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Compressed Sensing and Matrix Completion and their Applications in Communications

Mojahedian, Mohammad Mahdi | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 43166 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Babaiezadeh, Massoud; Ashtiani, Farid
  7. Abstract:
  8. Matrix completion is an emerging field that is proposed after new and attractive field of compressed sensing. Matrix completion is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. In general, accurate recovery of a matrix from a small number of entries is impossible, but the knowledge that the unknown matrix has low rank radically changes this premise, making the search for solutions meaningful. Matrix completion problem comes up in great number of applications,including collaborative filtering, machine learning, control, image processing, sensor networks, system identification and communications (spectrum sensing and network coding). In this project, we follow teo goals. First goal is improving the algorithms of matrix completion, sparse decomposition and robust matrix completion. For this purpose, we introduce new algorithms for solving sparse decomposition and robust matrix completion problems. Second goal is finding some applications of this problems and compressed sensing in communications. For this purpose, we introduce a new sparse decomposition based receiver and expand this idea for complex signaling and simultaneous transmition of different signals. we also introduce a new compressed sensing based opportunistic access method
  9. Keywords:
  10. Multiplicity ; Compressive Sensing ; Random Access ; Fading ; Robust Matrix Completion ; Sparse-Low Rank Decomposition

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