Estimation of partially observed graph signals by learning spectrally matched graph dictionaries

Date

2023-8-28

Author

Kar, Osman Furkan

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In the realm of modern data analysis and processing, the handling of observations obtained from irregular topologies such as network structures has become increasingly crucial. These data may be available in the form of measurements gathered from sensor networks such as radar measurements, temperature measurements or statistical information about users in social networks. To effectively analyze such data, a promising approach is to represent them as graph signals, which can exploit the underlying network structure. However, a prevalent challenge in many real-world applications lies in dealing with incomplete observations of graph signals. This incompleteness can arise from various factors, such as sensor malfunctions or communication breakdowns within sensor networks. Consequently, the task of estimating missing observations of graph signals has gained significant attention. In this thesis, we study the estimation of graph signals from their partial observations. We propose a method consisting of jointly learning a spectral graph dictionary and computing a sparse representation of graph signals on this dictionary. We formulate an optimization problem that aims to learn narrowband Gaussian kernels that are spectrally matched to the frequency content of the given observations and the sparse codes of graph signals using the information extracted from similar signals. As the proposed optimization problem is not jointly convex on both terms, we adopt an alternating optimization scheme, solving for the kernel parameters and the sparse codes iteratively. Experimental results on both synthetic and real datasets show that the proposed method gives significant improvements in the estimation performance compared to baseline approaches.

Subject Keywords

Graph signal processing, Graph signal inpainting, Graph signal interpolation, Graph dictionary learning

URI

https://hdl.handle.net/11511/105208

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Graduate School of Natural and Applied Sciences, Thesis