Efficient Hierarchical-PCA Dimension Reduction for Hyperspectral Imagery

Hyperspectral systems have improved significantly through recent advancements in sensor technology, which have made possible to acquire data with several hundred channels. These advances provide the possible benefit of not only collecting more detailed information than previously possible, but also of producing more accurate data. Some of the major challenges in handling such large data sets are removing redundant information and assuring the continued relevance of vital information to the application at hand. For example, conventional methods for land use and land cover classifications may not be applicable, due to the large data volumes used to characterize hyperspectral cubes. Therefore, these conventional methods may require a preprocessing step, namely dimension reduction. Dimension reduction can be seen as a transformation from a high order dimension to a low order dimension in order to conquer the so- called "curse of the dimensionality," which eliminates data redundancy. Principal Component Analysis (PCA) is one such data reduction technique, which is often used when analyzing remotely sensed data. In computing the principal components, the eigenvalues of the covariance matrix of the 3-D image must be computed. Since this is a global operation it requires high computational resources and requires whole image to be stored which increases memory requirements. This paper reports an hierarchical algorithm, which can effectively reduce the hyperspectral data to intrinsic dimensionality. In the hierarchical PCA, we break the image into various parts and then perform PCA on each part separately and then combine the results. The classification results over the original and the resulting reduced data have been compared. The results show that reduced data obtained by hierarchical PCA can compare favorably to the results obtained from original data.