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Ground-penetrating radar (GPR) is a vital tool in the domain of nondestructive testing; however, its capability to accurately discern subsurface targets faces challenges from substantial background clutter. Current methods aimed at clutter suppression often leave residual clutter or distort the hyperbolic tails of target-scattered signals, particularly in heterogeneous soil conditions. This study endeavors to tackle the complexities of clutter suppression in practical scenarios. To this end, we introduce a novel framework for GPR clutter suppression using stationary graph signal (SGS) processing techniques. In our proposed approach, GPR B-scan images are treated as graph signals and transformed into the graph frequency domain via graph Fourier transform (GFT). This framework incorporates B-scan images containing both targets and clutter alongside clutter-only B-scan images gathered within the same testing environment. B-scan images featuring both targets and clutter serve as reference data samples for constructing a graph shift operator (GSO), with clutter and targets’ scattering signals interpreted as SGS. Following the establishment of weak SGSs with respect to the GSO, a variant of the graph-based Wiener filter tailored for GPR applications is applied to effectuate clutter suppression. Through our proposed SGS processing-based filtering method, clutter can be effectively suppressed, thereby facilitating the restoration of target scattering signals. Extensive experiments conducted on both numerical simulation data and field test data underscore the efficacy of the proposed approach, which can be further applied to the general nondestructive testing realm.

Graphons are limit objects of sequences of graphs and are used to analyze the behavior of large graphs. Recently, graphon signal processing has been developed to study signal processing on large graphs. A major limitation of this approach is that any sparse sequence of graphs inevitably converges to the zero graphon, rendering the resulting signal processing theory trivial and inadequate for sparse graph sequences. To overcome this limitation, we propose a new signal processing framework that leverages the concept of generalized graphons and introduces the stretched cut distance as a measure to compare these graphons. Our framework focuses on the sampling of graph sequences from generalized graphons and explores the convergence properties of associated operators, spectra, and signals. Our signal processing framework provides a comprehensive approach to analyzing and processing signals on graph sequences, even if they are sparse. Finally, we discuss the practical implications of our theory for real-world large networks through numerical experiments.

In generalized graph signal processing (GGSP), the signal associated with each vertex in a graph is an element from a Hilbert space. In this paper, we study GGSP signal reconstruction as a kernel ridge regression (KRR) problem. By devising an appropriate kernel, we show that this problem has a solution that can be evaluated in a distributed way. We interpret the problem and solution using both deterministic and Bayesian perspectives and link them to existing graph signal processing and GGSP frameworks. We then provide an online implementation via random Fourier features. Under the Bayesian framework, we investigate the statistical performance under the asymptotic sampling scheme. Finally, we validate our theory and methods on real-world datasets.