2014 Fiscal Year Annual Research Report
スパース表現による不完全情報のデータからの源信号復元と形状イメージ再構成の研究
| Project/Area Number |
24500280
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| Research Institution | The University of Aizu |
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Principal Investigator |
丁 数学 会津大学, コンピュータ理工学部, 教授 (80372829)
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| Co-Investigator(Kenkyū-buntansha) |
奥山 祐市 会津大学, コンピュータ理工学部, 准教授 (90404897)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | Sparse representation / Dictionary Learning / Incoherence / Proximal operator / Alternating optimization |
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| Outline of Annual Research Achievements |
We worked out a fast, efficient algorithm for learning an overcomplete dictionary for sparse representation of signals. The whole problem is considered as a minimization of the approximation error function with a coherence penalty for the dictionary atoms and with the sparsity regularization of the coefficient matrix. Because the problem is nonconvex and nonsmooth, this minimization problem cannot be solved efficiently by an ordinary optimization method. We propose a decomposition scheme and an alternating optimization that can turn the problem into a set of minimizations of piecewise quadratic and univariate subproblems, each of which is a single variable vector problem, either of one dictionary atom or one coefficient vector. Although the subproblems are still nonsmooth, remarkably, they become much simpler so that we can find a closed-form solution by introducing a proximal operator. This leads an efficient algorithm for sparse representation. The main advantages of the proposed algorithm are that, as suggested by our analysis and simulation study, it has lower computational complexity and a higher convergence rate than state-of-the-art algorithms. In addition, for real applications, it shows good performance and significant reductions in computational time. The paper has been accepted for a publication by Neural computation. We also worked out a fast blind source separation algorithm based on the temporal structure of signals. The paper was published in Neurocomputing.
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