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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 48600 (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 approach, 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 in general 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 dictionary 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 epresentation 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. At the first of sparse signal processing approach formation, sparse coding was at the center of attention and developed rapidly while dictionaries were simply formed by concatenating two complete dictionaries or other elementary procedures. As the progress in sparse coding became saturated, the attention to dictionary learning was increased and it was placed at the center of attention. In this thesis, we first review some of the existing algorithms for sparse coding and dictionary learning. We then review some of available algorithms to solve image inpainting problem and classify them into three categories and then we focus on image inpainting problems using sparse representation and improve their operations and compare results. We then propose two ideas of image inpainting algorithm based on sparse epresentation, the first algorithm is based on image inpaintig using outlier aware dictionary learning which does image inpainting task without any knowledge of mask. This algorithm inpaints image with less aquracy than other inpainting algorithms that use mask. Second algorithm improve image inpainting speed using two dimentional signal sparse coding, finally we compare sparse representation image inpainting operation with other image inpainting algorithms
- Keywords:
- Sparse Representation ; Image Decomposition ; Image Inpainting ; Dictionary Learning
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