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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 40195 (05)
- University: Sharif University of Technology
- Department: Electrical Engineering
- Advisor(s): Babaiezadeh, Massoud
- Abstract:
- Sparse decomposition has recently attracted the attention of many researchers in dierent areas of signal processing. In mathematical viewpoint, sparse decomposition is nding a sparse solution of an Underdetermined System of Linear Equations (USLE). This concept has many applications in dierent signal processing elds including blind sourse separation, optical character recognition and image processing. In this thesis, we investigate the application of sparse decomposition in image denoising. One of the image denoising methods which is related to sparse decomposition concepts is the \transfrom domain method". In this method, the noisy image is rst transformed to another domain, and then noise attenuation is done by coecinet shrinkage. Finally the denoised image is obtained by applying the inverse transform on the thresholded coecients. There are two key questions in the transform domain method. The rst one is that which transfroms lead to a satisfactory denoising algorithm. Heuristically, the transfroms that can represent the signal more sparsely are more suitable for denoising. The matrix of the transform in sparse decomposition concept is usually called \dictionary" and the process of designing a dictionary that can represent a set of signals sparsely is called \dictionary learning". Since choosing a suitable transfrom is important in transfrom domain methods, we propose a new dictionary learning algorithm in this thesis. The second question in transform domain methods is the choices of the thresholding strategy and the value of thresholds. To respond this question, a new thresholding method is proposed in this thesis. In this method, a dierent threshold is used for each of the coecients, so it is called \adaptive thresholding" approach. Finally a new image denoising algorithm is presented. In this method, by using the proposed dictionary learning algorithm, a dictionary is designed based on the noisy image. Then noise is attenuated by thresholding the coecients in the domain of the learned dictionary
- Keywords:
- Image Denoising ; Sparse Decomposition ; Transform Domain ; Dictionary Learning
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