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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/83481完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 劉俊麟 | zh_TW |
| dc.contributor.advisor | Chun-Lin Liu | en |
| dc.contributor.author | 張祐銓 | zh_TW |
| dc.contributor.author | You-Quan Zhang | en |
| dc.date.accessioned | 2023-03-19T21:08:34Z | - |
| dc.date.available | 2023-11-10 | - |
| dc.date.copyright | 2022-09-12 | - |
| dc.date.issued | 2022 | - |
| dc.date.submitted | 2002-01-01 | - |
| dc.identifier.citation | [1] Z. Yue, S. Chen, and L. Tham, “Finite element modeling of geomaterials using digital image processing,” Computers and Geotechnics, vol. 30, no. 5, pp. 375–397, 2003.
[2] S. E. Reichenbach, S. K. Park, and R. Narayanswamy, “Characterizing digital image acquisition devices,” Optical Engineering, vol. 30, no. 2, pp. 170–177, 1991. [3] A. C. Bovik, Handbook of image and video processing. Academic press, 2010. [4] A. Buades, B. Coll, and J.-M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Modeling & Simulation, vol. 4, no. 2, pp. 490–530, 2005. [5] G. Papari, N. Petkov, and P. Campisi, “Artistic edge and corner enhancing smoothing,” IEEE Transactions on Image Processing, vol. 16, no. 10, pp. 2449–2462, 2007. [6] L. Fan, F. Zhang, H. Fan, and C. Zhang, “Brief review of image denoising techniques,” Visual Computing for Industry, Biomedicine, and Art, vol. 2, no. 1, pp. 1–12, 2019. [7] S. Esakkirajan, T. Veerakumar, A. N. Subramanyam, and C. PremChand, “Removal of high density salt and pepper noise through modified decision based unsymmetric trimmed median filter,” IEEE Signal Processing Letters, vol. 18, no. 5, pp. 287–290, 2011. [8] D. N. H. Thanh, V. B. S. Prasath, and L. T. Thanh, “Total variation l1 fidelity salt-and-pepper denoising with adaptive regularization parameter,” in 2018 5th NAFOSTED Conference on Information and Computer Science (NICS). IEEE, Nov. 2018. [Online]. Available: https://doi.org/10.1109%2Fnics.2018.8606870 [9] K. H. Jin and J. C. Ye, “Sparse and low-rank decomposition of a hankel structured matrix for impulse noise removal,” IEEE Transactions on Image Processing, vol. 27, no. 3, pp. 1448–1461, 2018. [10] Y. Lee and S. Kassam, “Generalized median filtering and related nonlinear filtering techniques,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 33, no. 3, pp. 672–683, 1985. [11] X. Jiang, Z. Zhong, X. Liu, and H. C. So, “Robust matrix completion via alternating projection,” IEEE Signal Processing Letters, vol. 24, no. 5, pp. 579–583, 2017. [12] X. Jiang, A. M. Zoubir, and X. Liu, “Robust matrix completion via ℓ p-greedy pursuits,” in ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2020, pp. 5984–5988. [13] D. Fleet and Y. Weiss, “Optical flow estimation,” in Handbook of mathematical models in computer vision. Springer, 2006, pp. 237–257. [14] C. Zach, T. Pock, and H. Bischof, “A duality based approach for realtime tv-l 1 optical flow,” in Joint pattern recognition symposium. Springer, 2007, pp. 214–223. [15] J. Xu, X. Feng, Y. Hao, and Y. Han, “Image decomposition and staircase effect reduction based on total generalized variation,” Journal of Systems Engineering and Electronics, vol. 25, no. 1, pp. 168–174, 2014. [16] C. R. Rojas and B. Wahlberg, “How to monitor and mitigate stair-casing in l1 trend filtering,” in 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2015, pp. 3946–3950. [17] J. Xiang, P. Ye, L. Wang, and M. He, “A novel image-restoration method based on high-order total variation regularization term,” Electronics, vol. 8, no. 8, p. 867, 2019. [18] K. H. Jin and J. C. Ye, “Annihilating filter-based low-rank hankel matrix approach for image inpainting,” IEEE Transactions on Image Processing, vol. 24, no. 11, pp. 3498–3511, 2015. [19] J. Azzeh, B. Zahran, and Z. Alqadi, “Salt and pepper noise: Effects and removal,” JOIV: International Journal on Informatics Visualization, vol. 2, no. 4, pp. 252–256, 2018. [20] H. C. Andrews and B. R. Hunt, “Digital image restoration,” 1977. [21] H. Rue and L. Held, Gaussian Markov random fields: theory and applications. Chapman and Hall/CRC, 2005. [22] G. R. Cross and A. K. Jain, “Markov random field texture models,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-5, no. 1, pp. 25–39, 1983. [23] R. Chellappa and S. Chatterjee, “Classification of textures using gaussian markov random fields,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 33, no. 4, pp. 959–963, 1985. [24] F. S. Cohen, Z. Fan, and M. A. Patel, “Classification of rotated and scaled textured images using gaussian markov random field models,” IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 13, no. 02, pp. 192–202, 1991. [25] B. Manjunath and R. Chellappa, “Unsupervised texture segmentation using markov random field models,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 5, pp. 478–482, 1991. [26] J. Woods, “Two-dimensional discrete markovian fields,” IEEE Transactions on Information Theory, vol. 18, no. 2, pp. 232–240, 1972. [27] L. R. Rabiner and B. Gold, “Theory and application of digital signal processing,” Englewood Cliffs: Prentice-Hall, 1975. [28] P. Sidén and F. Lindsten, “Deep gaussian markov random fields,” in International Conference on Machine Learning. PMLR, 2020, pp. 8916–8926. [29] D. A. Turkington, Generalized vectorization, cross-products, and matrix calculus. Cambridge University Press, 2013. [30] H. Jeffreys, The theory of probability. OUP Oxford, 1998. [31] H. Akaike, “Block toeplitz matrix inversion,” SIAM Journal on Applied Mathematics, vol. 24, no. 2, pp. 234–241, 1973. [32] M. Semelhago, B. L. Nelson, A. Wächter, and E. Song, “Computational methods for optimization via simulation using gaussian markov random fields,” in 2017 Winter Simulation Conference (WSC), 2017, pp. 2080–2091. [33] J. R. Magnus and H. Neudecker, Matrix differential calculus with applications in statistics and econometrics. John Wiley & Sons, 2019. [34] Y. Chen and Y. Chi, “Spectral compressed sensing via structured matrix completion,” in International Conference on Machine Learning. PMLR, 2013, pp. 414-422. [35] K. Hoffman, Linear algebra. Englewood Cliffs, NJ, Prentice-Hall, 1971. [36] H. Hwang and R. Haddad, “Adaptive median filters: new algorithms and results, IEEE Transactions on Image Processing, vol. 4, no. 4, pp. 499–502, 1995. [37] R. C. Gonzalez, Digital image processing. Pearson education india, 2009. [38] M. Fazel, “Matrix rank minimization with applications,” Ph.D. dissertation, PhD thesis, Stanford University, 2002. [39] M. Fazel, H. Hindi, and S. Boyd, “Rank minimization and applications in system theory,” in Proceedings of the 2004 American control conference, vol. 4. IEEE, 2004, pp. 3273–3278. [40] V. Koltchinskii, K. Lounici, and A. B. Tsybakov, “Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion,” The Annals of Statistics, vol. 39, no. 5, pp. 2302–2329, 2011. [41] C. Eckart and G. Young, “The approximation of one matrix by another of lower rank,” Psychometrika, vol. 1, no. 3, pp. 211–218, 1936. [42] J. E. Jackson, A user’s guide to principal components. John Wiley & Sons, 2005. [43] R. T. Rockafellar, “Lagrange multipliers and optimality,” SIAM Review, vol. 35, no. 2, pp. 183–238, 1993. [44] S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein et al., “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Foundations and Trends® in Machine learning, vol. 3, no. 1, pp. 1–122, 2011. [45] M. Signoretto, V. Cevher, and J. Suykens, “An svd-free approach to a class of structured low rank matrix optimization problems with application to system identification,” in IEEE Conference on Decision and Control (CDC). Citeseer, 2013. [46] E. J. Candes and Y. Plan, “Matrix completion with noise,” Proceedings of the IEEE, vol. 98, no. 6, pp. 925–936, 2010. [47] M. A. Davenport and J. Romberg, “An overview of low-rank matrix recovery from incomplete observations,” IEEE Journal of Selected Topics in Signal Processing, vol. 10, no. 4, pp. 608–622, 2016. [48] E. J. Candès and T. Tao, “The power of convex relaxation: Near-optimal matrix completion,” IEEE Transactions on Information Theory, vol. 56, no. 5, pp. 2053–2080, 2010. [49] B. Recht, M. Fazel, and P. A. Parrilo, “Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization,” SIAM Review, vol. 52, no. 3, pp. 471–501, 2010. [50] Z. Liu and L. Vandenberghe, “Interior-point method for nuclear norm approximation with application to system identification,” SIAM Journal on Matrix Analysis and Applications, vol. 31, no. 3, pp. 1235–1256, 2010. [51] P. McCullagh and J. A. Nelder, Generalized linear models. Routledge, 2019. [52] R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the Royal Statistical Society: Series B (Methodological), vol. 58, no. 1, pp. 267–288, 1996. [53] J. Fan and R. Li, “Variable selection via nonconcave penalized likelihood and its oracle properties,” Journal of the American Statistical Association, vol. 96, no. 456, pp. 1348–1360, 2001. [54] M. Y. Park and T. Hastie, “L1-regularization path algorithm for generalized linear models,” Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 69, no. 4, pp. 659–677, 2007. [55] B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression, The Annals of Statistics, vol. 32, no. 2, pp. 407–499, 2004. [56] N. Srebro, “Learning with matrix factorizations,” 2004. [57] J.-J. Wei, C.-J. Chang, N.-K. Chou, and G.-J. Jan, “Ecg data compression using truncated singular value decomposition,” IEEE Transactions on Information Technology in Biomedicine, vol. 5, no. 4, pp. 290–299, 2001. [58] A. Tarantola, Inverse problem theory and methods for model parameter estimation. SIAM, 2005. [59] ——, “Popper, Bayes and the inverse problem,” Nature Physics, vol. 2, no. 8, pp. 492–494, 2006. [60] J. J. Shynk, Probability, random variables, and random processes: theory and signal processing applications. John Wiley & Sons, 2012. [61] A. Chambolle, “An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, vol. 20, no. 1, pp. 89–97, 2004. [62] D. N. H. Thanh, L. T. Thanh, N. N. Hien, and S. Prasath, “Adaptive total variation l1 regularization for salt and pepper image denoising,” Optik, vol. 208, p. 163677, Apr. 2020. [Online]. Available: https://doi.org/10.1016%2Fj.ijleo.2019.163677 [63] A. Mordvintsev, “Rof and tv-l1 denoising with primal-dual algorithm,” 2017. [64] A. Chambolle, V. Caselles, D. Cremers, M. Novaga, and T. Pock, “An introduction to total variation for image analysis,” Theoretical Foundations and Numerical Methods for Sparse Recovery, vol. 9, no. 263-340, p. 227, 2010. [65] M. Lourakis, “Tv-l1 image denoising algorithm(https://www.mathworks.com/matlabcentral/fileexchange/57604-tv-l1-image denoising-algorithm),” 2022. [66] H. Hua Yang and Y. Hua, “On rank of block hankel matrix for 2-d frequency detection and estimation,” IEEE Transactions on Signal Processing, vol. 44, no. 4, pp. 1046–1048, 1996. [67] L. Brand, Vector and tensor analysis. Courier Dover Publications, 2020. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/83481 | - |
| dc.description.abstract | 在圖像處理中，由於各種原因，例如相機傳感器中的像素故障或硬體中的記 憶體位置錯誤，圖像通常會受到脈衝噪聲的破壞。脈衝噪聲有一種常見的類型， 稱為鹽和胡椒雜訊。當圖像被鹽和胡椒雜訊破壞時，噪聲像素僅取最大值或最小 值，從而導致圖像上出現白點和黑點。
目前已有一些處理鹽和胡椒雜訊的方法，這些方法包括基於中值濾波器的方 法、基於低秩矩陣補齊的方法、TV-L1 方法以及基於湮滅濾波器的方法。這些方 法在低強度的鹽和胡椒雜訊下都有著不錯的表現，但基於中值濾波器的方法及基 於低秩矩陣補齊的方法在高水平的鹽和胡椒雜訊下其效能並不令人滿意。 在我們的模擬中，對於高噪聲水平，基於湮滅濾波器的方法可以實現最高的 效能。作為交換，它們在過程中需要最多的時間，因為它們處理了大型漢克爾矩 陣 H (X) 的最佳化問題。 對於基於湮滅濾波器的方法，我們開發了一個停止標準，以獲得更好的去噪 性能。如果沒有停止標準，它通常會花更多的計算資源而獲得更低的效能。此外， 我們提出一種方法將最佳化問題分別作處理，對於矩陣 H (X)，我們將其分割成 p × q 塊，並分別對其作低秩最佳化。透過不同 p × q 值的選擇，在不同的情況下， 我們可以在峰值信噪比與時間成本之間做權衡。 我們對於漢克爾矩陣的結構進行了詳細的解釋，還介紹了運算子 H (·) 的逆運算。為了將基於湮滅濾波器的方法應用於彩色圖像，我們為彩色影像定義了 H3D(X)，並解釋如何構造 H3D(X)。 | zh_TW |
| dc.description.abstract | In image processing, images are usually corrupted by impulse noise due to a wide variety of reasons, such as malfunctioning pixels in camera sensors or faulty memory locations in hardware. The impulse noise has a common type called salt-and-pepper noise (SPN). When images are corrupted by SPN, the noisy pixels take only the maximum value or the minimum value, contributing to white and black dots on images.
There are some known methods for dealing with SPN. These methods include me- dian filter-based methods, low-rank matrix completion-based methods, TV-L1 method, and annihilating filter-based methods. These methods have a good performance on noise reduction for the low level of SPN. But the performance of median filter-based methods and low-rank matrix completion-based methods are not satisfactory for the high level of SPN noise. In our simulation, for high noise levels, annihilating filter-based methods achieve the highest performance. In exchange, they need the most time in the process, because they solve optimization problems for a large Hankel matrix H (X). For annihilating filter-based methods, a stop criterion is developed for a good perfor- mance of denoising. Without the stop criterion, it often uses more computing resources to obtain lower performance. Further, we propose an approach that solves the optimization problem separately, for matrix H (X), we split it into p × q pieces and apply low-rank op- timization to each piece. With different choices of p × q, we can make a trade-off between PSNR value and time cost in some cases. The interpretation of the Hankel matrix structure is explained in detail. We also in- troduce the inverse operation of the operator H (·). To apply annihilating filter-based methods to a color image, we define H3D(X) for a color image, and we explain how to construct H3D(X). | en |
| dc.description.provenance | Made available in DSpace on 2023-03-19T21:08:34Z (GMT). No. of bitstreams: 1 U0001-1708202215275700.pdf: 30286760 bytes, checksum: 7234c9b2e91ae15e7c415d4e48aabdd0 (MD5) Previous issue date: 2022 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i
Acknowledgements iii 摘要 v Abstract vii Contents ix List of Figures xiii List of Tables xv Chapter 1 Introduction 1 1.1 Overview and Motivation . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Chapter 2 Preliminaries 7 2.1 Introduction of salt-and-pepper noise . . . . . . . . . . . . . . . . . 7 2.2 Review of Annihilating Filter-Based Hankel matrix . . . . . . . . . . 10 2.2.1 Gaussian Markov Random Fields . . . . . . . . . . . . . . . . . . . 10 2.2.2 Introduction of Hankel operator . . . . . . . . . . . . . . . . . . . . 12 Chapter 3 Review of Salt-and-Pepper Noise Removal Methods 21 3.1 Median Filter-Based methods . . . . . . . . . . . . . . . . . . . . . 21 3.1.1 Median Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.1.2 Adaptive Median Filter . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1.3 Modified Decision Based Unsymmetric Trimmed Median Filter . . 25 3.2 Low-Rank Matrix Completion-Based methods . . . . . . . . . . . . 27 3.2.1 Alternating Projection Method . . . . . . . . . . . . . . . . . . . . 27 3.2.1.1 Problem Formulation . . . . . . . . . . . . . . . . . . 27 3.2.1.2 Two Projection Operators . . . . . . . . . . . . . . . . 28 3.2.1.3 Alternating Projection Algorithm . . . . . . . . . . . . 30 3.2.2 ℓP -Greedy Pursuits Method . . . . . . . . . . . . . . . . . . . . . . 32 3.2.2.1 Problem Formulation . . . . . . . . . . . . . . . . . . 32 3.2.2.2 Derivation of Optimization Problems . . . . . . . . . . 34 3.2.2.3 ℓP Greedy Pursuits Algorithm . . . . . . . . . . . . . . 35 3.2.3 Illustration of Low-Rank Matrix Completion Based Methods . . . . 37 3.3 Annihilating Filter-Based Low-Rank Hankel Matrix Methods . . . . 42 3.3.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.3.2 Alternating Direction Method of Multiplier . . . . . . . . . . . . . 45 Chapter 4 Extension of Hankel-based Methods 49 4.1 Stop Criterion of the Iteration . . . . . . . . . . . . . . . . . . . . . 49 4.2 Indicator Function in the Loss of Optimization Problem . . . . . . . 56 4.3 Simulation of Salt-and-Pepper Noise Removal . . . . . . . . . . . . 58 4.3.1 Simulated environment . . . . . . . . . . . . . . . . . . . . . . . . 58 4.3.2 Parameter Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.3.3 Simulation Result . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.4 Splitted Low-Rank Hankel Matrix Method for Image Denoising . . . 70 4.4.1 Grouping of H(X) . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.4.2 Problem Derivation and Proposed Method . . . . . . . . . . . . . . 75 4.4.3 Simulation of Splitted Low-Rank Hankel Matrix Method . . . . . . 77 4.4.3.1 Parameter Setting . . . . . . . . . . . . . . . . . . . . 77 4.4.3.2 Simulation Result . . . . . . . . . . . . . . . . . . . . 78 4.5 Application on Color Images . . . . . . . . . . . . . . . . . . . . . . 88 4.5.1 Introduction of H3D(X) . . . . . . . . . . . . . . . . . . . . . . . . 88 4.5.1.1 Case of Filter in Size of m × n × 1 . . . . . . . . . . . 89 4.5.1.2 Case of Filter in Size of m × n × 3 . . . . . . . . . . . 90 4.5.2 Algorithm Reformulation . . . . . . . . . . . . . . . . . . . . . . . 90 4.5.3 Illustration of color image denoising . . . . . . . . . . . . . . . . . 92 Chapter 5 Conclusion and Future Outlook 97 References 99 Appendix A — Introduction of H {X} 107 A.1 The definition of block Hankel matrix . . . . . . . . . . . . . . . . . 107 A.2 The other interpretation of H (X) . . . . . . . . . . . . . . . . . . . 108 A.3 Pseudo inverse of operator H . . . . . . . . . . . . . . . . . . . . . 109 | - |
| dc.language.iso | zh_TW | - |
| dc.subject | 影像去噪 | zh_TW |
| dc.subject | 鹽和胡椒雜訊 | zh_TW |
| dc.subject | 低秩最佳化 | zh_TW |
| dc.subject | Low Rank Optimization | en |
| dc.subject | Image Denoising | en |
| dc.subject | Salt and Pepper Noise | en |
| dc.title | 基於低秩漢克爾方法實現鹽和胡椒去噪 | zh_TW |
| dc.title | Low-Rank Hankel Matrix-Based Methods for Salt-and-Pepper Denoising | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 110-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 馮世邁;蘇柏青 | zh_TW |
| dc.contributor.oralexamcommittee | See-May Phoong;Borching Su | en |
| dc.subject.keyword | 影像去噪,鹽和胡椒雜訊,低秩最佳化, | zh_TW |
| dc.subject.keyword | Image Denoising,Salt and Pepper Noise,Low Rank Optimization, | en |
| dc.relation.page | 110 | - |
| dc.identifier.doi | 10.6342/NTU202202514 | - |
| dc.rights.note | 未授權 | - |
| dc.date.accepted | 2022-09-08 | - |
| dc.contributor.author-college | 電機資訊學院 | - |
| dc.contributor.author-dept | 電信工程學研究所 | - |
| 顯示於系所單位： | 電信工程學研究所 | |
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