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Applications of Sparse Representation in Image Processing

Nayyer, Sara | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: English
  3. Document No: 42963 (55)
  4. University: Sharif University of Technology, International Campus, Kish Island
  5. Department: Science and Engineering
  6. Advisor(s): Babaie Zadeh, Massoud
  7. Abstract:
  8. The sparse decomposition problem or nding sparse solutions of underdetermined linear systems of equations is one of the fundamental issues in signal processing and statistics. In recent years, this issue has been of great interest to researches in various elds of signal processing and accordingly found to be greatly benecial in those elds. This thesis aims at the investigation of the applications of the sparse decomposition problem in image processing. Among dierent applications such as compression, reconstruction, separation and image denoising, this thesis mainly focuses on the last one. One of the methods of image denoising which is closely tied to the sparse decomposition, is the method of transform domain. Two basic points which are eective in this method are the selection of an appropriate transformation and also an appropriate thresholding which are studied in this thesis. Regarding the importance of these two points and multiple applications of two dimensional signals, a new method for adaptive thresholding of two dimesnional signals and also a new method for complete dictionary learning for these kinds of signals are presented in the present thesis. While using transform domain methods for image denoising, it is possible to integrate the rst and second steps by applying a group of sparse coding methods which don't completely establish the equation relevant to the condition. Consequently, an implicit thresholding will be possible. In this thesis, a new algorithm for image denoising is introduced which uses the noise-aware version of SL0 method. Eventually, the noise-aware version of SL0 or Robust-SL0 will be two dimensioned and accordingly called Robust-2D-SL0. Afterwards, using a new algorithm for denoising, this noise resistant two dimensional version will be applied for image enhancement
  9. Keywords:
  10. Image Denoising ; Sparse Decomposition ; Transform Domain ; Dictionary Learning ; Two Dimensional Signals

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