Non-Bayesian Estimation Framework for Signal Recovery on Graphs

Graph signals arise from physical networks, such as power and communication systems, or a result of convenient representation data with complex structure, social networks. We consider the problem general graph signal recovery noisy, corrupted, incomplete measurements under structural parametric constraints, smoothness in frequency domain. In this paper, we formulate non-Bayesian estimation weighted mean-squared-error (WMSE) criterion, which is based on quadratic form Laplacian matrix its trace WMSE Dirichlet energy error w.r.t. graph. The Laplacian-based penalizes errors according to their spectral content difference-based cost function accounts for fact that many cases graphs can only be achieved up constant addend. develop new Cram\'er-Rao bound (CRB) present associated Lehmann unbiasedness condition discuss CRB methods fundamental problems 1) A linear Gaussian model relative measurements; 2) Bandlimited recovery. sampling allocation policies optimize sensor locations network these proposed CRB. Numerical simulations random electrical are used validate performance policies.