2023 Fiscal Year Final Research Report
Enhancing Signal Processing Algorithms with Real-Algebraic Methods
| Project/Area Number |
18K18122
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 61040:Soft computing-related
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| Research Institution | Hosei University (2023)
Tokyo Institute of Technology (2018-2022) |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2024-03-31
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| Keywords | 信号処理工学 / 最適化工学 / 最適化アルゴリズム |
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| Outline of Final Research Achievements |
To develop advanced methods that simultaneously utilize observation and prior information for various problems in signal processing, we have proposed algorithmic solutions for several non-convex optimization problems. Our research achievements include (i) effective non-convex regularizations that promote sparsity in vectors and low-rankness in matrices, as well as least squares estimation with the proposed regularizations, (ii) an algorithm for estimating piecewise continuous functions, and (iii) a method for automatic design of the sparsity-controlling parameter in sparse adaptive filtering through a reduction to the minimization of piecewise quadratic functions.
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| Free Research Field |
信号処理工学，最適化工学
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| Academic Significance and Societal Importance of the Research Achievements |
信号処理は，劣悪な環境で観測された信号から雑音などを取り除き，有益な情報を顕在化する処理は様々な分野で陰に陽に役立っている．著名な例として,MRI画像の撮影にかかる時間を短縮し被撮影者の負担を軽減する技術の実現やEHT Collaborationによるブラックホール撮影では，推定対象のスパース性の活用が重要な役割を果たしている．本研究の成果は，スパース性のさらなる活用を実現する基盤的な手法を与えており，スパース性を活用している既存手法に対して，推定精度の改善方法を提示している．
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