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Sparse Component Analysis and its Applications

Zayyani, Hadi | 2010

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 40519 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Babaiezadeh, Massoud
  7. Abstract:
  8. Nowadays, using sparsity of signals has been utilized in diverse applications in signal processing community. Two important applications of signal sparsity are sparse source separation and sparse signal representation. These two problems are joined with a Sparse Component Analysis (SCA) framework. In SCA, the problem is divided into two subproblems which are matrix estimation and sparse vector estimation. In this thesis, a MAP-based algorithm is suggested for sparse vector estimation with a Bernoulli-Gaussian distribution for sparse vector elements. To reduce the complexity, an iterative Bayesian algoritm is used in which an steepest-ascent is utilized for maximization. A complete convergence analysis is derived for the iterative Bayesian algorithm. In addition, a Bayesian hypothesis testing is suggested for detecting the active atoms for sparse representation. This Bayesian hypothesis testing algorithm outperforms many state-of-the-art algorithms in most of the cases in terms of recoustruction accuracy of sparse vector, of course with a higher complexity than all of them. For dictionay matrix estimation, a new dictionary matrix estimation algorithm is proposed which is superior to the most famous algorithm in the literature. Moreover to suggesting the practical estimation algorithms, for the first time, we calculated some Cramer-Rao bounds for estimating the mixing matrix in SCA. To compute the bounds in a closed form, some reasonable approximations are used in our calculations. In addition, decodong real-field codes and sparse channel estimation are selected as special applications of SCA. In this way, a new Compreesed sensing block adaptive filter is proposed and a Cramer-Rao bound and a Bayesian Cramer-Rao bound are also calculated for estimating the sparse channel
  9. Keywords:
  10. Dictionary Learning ; Parameter Estimation ; Sparse Component Analysis (SCA) ; Sparse Signal Representation ; Cramer-Rao Bound ; Parameter Estimation ; Bayesian Hypothesis Testing

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