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Low Rank Matrix Decomposition and its Applications in Image Processing

Zarmehi Shahrebabak, Nematollah | 2019

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 53067 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Marvasti, Farokh; Amini, Arash
  7. Abstract:
  8. In this thesis, we focus on decomposition of a matrix into low rank and sparse matrices. We propose two algorithms. The first one is based on smoothed l0-norm where the l0-norm is approximated by smoothed one. Almost all previous works are based on l1-norm where the l0-norm is approximated by the l1-norm. The second algorithm is based on adaptive thresholding; to make a matrix low rank, its singular values are thresholded and to make a matrix sparse, its entries are also thresholded. Various simulations have been performed to compare the proposed algorithms with the previous ones. The results confirm the fact that the proposed algorithms have better performance in terms of quality and speed (run-time).Moreover, we propose several algorithms for rank minimization under affine constraints and the removal of sparse noise from sparse signal. Our algorithm for the rank minimization under affine constraints is based on the adaptive thresholding idea. We show that using adaptive thresholding yields better performance in terms of quality and speed in comparison to the fixed thresholding. We also propose two algorithms for the removal of sparse noise from sparse signal. The proposed algorithms are compared with the state-of-the-art algorithms under different scenarios and the simulation results show that the proposed algorithms outperforms the other ones
  9. Keywords:
  10. Smoothed L0 Norm (SLO)Algorithm ; Low-Rank Matrix Factorization ; Sparse-Low Rank Decomposition ; Sparse Corrupted Matrix Decomposition ; Image Denoising ; Image Processing

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