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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳宜良(I-Liang Chern) | |
| dc.contributor.author | Yu-Shiuan Tsai | en |
| dc.contributor.author | 蔡宇軒 | zh_TW |
| dc.date.accessioned | 2021-06-13T16:26:17Z | - |
| dc.date.available | 2007-07-27 | |
| dc.date.copyright | 2005-07-27 | |
| dc.date.issued | 2005 | |
| dc.date.submitted | 2005-07-15 | |
| dc.identifier.citation | [1] L.Rudin; S.Osher; E.Fatemi. Nonlinear total variation based noise removal
algorithms.'Phys.D,60(1992),pp.73{130. [2] Rieder, Andreas. Wavelet multilevel solvers for linear ill-posed problems stabilized by Tikhonov regularization.' Multiscale wavelet methods for partial di erential equations, 347{380, Wavelet Anal. Appl., 6, Academic Press, San Diego, CA, 1997. [3] Hanke, Martin; Vogel, Curtis R. Two-level preconditioners for regularized inverse problems. I. Theory.' (English. English summary) Numer. Math. 83 (1999), no. 3, 385{402. [4] Acar, R.; Vogel, C. R. Analysis of bounded variation penalty methods for illposed problems.' Inverse Problems 10 (1994), no. 6, 1217{1229. [5] R.Chan; T.Chan; H.Zhou. In proceedings of the International Society of Photo- Optical Instrumentation Engineers.' Advanced signal processing algorithms. F.Luk,ed.SPIE(1995),pp.314{325. [6] Chan, Raymond H.; Chan, Tony F.; Wan, W. L. Multigrid for di erentialconvolution problems arising from image processing.' Scienti c computing (Hong Kong, 1997), 58{72, Springer, Singapore, 1997. [7] Chang, Qianshun; Chern, I-Liang Acceleration methods for total variationbased image denoising.' (English. English summary) SIAM J. Sci. Comput. 25 (2003), no. 3, 982{994 (electronic). [8] R. Chan and X.Q. Jin. A family of block preconditioners for block system.' SIAM J. Sci. Comput., 13(5), 1218{1235, 1992. [9] Vogel, Curtis R.; Oman, Mary E. Fast, robust total variation-based reconstruction of noisy, blurred images.' (English. English summary) IEEE Trans. Image Process. 7 (1998), no. 6, 813{824. [10] Dobson, David C.; Vogel, Curtis R. Convergence of an iterative method for total variation denoising.' (English. English summary) SIAM J. Numer. Anal. 34 (1997), no. 5, 1779{1791. [11] Vogel, C. R. A multigrid method for total variation-based image denoising.' Computation and control, IV (Bozeman, MT, 1994), 323{331, Progr. Systems Control Theory, 20, Birkhauser Boston, Boston, MA, 1995. [12] Dalmasso, Robert An inverse problem for an elliptic equation with an a ne term.' (English summary) Math. Ann. 316 (2000), no. 4, 771{792. [13] Vogel, Curtis R. An overview of numerical methods for nonlinear ill-posed problems.' Inverse and ill-posed problems (Sankt Wolfgang, 1986), 231{245, Notes Rep. Math. Sci. Engrg., 4, Academic Press, Boston, MA, 1987. [14] Vogel, C. R. Numerical solution of a nonlinear ill-posed problem arising in inverse scattering.' Inverse Problems 1 (1985), no. 4, 393{403. [15] Vogel, C. R.; Oman,M. E. Iterative methods for total variation denoising.' (English summary) Special issue on iterative methods in numerical linear algebra (Breckenridge, CO, 1994). SIAM J. Sci. Comput. 17 (1996), no. 1, 227{238. [16] Acar, R.; Vogel, C. R. Analysis of bounded variation penalty methods for illposed problems.' (English. English summary) Inverse Problems 10 (1994), no. 6, 1217{1229. [17] Vogel, C. R.; Wade, J. G. Iterative SVD-based methods for ill-posed problems.' (English. English summary) Iterative methods in numerical linear algebra (Copper Mountain Resort, CO, 1992). SIAM J. Sci. Comput. 15 (1994), no. 3, 736{754. [18] A.K.Jain. Fundamentals of Digital Image Processing. Prentice-Hall, New York(1989). [19] Vogel, Curtis R. Computational Methods for Inverse Problems. SIAM.Philadelphia(2002). [20] Hanke, Martin; Nagy, James G.; Vogel, Curtis Quasi-Newton approach to nonnegative image restorations.' (English. English summary) Conference Celebrating the 60th Birthday of Robert J. Plemmons (Winston-Salem, NC, 1999). Linear Algebra Appl. 316 (2000), no. 1-3, 223{236. [21] C.W.Groetsch. Inverse problems in the Mathematical Sciences, Vieweg, Braunschweig (1993). [22] R. Chan, J. Nagy, and R. Plemmons. Circulant preconditioned Toeplitz least squares iterations.' SIAM J. Matrix Anal. Appl., 15(1) 80{97, 1994. [23] C.R. Vogel and M. Hanke,Two-level preconditioners for regularized inverse problems II: Implementation and numerical results', preprint [24] Kyle Riley, Two-Level Preconditioners for Regularized Ill-Posed Problems', Ph.D. Thesis, July 1999. [25] K. Riley and C.R. Vogel, Preconditioners for Linear Systems Arising in Image Reconstruction', Proc. SPIE 3461-37, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII (1998). [26] Chan, Tony F.; Mulet, Pep, Iterative methods for total variation image restoration.' Iterative methods in scienti c computing (Hong Kong, 1995), 359{381, Springer, Singapore, 1997. [27] T.F. Chan and J. Olkin. Circulant preconditioners for Toeplitz-block matrices.' Numer. Algorithms, 6, 89{101, 1994. [28] Gene H. Golub, Charles F. Van Loan. Matrix computations.Johns Hopkins University Press, 1996. 3rd ed. [29] Yousef Saad. Iterative methods for sparse linear systems.' Boston : PWS Pub. Co., c1996. [30] G.Strang. A proposal for Toeplitz matrix calculations.' Stud. Appl. Math, 74, 171{176, 1986. [31] T.F. Chan. An optimal circulant preconditioner for Toeplitz systems.' SIAM Sci. Stat. Comput., 9 766{771, 1988. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/38090 | - |
| dc.description.abstract | 在影像處理中，對於影像的去雜訊與去模糊問題一直研究的課題，而去雜訊與去模糊本身就是背道而馳。
在第二章中，定義 toeplitz 與 circulant 矩陣以及 block toeplitz 與 block circulant 結構，並將離散型傅立葉變換應用於模糊算子K中，加速模糊算子作用於影像的速度。最後定義粗網格子空間以供網格的分解。 在第三章中，利用 two-level preconditioner 於 ill-conditiond 方程組 Au=b，並對粗網格使用共軛梯度法。之後使用Schur Complement Conjugate Gredient 演算法。 在第四章中，介紹實際使用此演算法的細節，並將結果畫於圖中。 | zh_TW |
| dc.description.abstract | This paper is organized as follows. In section 2, we introduce some notations and properties which will be used. In section 3, two-level preconditioner is referred. And finally, in chapter 4 we make numerical test based on the above methods. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T16:26:17Z (GMT). No. of bitstreams: 1 ntu-94-R91221016-1.pdf: 439550 bytes, checksum: 2c763679f80360e2a0f77fc9bdc51ab9 (MD5) Previous issue date: 2005 | en |
| dc.description.tableofcontents | Table of Contents iv
1 Introduction 1 2 Notations 4 2.1 Toeplitz and Circulant matrices. . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Block Toeplitz and Block circulant Matrices . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Discrete Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Coarse Grid Subspace . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Two-Level Preconditioning 9 3.1 Schur Complement Method . . . . . . . . . . . . . . . . . . . . . . . . . 10 4 Implementation 14 4.1 What is the question? . . . . . . . . .. . . . . . . . . . . . . . . 14 4.2 Details . . . . . . . . . . .. . . . . . . . . . . . . . 15 4.2.1 Implementation for and . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2.2 Approximation of KK . . . . . . . . . . . . . . . . . . . . . . . . . . .18 4.2.3 Compute A.......................................19 Bibliography...........................................23 | |
| dc.language.iso | en | |
| dc.subject | 影像重建 | zh_TW |
| dc.subject | 雙重預處理矩陣 | zh_TW |
| dc.title | 雙重預處理矩陣於影像重建的應用 | zh_TW |
| dc.title | Two-Level preconditioners for Image Restoration Problem | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 93-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王偉成(Wei-Cheng Wang),黃文良(Wen-Liang Hwang),周謀鴻(Mo-Hong Chou) | |
| dc.subject.keyword | 雙重預處理矩陣,影像重建, | zh_TW |
| dc.subject.keyword | Two-Level preconditioners,Image Restoration, | en |
| dc.relation.page | 26 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2005-07-15 | |
| 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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