DUALITY IN GRAPH SIGNAL PROCESSING

Mubeen, Abdul and Siripuram, Aditya (2019) DUALITY IN GRAPH SIGNAL PROCESSING. Masters thesis, Indian institute of technology Hyderabad.

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Abstract

In recent years ,there has been a lot of data being collected from diverse sources like temperature measurement of sensor networks, transportation networks, social networks, biological networks and brain connectivity. A common feature in these data is that it resides on a complex and irregular structures. Graphs offer the ability to model such complex and irregular structures and interactions between them, analyzing signals residing on this graph leads us to Graph signal processing framework. The important aspect of Graph signal processing is that not just analyzing the signals it also takes into account of the inherent structure on which data is evolving. Researchers in the past decade have tried to extend the concepts of classical signal processing like Fourier transform, filtering, frequency response, sampling to Graph signal processing. In classical signal processing, duality property says that,when we apply Fourier transform twice on a signal we get the reversal of the signal.In this thesis we are trying to extend the concept of duality in Graph signal processing. We define the notion of dual graph and propose an optimization based algorithm to find the dual of an arbitrary graph.

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