A New Approach for Graph Signal Separation Based on Smoothness

Blind source separation (BSS) is a signal processing subject that has recently been extended to graph signals. Graph signals that are smooth on their own graphs provide an opportunity to separate them from their summation by knowing their underlying graphs, which is different from the conventional BSS that requires at least two mixtures of source signals. In this paper, we introduce an approach to separate smooth graph signals whose energy is concentrated on their first frequency components. This approach tries to decompose the summation signal into signals that are as smooth as possible on their underlying graphs and non-smooth on the other graphs. Moreover, in the case that the number of source signals is two, the uniqueness of our separation approach is shown, up to the uncertainty of the average value of the signals. Furthermore, we interpret the solution of our approach in the case of complement graphs by deriving exact error formulas. Finally, simulations demonstrate the efficiency of the proposed approach and its superiority over other approaches in this setting.