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arXiv2024

Joint Data Inpainting and Graph Learning via Unrolled Neural Networks

Given partial measurements of a time-varying graph signal, we propose an algorithm to simultaneously estimate both the underlying graph topology and the missing measurements. The proposed algorithm operates by training an interpretable neural network, designed from the unrolling framework. The proposed technique can be used both as a graph learning and a graph signal reconstruction algorithm. This work enhances prior work in graph signal reconstruction by allowing the underlying graph to be unknown; and also builds on prior work in graph learning by tailoring the learned graph to the signal reconstruction task.

eess.SP↗

arXiv2019

Investigating the relationship between graph eigenvector ordering and the signal processing dual

Graph signal processing uses the graph eigenvector basis to analyze signals. However, these graph eigenvectors are typically linearly ordered (by total variation), which may not be reasonable for many graph structures. There have been structure based similarity metrics proposed in the literature that better capture the geometry of graph eigenvectors. On the other hand, there has been work that attempts to generalize the concept of duality to graph signal processing. The (signal processing) the dual graph captures the relationship between graph frequencies and is obtained by typically inverting the graph Fourier transform operation. In this work, we investigate the connections between these two concepts. We propose a dualness measure of two graphs, which quantifies how close the graphs are being (signal processing) duals of each other. We show that this definition satisfies some desirable properties and develop an algorithm based on coordinate descent and perfect matching to compute an approximation to dualness. By computing the dualness measure, we observe that for structured graphs, the similarity metric-based techniques give a better dual graph (and vice-versa for ER graphs), suggesting a potentially novel approach unifying the two methods.

cs.IT↗