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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 45973 (05)
- University: Sharif University of Technology
- Department: Electrical Engineering
- Advisor(s): Babaiezadeh, Masoud
- Abstract:
- Over-complete transforms due to their maneuverability in signal representation have been under focus during the last decade. Different properties for the representation can be useful in different applications. These properties includes minimum ℓ2 representation, minimum ℓ1 representation, minimum ℓ0 representation and so on. Among these properties, minimum ℓ0 representation (also known as sparse representation) has been shown to be efficient in many applications including image denoising, data compression, blind source separation and so on, and create a new approach in signal processing area named sparse signal processing. Sparse signal processing is based on two principles, the first one is properly chosen basis signals or “atoms” and the second one is efficient algorithms to find the sparse representation over a set of atoms or “dictionary”. The first principle is known as “dictionary learning” and the second one as “sparse coding”. 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. Dictionary learning is a training procedure and as a result need some training signals to learn a dictionary . Basic model for dictionary learning considers each training signal to be contaminated with AWGN and as a result, they are robust to AWGNa. Recent advances in dictionary learning have led to algorithms that are robust to outliers in training signals but contamination of training signals with AWGN is omitted in their model. In this thesis, we briefly review some topics including formulation, uniqueness and algorithms for both principles in sparse signal processing. To show an application of sparse signal processing, we consider image denoising and investigate newly developed image denoising methods in the literature with an emphasis on image denoising based on dictionary learning. Then we start to introduce our proposed methods. We totally work on considering both AWGN contamination and outliers in our training signals. We put two assumptions on the locations of outliers. Our first assumption is to consider a few samples in each training signal to be outliers and the second one is to consider all samples of a few training signals to be outliers. Based on each of these two assumptions, we propose a dictionary learning method and show their efficiency in estimating the dictionary in comparison to traditional dictionary learning methods. Finally to show the applicability of our methods, we propose an image denoising scheme based on each of our dictionary learning methods and show their superior performance for denoising noisy images with some specific conditions
- Keywords:
- Sparse Representation ; Dictionary Learning ; Image Denoising ; Robust Dictionary Learning
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