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題名 奇異值分解在影像處理上之運用
Singular Value Decomposition: Application to Image Processing
作者 顏佑君
Yen, Yu Chun
貢獻者 薛慧敏
顏佑君
Yen, Yu Chun
關鍵詞 奇異值分解
低階近似
影像處理
影像壓縮
去除影像雜訊
singular value decomposition
low rank approximation
image processing
image compression
image denoising
日期 2015
上傳時間 2-Nov-2015 15:59:52 (UTC+8)
摘要 奇異值分解(singular valve decomposition)是一個重要且被廣為運用的矩陣分解方法，其具備許多良好性質，包括低階近似理論(low rank approximation)。在現今大數據(big data)的年代，人們接收到的資訊數量龐大且形式多元。相較於文字型態的資料，影像資料可以提供更多的資訊，因此影像資料扮演舉足輕重的角色。影像資料的儲存比文字資料更為複雜，若能運用影像壓縮的技術，減少影像資料中較不重要的資訊，降低影像的儲存空間，便能大幅提升影像處理工作的效率。另一方面，有時影像在被存取的過程中遭到雜訊汙染，產生模糊影像，此模糊的影像被稱為退化影像(image degradation)。近年來奇異值分解常被用於解決影像處理問題，對於影像資料也有充分的解釋能力。本文考慮將奇異值分解應用在影像壓縮與去除雜訊上，以奇異值累積比重作為選取奇異值的準則，並透過模擬實驗來評估此方法的效果。
Singular value decomposition (SVD) is a robust and reliable matrix decomposition method. It has many attractive properties, such as the low rank approximation. In the era of big data, numerous data are generated rapidly. Offering attractive visual effect and important information, image becomes a common and useful type of data. Recently, SVD has been utilized in several image process and analysis problems. This research focuses on the problems of image compression and image denoise for restoration. We propose to apply the SVD method to capture the main signal image subspace for an efficient image compression, and to screen out the noise image subspace for image restoration. Simulations are conducted to investigate the proposed method. We find that the SVD method has satisfactory results for image compression. However, in image denoising, the performance of the SVD method varies depending on the original image, the noise added and the threshold used.
參考文獻 Aronoff, S., (1989). Geographic information systems: A management perspective. Geocarto international, 4, 4, 58.

Banham, M.R., Katsaggelos, A.K., (1997). Digital image restoration. Signal processing magazine, IEEE, 14, 2, 24-41.

Eckart, C., Young, G.,(1936). The approximation of one matrix by another of lower rank. Psychometrika, 1, 3, 211-218.

Ganic, Zubair, N., and Eskicioglu, A.M., (2003). An optimal watermarking scheme based on singular value decomposition. Proceedings of the IASTED international conference on communication, network, and information security (CNIS), 85-90.

Gorodetski, V.I., Popyack, L.J., Samoilov, V., and Skormin, V.A., (2001). SVD-Based approach to transparent embedding data into digital images. Proc. Int. workshop on mathematical methods, models and architecture for computer network security, lecture notes in computer science, 2052, 263-274.

Kamm, J. L., (1998). SVD-Based methods for signal and image restoration, PhD thesis.

Karadimitriou, K., Fenstermacher, M., (1997). Image compression in medical image databases using set redundancy. Data compression conference, 1997. DCC `97. proceedings, IEEE.

Konstantinides, K., Natarajan, B., and Yovanof, G.S., (1997). Noise estimation and filtering using block-based singular value decomposition. IEEE Trans. Image Processing, 6, 479- 483.

Menze, B.H., (2015). The multimodal brain tumor image segmentation benchmark (BRATS). Medical imaging, IEEE transactions on, 34, 10, 1993-2024.

Sadek, R. A., (2012). SVD based image processing applications: state of
the art, contributions and research challenges. International Journal of Advanced Computer Science and Applications (IJACSA), 3, 7, 26-34.

Sanches, J.M., Nascimento, J.C., Marques, J.S.(2008). Medical image noise reduction using the Sylvester–Lyapunov equation. Image processing, IEEE Transactions on, 17, 9, 1522-1539.
描述 碩士
國立政治大學
統計研究所
102354003
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0102354003
資料類型 thesis
dc.contributor.advisor 薛慧敏zh_TW
dc.contributor.author (Authors) 顏佑君zh_TW
dc.contributor.author (Authors) Yen, Yu Chunen_US
dc.creator (作者) 顏佑君zh_TW
dc.creator (作者) Yen, Yu Chunen_US
dc.date (日期) 2015en_US
dc.date.accessioned 2-Nov-2015 15:59:52 (UTC+8)-
dc.date.available 2-Nov-2015 15:59:52 (UTC+8)-
dc.date.issued (上傳時間) 2-Nov-2015 15:59:52 (UTC+8)-
dc.identifier (Other Identifiers) G0102354003en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/79274-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 102354003zh_TW
dc.description.abstract (摘要) 奇異值分解(singular valve decomposition)是一個重要且被廣為運用的矩陣分解方法，其具備許多良好性質，包括低階近似理論(low rank approximation)。在現今大數據(big data)的年代，人們接收到的資訊數量龐大且形式多元。相較於文字型態的資料，影像資料可以提供更多的資訊，因此影像資料扮演舉足輕重的角色。影像資料的儲存比文字資料更為複雜，若能運用影像壓縮的技術，減少影像資料中較不重要的資訊，降低影像的儲存空間，便能大幅提升影像處理工作的效率。另一方面，有時影像在被存取的過程中遭到雜訊汙染，產生模糊影像，此模糊的影像被稱為退化影像(image degradation)。近年來奇異值分解常被用於解決影像處理問題，對於影像資料也有充分的解釋能力。本文考慮將奇異值分解應用在影像壓縮與去除雜訊上，以奇異值累積比重作為選取奇異值的準則，並透過模擬實驗來評估此方法的效果。zh_TW
dc.description.abstract (摘要) Singular value decomposition (SVD) is a robust and reliable matrix decomposition method. It has many attractive properties, such as the low rank approximation. In the era of big data, numerous data are generated rapidly. Offering attractive visual effect and important information, image becomes a common and useful type of data. Recently, SVD has been utilized in several image process and analysis problems. This research focuses on the problems of image compression and image denoise for restoration. We propose to apply the SVD method to capture the main signal image subspace for an efficient image compression, and to screen out the noise image subspace for image restoration. Simulations are conducted to investigate the proposed method. We find that the SVD method has satisfactory results for image compression. However, in image denoising, the performance of the SVD method varies depending on the original image, the noise added and the threshold used.en_US
dc.description.tableofcontents 第一章、 緒論 1
第二章、 研究方法 4
一. 奇異值分解基本介紹 4
二. 奇異值分解之低階近似性質(low rank approximation) 5
三. 奇異值分解在影像壓縮的應用與評估 6
四. 奇異值分解在消除影像雜訊的應用與評估 9
第三章、 實證分析 11
一. 奇異值分解在影像壓縮的應用 11
實驗設計 11
結果呈現：實驗一 12
結果呈現：實驗二 17
結果呈現：實驗三 22
二. 奇異值分解在雜訊消除上的應用 27
實驗設計 27
結果呈現：實驗一 28
結果呈現：實驗二 34
第四章、 結論 40
參考文獻 42		zh_TW
dc.format.extent 2438654 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0102354003en_US
dc.subject (關鍵詞) 奇異值分解zh_TW
dc.subject (關鍵詞) 低階近似zh_TW
dc.subject (關鍵詞) 影像處理zh_TW
dc.subject (關鍵詞) 影像壓縮zh_TW
dc.subject (關鍵詞) 去除影像雜訊zh_TW
dc.subject (關鍵詞) singular value decompositionen_US
dc.subject (關鍵詞) low rank approximationen_US
dc.subject (關鍵詞) image processingen_US
dc.subject (關鍵詞) image compressionen_US
dc.subject (關鍵詞) image denoisingen_US
dc.title (題名) 奇異值分解在影像處理上之運用zh_TW
dc.title (題名) Singular Value Decomposition: Application to Image Processingen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Aronoff, S., (1989). Geographic information systems: A management perspective. Geocarto international, 4, 4, 58.

Banham, M.R., Katsaggelos, A.K., (1997). Digital image restoration. Signal processing magazine, IEEE, 14, 2, 24-41.

Eckart, C., Young, G.,(1936). The approximation of one matrix by another of lower rank. Psychometrika, 1, 3, 211-218.

Ganic, Zubair, N., and Eskicioglu, A.M., (2003). An optimal watermarking scheme based on singular value decomposition. Proceedings of the IASTED international conference on communication, network, and information security (CNIS), 85-90.

Gorodetski, V.I., Popyack, L.J., Samoilov, V., and Skormin, V.A., (2001). SVD-Based approach to transparent embedding data into digital images. Proc. Int. workshop on mathematical methods, models and architecture for computer network security, lecture notes in computer science, 2052, 263-274.

Kamm, J. L., (1998). SVD-Based methods for signal and image restoration, PhD thesis.

Karadimitriou, K., Fenstermacher, M., (1997). Image compression in medical image databases using set redundancy. Data compression conference, 1997. DCC `97. proceedings, IEEE.

Konstantinides, K., Natarajan, B., and Yovanof, G.S., (1997). Noise estimation and filtering using block-based singular value decomposition. IEEE Trans. Image Processing, 6, 479- 483.

Menze, B.H., (2015). The multimodal brain tumor image segmentation benchmark (BRATS). Medical imaging, IEEE transactions on, 34, 10, 1993-2024.

Sadek, R. A., (2012). SVD based image processing applications: state of
the art, contributions and research challenges. International Journal of Advanced Computer Science and Applications (IJACSA), 3, 7, 26-34.

Sanches, J.M., Nascimento, J.C., Marques, J.S.(2008). Medical image noise reduction using the Sylvester–Lyapunov equation. Image processing, IEEE Transactions on, 17, 9, 1522-1539.		zh_TW