrGFT. Next, a new denoising method is introduced, which considers the trade-off between signal distortion and TV using FrGFT. A step-by-step procedure for computing the denoised signal is also provided, making it easy to apply in various applications. Finally, the effectiveness of the proposed denoising method based on TV regularization and FrGFT is demonstrated using temperature data from a sensor network in the USA. The signal-to-noise ratio (SNR) improvement is used to determine the optimal fractional order of the FrGFT for achieving the best-denoised signal.