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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 陳宜良(I-Liang Chern) | |
dc.contributor.author | Yu-Guo Liu | en |
dc.contributor.author | 劉于國 | zh_TW |
dc.date.accessioned | 2021-07-11T15:47:59Z | - |
dc.date.available | 2021-08-14 | |
dc.date.copyright | 2018-08-14 | |
dc.date.issued | 2018 | |
dc.date.submitted | 2018-08-02 | |
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dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/79148 | - |
dc.description.abstract | 本論文對電阻抗斷層掃描協同一普遍類型的非光滑正則提出了一統整的最佳化-最小限度化(MM) 演算法,其中包含了稀疏與總變差正則。我們證明此提出之MM 演算法的全域收斂性,且呈現源自模擬數據的數值重建結果。此MM 演算法的數值結果顯示了對目標能量的快速遞減及對內含物的強度和位置有好的估計。此外,我們比較此MM演算法和廣為所用的高斯-牛頓法,此MM 演算法對模擬導電率有較好的逼近。 | zh_TW |
dc.description.abstract | In this paper, a unified majorization-minimization (MM) algorithm is proposed for electrical impedance tomography with a general type of nonsmooth convex regularization, including sparse and total variation regularizations.
We prove the global convergence of the proposed MM algorithm and show numerical reconstructions from simulated data. The numerical results of the MM algorithm show a fast decrease in objective energy and good estimates of the intensity and location of inclusions. Besides, we compare the MM algorithm to the widely used Gauss-Newton method, and the MM algorithm shows better approximation to the simulated conductivity. | en |
dc.description.provenance | Made available in DSpace on 2021-07-11T15:47:59Z (GMT). No. of bitstreams: 1 ntu-107-D97221004-1.pdf: 7165353 bytes, checksum: a54ff3f9165b04d68669f6ad334cc343 (MD5) Previous issue date: 2018 | en |
dc.description.tableofcontents | 1 Introduction 1
2 preliminary 3 3 Mathematical Modeling 5 3.1 Complete Electrode Model . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Finite Element Method based Model . . . . . . . . . . . . . . . . . . . . 8 3.3 Reconstruction using Regularization Problems . . . . . . . . . . . . . . . 10 4 A Majorizaton-Minimization Algorithm 15 5 The Computation 19 6 Numerical Results 25 6.1 FEM Simulation and Reconstruction Setup . . . . . . . . . . . . . . . . 26 6.2 Precalculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.3 Reconstructions using the MM-CP algorithm . . . . . . . . . . . . . . . 32 6.4 Comparison with the Gauss-Newton Method . . . . . . . . . . . . . . . . 41 7 Discussion 45 8 Conclusion 47 Appendices 49 A Proof of Proposition 1 49 B Proof of Proposition 2 51 C Proximity Operator Formulas 59 Bibliography 63 | |
dc.language.iso | en | |
dc.title | 電阻抗斷層掃描的一種最佳化-最小限度化演算法 | zh_TW |
dc.title | A Majorization-Minimization Algorithm for Electrical Impedance Tomography | en |
dc.type | Thesis | |
dc.date.schoolyear | 106-2 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 王振男(Jenn-Nan Wang),林發暄(Fa-Hsuan Lin),陳界山(Jein-Shan Chen),蔡德明(Charles T M Choi) | |
dc.subject.keyword | 電阻抗斷層掃描,最佳化-最小限度化演算法, | zh_TW |
dc.subject.keyword | Electrical impedance tomography,majorization-minimization algorithm, | en |
dc.relation.page | 66 | |
dc.identifier.doi | 10.6342/NTU201802389 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2018-08-02 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 數學研究所 | zh_TW |
顯示於系所單位: | 數學系 |
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