| Hyperspectral imaging provides researchers with abundant information with which to study the characteristics of objects in a scene. Processing the massive hyperspectral imagery datasets in a way that efficiently provides useful information becomes an important issue. In this thesis, we consider methods which reduce the dimension of hyperspectral data while retaining as much useful information as possible.;Traditional deterministic methods for low-rank approximation are not always adaptable to process huge datasets in an effective way, and therefore probabilistic methods are useful in dimension reduction of hyperspectral images. In this thesis, we begin by generally introducing the background and motivations of this work. Next, we summarize the preliminary knowledge and the applications of SVD and PCA. After these descriptions, we present a probabilistic method, randomized Singular Value Decomposition (rSVD), for the purposes of dimension reduction, compression, reconstruction, and classification of hyperspectral data. We discuss some variations of this method. These variations offer the opportunity to obtain a more accurate reconstruction of the matrix whose singular values decay gradually, to process matrices without target rank, and to obtain the rSVD with only one single pass over the original data. Moreover, we compare the method with Compressive-Projection Principle Component Analysis (CPPCA). From the numerical results, we can see that rSVD has better performance in compression and reconstruction than truncated SVD and CPPCA. We also apply rSVD to classification methods for the hyperspectral data provided by the National Geospatial-Intelligence Agency (NGA). |
