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Study on Non-Linear Approaches for Accelerating Iterative Methods

Shamsi, Mahdi | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51361 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Marvasti, Farokh
  7. Abstract:
  8. In this correspondence, a non-linear method of convergence accelerating and improving for iteration based algorithms is introduced. After convergence analysis, some enough conditions are proposed to guarantee convergence of the algorithm.For the sake of low complexity implementation of the proposed algorithm, some simple stabilizing methods are suggested. Simulation results show desirable performance of the proposed method and its capability to stabilize the iteration based algorithms. In the literature of missing samples recovery, the proposed method is applied to an Iterative Method (IM) as a general signal reconstruction method,then it is extended to the image recovery problem where simulation results are reported in terms of full-reference and no-reference Image Quality Assessments (IQA). Then Chebyshev Acceleration (CA) is considered as an accelerating method.In this case, stabilization and quality improvement with use of the proposed algorithm are shown. As a sparse signal recovery method, SL0 (Smoothed ℓ0) is considered.Applying the introduced method to the SL0 is simulated in different scenarios of missing samples. At the end, Iterative Method with Adaptive Thresholding (IMAT) as a strong (sparse and non-sparse) signal recovery method is studied and by applying the proposed algorithm to the IMAT, convergence and sensitivity to selection of parameter values are simulated. The same approach is used for IMAT with Interpolation (IMATI) as a modification of the IMAT which results in the same simulation results
  9. Keywords:
  10. Nonlinear Method ; Sparse Signal Reconstruction ; Iteration Method ; Smoothed L0 Norm (SLO)Algorithm ; Signal Recovery ; Convergence Acceleration

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