Node varying regularization for graph signals

While regularization on graphs has been successful for signal reconstruction, strategies for controlling the bias-variance trade-off of such methods have not been completely explored. In this work, we put forth a node varying regularizer for graph signal reconstruction and develop a minmax approach to design the vector of regularization parameters. The proposed design only requires as prior information an upper bound on the underlying signal energy; a reasonable assumption in practice. With such formulation, an iterative method is introduced to obtain a solution meeting global equilibrium. The approach is numerically efficient and has convergence guarantees. Numerical simulations using real data support the proposed design scheme.