  This paper proposes a method for properly sampling graph signals under
smoothness priors. Unlike many existing approaches that assume bandlimited
graph signals, our method designs a sampling operator for graph signals that
are not necessarily bandlimited based on the generalized sampling theory.
First, we formulate the sampling operator design under smoothness priors as a
feasibility problem. Then, we transform this problem into a
Difference-of-Convex (DC) problem by relaxing a certain invertibility
constraint in the original problem using the nuclear norm. Furthermore, we
develop an efficient algorithm to solve this DC problem based on the proximal
linearized difference-of-convex algorithm and guarantee its convergence to a
critical point of the problem. Finally, we demonstrate the effectiveness of our
method for several graph signal models through sampling-and-reconstruction
experiments.
