The Strong Restricted Isometry Property of Sub-Gaussian Matrices and the Erasure Robustness Property of Gaussian Random Frames

  • Author / Creator
    Lu, Ran
  • In this thesis we will study the robustness property of sub-gaussian random matrices. We first show that the nearly isometry property will still hold with high probability if we erase a certain portion of rows from a sub-gaussian matrix, and we will estimate the erasure ratio with a given small distortion rate in the norm. With this, we establish the strong restricted isometry property (SRIP) and the robust version of Johnson-Lindenstrauss (JL) Lemma for sub-gaussian matrices, which are essential in compressed sensing with corruptions. Then we fix the erasure ratio and deduce the lower and upper bounds of the norm after a erased sub-gaussian matrix acting on a vector, and in this case we can also obtain the corresponding SRIP and the robust version of JL Lemma. Finally, we study the robustness property of Gaussian random finite frames, we will improve existing results.

  • Subjects / Keywords
  • Graduation date
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Applied Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Han, Bin (Mathematical and Statistical Sciences)
    • Wong, Yau S (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Han, Bin (Mathematical and Statistical Sciences)
    • Alexander Litvak (Mathematical and Statistical Sciences)
    • Dai, Feng (Mathematical and Statistical Sciences)
    • Lau, Anthony T-M (Mathematical and Statistical Sciences)
    • Wong, Yau Shu (Mathematical and Statistical Sciences)