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Over-complete Dictionary Learning for Sparse Representation

Parsa, Javad | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51921 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Babaie-Zadeh, Massoud
  7. Abstract:
  8. Sparse representation has been an important problem in recent decade. The main idea in this problem is that natural signals have information contents much lower than their ambient dimensions and as such, they can be represented by using only a few atoms. For example, if the dimension of signal is n, the purpose in sparse representation is to achieve the representation of signal in terms of s atom (s ≪ n). In sparse coding, the dictionary depends on the used signal. In some of the problem, dictionary is specified and sparse representation is obtained by this dictionary. In this case, because the dictionary is known, maybe sparse representation is not suitable for this signal. For this reason, in recent years, dictionary learning problem has been expressed for sparse coding. Nevertheless, in this problem, the purpose is to achieve a dictionary by the training data and sparse representation is obtained by this dictionary. In second and third chapter, sparse coding and dictionary learning have been explained completely.Since the dictionary learning problem is a non-convex problem, the major goal in this thesis is to change this problem to a convex problem. In the fourth chapter, a new method is introduced for reducing the mutual and average coherence between the atoms of dictionary,while in this approach, mutual and average coherence reduce as well. In the fifth chapter,we have proposed a new approximation to change the dictionary learning problem to a convex problem. According to the results, this approximation increases convergence rate and reduces the RMSE noticeably. This approximation can be applied to most of dictionary learning algorithms. Finally, we have introduced a new method to convert the dictionary learning problem with reducing coherence constraint to a convex problem. Due to this innovation, RMSE reduces and the convergence rate increases, while, mutual and average coherences decrease as well
  9. Keywords:
  10. Sparse Representation ; Dictionary Learning ; Convergence Rate ; Convex Approximation ; Average Coherence ; Mutual Coherence of Measurement Matrix

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