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Deterministic Sensing Matrix Design in Compressive Sensing

Bagh-Sheikhi, Hamed | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49179 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Amini, Arash
  7. Abstract:
  8. Sampling and recovery of a signal is one of the crucial issues in communication systems. In conventional methods, proper recovery is achieved by sampling the signal at the Nyquist rate, which is twice the signal bandwidth. There have been attempts on reducing the required sampling rate, all of which end in rates equal to a factor of the signal bandwidth. Assuming the sparse nature of the signal in hand, which is a reasonable assumption in many real world scenarios, the theory of Compressed Sensing suggests a sampling rate much less than the Nyquist rate. Designing suitable sensing matrices and efficient recovery of the signal from its samples are the two major challenges of Compressed Sensing. Designing sensing matrices was initially approached through the idea of random sensing matrices. In fact, these matrices provided proof for the feasibility of the original compressed sensing method. However, since the use of random sensing matrices entails intensive complexity and storage problems, these matrices fail to meet practical necessities. This issue explains the need for deterministic sensing matrices. Prior research has approached the problem of designing these matrices through reducing the coherency coefficient of such matrices. Some of the most important works in this field include designing methods based on error-correcting codes, algebraic curves, algebraic theory and some types of graphs. This thesis is dedicated to introduce a novel design of deterministic sensing matrices based on eigen-decomposition of an arbitrary, real-valued matrix. We will show that the adjacency matrix of strongly regular graphs is a proper choice and results in favorable performance. The thesis is organized as follows:First a concise introduction of compressed sensing is provided. We will introduce the necessary tools of designing deterministic sensing matrices in this section. Then a description of the former methods of design will be provided along with comments on their pros and cons. Finally, we will introduce a method for designing deterministic sensing matrices using the eigen-decomposition of matrices and compare their performance with the former techniques through simulation
  9. Keywords:
  10. Compressive Sensing ; Strongly Regular Graph ; Compressive Sampling ; Graph Spectrum ; Deterministic Sensing Matrix

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