Hyperspectral data compression based upon the principal component analysis

The paper is aimed at developing an algorithm of hyperspectral data compression that combines small losses with high compression rate. The algorithm relies on a principal component analysis and a method of exhaustion. The principal components are singular vectors of an initial signal matrix, which are found by the method of exhaustion. A retrieved signal matrix is formed in parallel. The process continues until a required retrieval error is attained. The algorithm is described in detail and input and output parameters are specified. Testing is performed using AVIRIS data (Airborne Visible-Infrared Imaging Spectrometer). Three images of differently looking sky (clear sky, partly clouded sky, and overcast skies) are analyzed. For each image, testing is performed for all spectral bands and for a set of bands from which high water-vapour absorption bands are excluded. Retrieval errors versus compression rates are presented. The error formulas include the root mean square deviation, the noise-to-signal ratio, the mean structural similarity index, and the mean relative deviation. It is shown that the retrieval errors decrease by more than an order of magnitude if spectral bands with high gas absorption are disregarded. It is shown that the reason is that weak signals in the absorption bands are measured with great errors, leading to a weak dependence between the spectra in different spatial pixels. A mean cosine distance between the spectra in different spatial pixels is suggested to be used to assess the image compressibility.