請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10466完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳宜良(I-Liang Chern) | |
| dc.contributor.author | Hao-Pin Wu | en |
| dc.contributor.author | 吳浩平 | zh_TW |
| dc.date.accessioned | 2021-05-20T21:31:46Z | - |
| dc.date.available | 2011-08-22 | |
| dc.date.available | 2021-05-20T21:31:46Z | - |
| dc.date.copyright | 2011-08-22 | |
| dc.date.issued | 2011 | |
| dc.date.submitted | 2011-08-18 | |
| dc.identifier.citation | [1] H. Aben and C. Guillemet, Photoelasiticity of Glass, Springer-Verlag Berlin Heidelberg, 1993.
[2] M. Baake and U. Schlagel, The peano-baker series. 2010. [3] Y. A. Kravtsov, O. N. Naida, and A. A. Fuki, Waves in weakly anisotropic 3d inhomogeneous media: quasi-isotropic approximation of geometrical optics, Physics–Uspekhi, 39 (1996), pp. 129–154. [4] W. Lionheart and V. Sharafutdinov, Reconstuction algorithm for the linearized polarization tomography problem with incomplete data, Imaging Microstructures: Mathematical and Computational Challenges, 494 (2009), pp. 131–159. [5] R. Novikov and V. Sharafutdinov, On the problem of polarization tomography: I, Inverse Problems, 23 (2007), pp. 1229–1257. [6] V. Sharafutdinov, Integral Geometry of Tensor Fields, Walter de Gruyter, 1994. [7] V. Sharafutdinov, Slice-by-slice reconstruction algorithm for vector tomography with incomplete data, Inverse Problems, 23 (2007), p. 2603–2627. [8] V. Sharafutdinov, On the problem of polarization tomography: Ii, Inverse Problems, 24 (2008), p. 035010. [9] X.-C. Tai and C. Wu, Augmented lagrangian method, dual methods and split bregman iteration for rof model, in Scale Space and Variational Methods in Computer Vision, X.-C. Tai, K. Mørken, M. Lysaker, and K.-A. Lie, eds., vol. 5567 of Lecture Notes in Computer Science, Springer Berlin / Heidelberg, 2009, pp. 502–513. [10] J. Yang, Y. Zhang, and W. Ying, A fast alternating direction method for tvl1-l2 signal reconstruction from partial fourier data, IEEE Journal of Selected Topics in Signal Processing, 4 (2010), pp. 288–297. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10466 | - |
| dc.description.abstract | 集成光彈是一藉由偏振光學技術來測定光彈材料內應力分佈的方法,其造影過程可由 Sharafutdinov 提出的截斷橫向射線變換所描述。在這篇論文中,我們利用此一模型將其重建問題置於 TV-L2 極小化的框架下,並結合代數重建法和增廣拉格朗日法提出其對應的數值重建過程。 | zh_TW |
| dc.description.abstract | Integrated photoelsticity is a method for determining stress distribution in photoelastic materials by polaried optical techniques. An important model describes the imaging process is truncated transverse ray transform (TTRT) proposed by Sharafutdinov. In this article, we use this model to fit the reconstruction problem into a TV-L2 minimization scheme and propose a numerical reconstruction method combining algebraic reconstruction technique and augmented Lagrangian method. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T21:31:46Z (GMT). No. of bitstreams: 1 ntu-100-R97221026-1.pdf: 1001754 bytes, checksum: 516e84ab96f3675dbfec7ef3114e8c06 (MD5) Previous issue date: 2011 | en |
| dc.description.tableofcontents | 中文摘要 i
Abstract ii 1 Introduction 1 2 Photoelasticity 3 2.1 Stress-Optic Law 3 2.2 Polarized light 7 2.3 Integrated Photoelasticity 11 2.4 Transverse Ray Transform 14 2.5 The Polarization Ellipse 16 2.6 Truncated Transverse Ray Transform 19 3 Reconstruction Methods 21 3.1 Aben's method 21 3.2 Sharafutdinov's Methods 24 3.3 Lioheart and Sharafutdinov's Method 25 3.3.1 Logitudinal Ray Transform (LRT) 26 3.3.2 Inversion Formula of LRT 27 3.3.3 Algebraic Equations in Fourier Space 28 4 Augmented Lagragian Method 30 4.1 Augmented Lagrangian Method 30 4.2 Alternating Direction Method 31 5 Numerical Results 33 5.1 Numerical Settings 33 5.2 Results 33 5.3 Summary 47 6 Conclusion and Future Works 48 Bibliography 50 | |
| dc.language.iso | en | |
| dc.title | 利用增廣拉格朗日法重建光彈斷層掃描影像 | zh_TW |
| dc.title | Reconstruct Photoelastic Tomography via Augmented Lagrangian Method | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 99-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王偉成(Wei-Cheng Wang),陳鵬文(Pengwen Chen) | |
| dc.subject.keyword | 增廣拉格朗日法,光彈斷層掃描,偏振光,重建,截斷橫向射線變換,總變差正規化, | zh_TW |
| dc.subject.keyword | augmented Lagrangian method,photoelastic tomography,polarized light,reconstruction,truncated transverse ray transform,TV regularization, | en |
| dc.relation.page | 51 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2011-08-19 | |
| 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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|---|---|---|---|
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