Optimized band elimination and dimensionality reduction of hyperspectral images
Dimensionality reduction is a very important step in the anahsis of hyperspectral images. There should be an optimal tradeoff between the reduction in dimensionality and loss of information. Principal component analysis (PCA) is used as the main approach for the dimensionality reduction of hyperspectral data. PCA is basically an orthogonal projection of the data onto a subspace of lower dimensionality. An important preprocessing step before performing PCA is the registration of the individual bands of the hyperspectral image. Spatial image registration is performed using the properties of power cepstmm and the Fourier shift theorem. It is also unwise in terms of computational efficiency to use all the bands of the hyperspectral image for PCA. Therefore, an efficient hierarchical dimensionality reduction technique is implemented. It is used in conjunction with an entropy measure to pre-select the bands of the image, which are to be used for performing PCA. PCA relies heavily on second order moments, which result in a high sensitivity of the algorithm to outliers in the data. Hence, an efficient version of principal component analysis is also implemented, using a robust estimate of the covariance matrix to do the transformation. The scree plots and performance measures for PCA are analyzed for the given hyperspectral imagery.