A Closed-Form Solution for Graph Signal Separation Based on Smoothness
Mohammad Hassan Ahmad Yarandi, Massoud Babaie‐Zadeh · IEEE Transactions on Signal and Information Processing over Networks · 2023
Using smoothness criteria to separate smooth graph signals from their summation is an approach that has recently been proposed [1] and shown to have a unique solution up to the uncertainty of the average values of source signals. In this correspondence, closed-form solutions of both exact and approximate decompositions of that approach are presented. This closed-form solution in the exact decomposition also answers the open problem of the estimation error. Additionally, in the caseofGaussiansourcesignalsinthepresenceofadditiveGaussiannoise, it is shown that the optimization problem of that approach is equivalent to the Maximum A Posteriori (MAP) estimation of the sources