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.

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