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Compressive Sensing in Complex Networks with Topological Constraints

Hashemifar, Zakieh | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44565 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Rabiee, Hamid Reza
  7. Abstract:
  8. Compressive Sensing (CS) is a new paradigm in signal processing and information theory, which proposes to sample and compress sparse signals simultaneously and has drawn much attention in recent years. Many signals in lots of applications have a sparse representation in some bases, so CS is used as an efficient way of data compression in many applications such as image processing and medical applications in the last couple of years. Since some of the distributed information in complex networks are compressible too, CS can be used in order to gather the distribted information on the nodes or links efficiently. Traffic analysis and performance monitoring in computer networks, topology reconstruction in complex networks, information gathering in wireless sensor networks and peer to peer networks are some applications of CS in networking.In most existing CS literature, no restriction is assumed on the design of measurement matrix and random Gaussian matrixes are usually among common choices which can recover data vectors with high probability. However in complex networks, the measurement matrix should be nonnegative and the design of the measurements is restricted by the graph topological constraints. In other words, only nodes or links that form a path or a cycle on the underlying graph, or induce a connected subgraph can be aggregated together in the same measurement. Also in weighted networks, each measurement would impose a cost. So the total imposed cost of the measurements would be considerable.In this project, we propose a novel algorithm called unbiased compressive sensing. This algorithm can reach a higher precision in data recovery with a number of measurements less than similar related works. In another algorithm as a first work in weighted networks, the unbiased compressive sensing has changed in a way that reaches a higher recovery precision with a total measurements cost less than similar methods. The last proposed framework is called deterministic compressive sensing and constructs a measurement matrix such that the data vactor can be exactly recovered and there is no possibility of wrong answer
  9. Keywords:
  10. Compressive Sensing ; Complex Network ; Measurement Matrix ; Graph Topological Constraints

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