Generalized Graph Signal Sampling under Subspace Priors by Difference-of-Convex Minimization

This paper proposes an effective approach for sampling graph signals under the subspace prior. Unlike conventional methods that assume bandlimited signals, our method, based on generalized sampling theory, designs a sampling operator suitable for general graph signals beyond bandlimitedness. We formulate a feasibility problem for designing the sampling operator for graph signals under the subspace prior, and then transform it into a difference-of-convex (DC) minimization problem. The DC problem involves a tight relaxation of the intractable rank constraint in the original problem via the nuclear norm. To solve this DC problem, we present an algorithm based on the general double-proximal gradient DC algorithm (GDPGDC), which ensures convergence to a critical point of our DC problem. The effectiveness of our approach is validated by sampling and recovery experiments on various graph signal models.

I. Introduction

Graph Signal Processing (GSP) is a novel framework for analyzing data represented as signals located at the vertices of a graph. Currently, GSP is a thriving area of research within the signal processing field, covering a wide range of studies from theoretical approaches to practical applications. For a comprehensive overview of GSP, see, for example, [1]–[3].