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| DC 欄位 | 值 | 語言 |
|---|---|---|
| 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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[2] H. Attouch, J. Bolte, and B. F. Svaiter. Convergence of descent methods for semialgebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized gauss–seidel methods. Mathematical Programming, 137(1):91–129, 2013. [3] H. H. Bauschke and P. L. Combettes. Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer International Publishing, 2 edition, 2017. [4] A. Borsic, B. M. Graham, A. Adler, and W. R. Lionheart. In vivo impedance imaging with total variation regularization. IEEE transactions on medical imaging, 29(1):44-54, 2010. [5] S. Boyd and L. Vandenberghe. Convex optimization. Cambridge university press, 2004. [6] A. Chambolle and T. Pock. A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of Mathematical Imaging and Vision, 40(1):120-145, May 2011. [7] K.-S. Cheng, D. Isaacson, J. C. Newell, and D. G. Gisser. Electrode models for electric current computed tomography. IEEE Transactions on Biomedical Engineering, 36(9):918-924, Sept 1989. [8] H. Garde and S. Staboulis. Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography. Numerische Mathematik, 135(4):1221-1251, Apr 2017. [9] M. Gehre, T. Kluth, A. Lipponen, B. Jin, A. Seppanen, J. P. Kaipio, and P. Maass. Sparsity reconstruction in electrical impedance tomography: An experimental evaluation. Journal of Computational and Applied Mathematics, 236(8):2126-2136, 2012. Inverse Problems: Computation and Applications. [10] G. Gonzalez, J. M. J. Huttunen, V. Kolehmainen, A. Seppanen, and M. Vauhkonen. Experimental evaluation of 3d electrical impedance tomography with total variation prior. Inverse Problems in Science and Engineering, 24(8):1411-1431, 2016. [11] G. Gonzalez, V. Kolehmainen, and A. Seppanen. Isotropic and anisotropic total variation regularization in electrical impedance tomography. Computers & Mathematics with Applications, 74(3):564-576, 2017. [12] P. C. Hansen. Analysis of discrete ill-posed problems by means of the l-curve. SIAM Review, 34(4):561-580, 1992. [13] B. Harrach and J. K. Seo. Exact shape-reconstruction by one-step linearization in electrical impedance tomography. SIAM Journal on Mathematical Analysis, 42(4):1505-1518, 2010. [14] B. Harrach and M. Ullrich. Resolution guarantees in electrical impedance tomography. IEEE transactions on medical imaging, 34(7):1513-1521, 2015. [15] D. R. Hunter and K. Lange. A tutorial on MM algorithms. The American Statistician, 58(1):30-37, 2004. [16] B. Jin, T. Khan, and P. Maass. A reconstruction algorithm for electrical impedance tomography based on sparsity regularization. International Journal for Numerical Methods in Engineering, 89(3):337-353. [17] J. P. Kaipio, V. Kolehmainen, E. Somersalo, and M. Vauhkonen. Statistical inversion and monte carlo sampling methods in electrical impedance tomography. Inverse Problems, 16(5):1487, 2000. [18] V. Kolehmainen, M. Vauhkonen, P. A. Karjalainen, and J. P. Kaipio. Assessment of errors in static electrical impedance tomography with adjacent and trigonometric current patterns. Physiological Measurement, 18(4):289, 1997. [19] D. Liu, A. K. Khambampati, and J. Du. A parametric level set method for electrical impedance tomography. IEEE Transactions on Medical Imaging, 37(2):451-460, Feb 2018. [20] Y. Nesterov. Introductory Lectures on Convex Optimization, volume 87. Springer US, 2004. [21] T. Pock and A. Chambolle. Diagonal preconditioning for first order primal-dual algorithms in convex optimization. In 2011 International Conference on Computer Vision, pages 1762-1769, Nov 2011. [22] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, New York, NY, USA, 3 edition, 2007. [23] R. T. Rockafellar and R. J.-B. Wets. Variational Analysis, volume 317. Springer-Verlag Berlin Heidelberg, 1998. [24] S. L. Shmakov. A universal method of solving quartic equations. International Journal of Pure and Applied Mathematics, 71(2):251-259, 2011. [25] E. Somersalo, M. Cheney, and D. Isaacson. Existence and uniqueness for electrode models for electric current computed tomography. SIAM Journal on Applied Mathematics, 52(4):1023-1040, 1992. [26] M. Vauhkonen, D. Vadasz, P. A. Karjalainen, E. Somersalo, and J. P. Kaipio. Tikhonov regularization and prior information in electrical impedance tomography. IEEE transactions on medical imaging, 17(2):285-293, 1998. [27] P. J. Vauhkonen, M. Vauhkonen, T. Savolainen, and J. P. Kaipio. Three-dimensional electrical impedance tomography based on the complete electrode model. IEEE Transactions on Biomedical Engineering, 46(9):1150-1160, 1999. [28] S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo. Sparse reconstruction by separable approximation. IEEE Transactions on Signal Processing, 57(7):2479-2493, July 2009. | |
| 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.subject | 電阻抗斷層掃描 | zh_TW |
| dc.subject | 最佳化-最小限度化演算法 | zh_TW |
| dc.subject | Electrical impedance tomography | en |
| dc.subject | majorization-minimization algorithm | 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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