Recovery of Bandlimited Graph Signals Based on the Reproducing Kernel Hilbert Space

Abstract

Signal recovery on graphs is attracting more and more attentions. Based on the smoothness assumption, the signal recovery problem can be formulated as an unconstrained optimization model. Although the model can be solved analytically, the computational cost is too expensive. In this paper, to reduce the computational complexity, we skillfully construct a kernel function, such that the smoothness item is equivalent to the norm of the signal modulo a constant in the reproducing kernel Hilbert space. Based on this, by using the Representer Theorem of reproducing kernel Hilbert space, the optimization problem for recovering the signal from a given bandlimited space, can be solved in a lower-dimensional subspace corresponding to the known labeled set. Experiments for the recovery of artificial graph signals in GSPBOX and real data in the recommendation system show very encouraging results.