Design of graph filter in ill-posed condition using Tikhonov regularization

In this paper, the design of graph filter in ill-posed condition using Tikhonov regularization method is presented. First, the design problem of graph filter is described. Then, the Tikhonov regularization method is used to determine the filter coefficients. Because the explicit solution is obtained, it is easily computed and used in the applications. Finally, a numerical example for graph filter design of Markov chain data is illustrated to show the effectiveness of the proposed method.