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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 43705 (05)
- University: Sharif University of Technology
- Department: Electrical Engineering
- Advisor(s): Babaie Zadeh, Massoud
- Abstract:
- Sparse signal processing (SSP), as a powerful tool and an efficient alternative to traditional complete transforms, has become a focus of attention during the last decade. In this ap-proach, we want to approximate a given signal as a linear combination of as few as possible basis signals. Each basis signal is called an atom and their collection is called a dictionary. This problem is generally difficult and belongs to the NP-hard problems; since it requires a combinatorial search. In recent years however, it has been shown both theoretically and experimentally that the sparset possible representation of a signal in an overcomplete dictio-nary is unique under some conditions and can be found in polynomial time. Consequently, this subject was rapidly used in many applications such as data compression, blind source separation (BSS), image enhancement, medical imaging, pattern recognition, and so on. There are two important problems in SSP. One is to find an appropriate overcomplete dictionary for a given class of signals, i.e. a dictionary that provides sufficient sparse repre-sentation for all members of that class. This has led to the development of the dictionary learning algorithms. The second problem is to have an efficient algorithm that recovers the sparset possible representation of a signal. This has also led to the development of different sparse coding algorithms. In this thesis, we first review some of the existing algorithms for sparse coding and dictionary learning. We also consider the image denoising problem using sparse representation. We then propose a new sparse coding algorithm. This algorithm is a generalization of the Iteratively Re-weighted Least Squares (IRLS) algorithms. We continue by proposing some new dictionary learning algorithms. Two of these algorithms are indeed a combination of the ideas of K-Singular Value Decomposition (K-SVD) and Method of Optimal Directions (MOD) algorithms. In order to overcome the high computa-tional burden of K-SVD, we propose an efficient algorithm. The simulations performed on both synthetic and real data show the advantage of the proposed algorithm over K-SVD in both execution time and quality of the results. We then propose three new algorithms which differ structurally from the existing algorithms while performing averagely better. In order to improve the performance of image denoising using sparse representation, we propose a method which is based on averaging the different estimations of the image blocks during the learning process. The simulation results show the promising performance of this method
- Keywords:
- Sparse Representation ; Dictionary Learning ; Compressive Sensing ; Image Denoising
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