穩定主成份分析以及其延伸

Abstract

主成份分析 (Principal Component Analysis) 已經被廣泛運用在各種 影像處理上, 但是越來越複雜的影像導致主成份分析的假設已被破壞。 所以 Candés et al. (2011) 提出了穩定主成份分析，來應對這些新的挑 戰，例如 sensor failure 以及 corrupted sample。在這篇碩士論文裡，我 們針對穩定主成份分析做了一些調整，以擴展其應用。我們運用了策 略抽樣的方法，讓數據可以滿足 RPCA 。

Principal Component Analysis (PCA) has been used in an overwhelming manner for data analysis. However, PCA did not perform well when data did not follow the model well like sensor failure or corrupted sample. Can- dés et al. (2011) proposed Robust Principal Component Analysis (RPCA) to recover the data and proved that it can perform very well when data has the sparsity property for the signal with a low rank background. Unfortunately, the FRET data set does not satisfy the working condition. Here, we employ a sampling scheme to enable the application for the FRET data. For extremely large number of pixel image application, RPCS may suffer from computation loading. Thus, we also extend RPCA to a high order SVD version.