2015 Fiscal Year Final Research Report
Sparse signal processing based on convex analysis and information geometry and its applications
| Project/Area Number |
24760292
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Communication/Network engineering
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| Research Institution | Keio University (2013-2015)
Niigata University (2012) |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | スパース最適化 / Lp準ノルム / LARS法 / ホモトピー法 |
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| Outline of Final Research Achievements |
The structures of two least square problems (Lp-regularized least squares and Lp-constrained least squares for 0<p<1) have been elucidated. First, for the over-determined linear system, the essential difference between the two problems has been clarified, and the relation between the least squares based on the Lp quasi-norm and the greedy algorithm for sparse optimization has been established. Second, for the under-determined system, the existence of a continuous path that connects the origin and the sparsest least square solution has been proven mathematically under a certain condition. Third, the obtained results have been applied to the sparse/kernel adaptive filters.
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| Free Research Field |
信号処理
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