Linear Modelling for Spectral Images based on Truncated Fourier Series

Reflectance spectra of hyperspectral images of the natural scenes are supposed to represent the real world better than any certain classes of natural and man-made spectral reflectance. But spectral images contain a large volume of data and place considerable demands on computer hardware and software compared with standard trichromatic images. Although principal component analysis (PCA) based low-dimensional linear models have been widely used in spectral image encoding and compression, there is no a single PCA linear model derived from one data set can be guaranteed to accurate represent other data sets. In this study, we proposed a spectral image encoding method by a single linear model constructed by truncated Fourier series, in which a limited number of parameters that is proportional to the highest frequency cut off if the low-pass hypothesis is valid for any of the data sets. In this paper, several groups of hyperspectral images have been processed using truncated Fourier series, the encoded images are analysed in terms of chromaticity and spectral root mean square (RMS) errors. Results show spectral images can be efficiently compressed when the frequency reach a certain limit, and the color information can be well preserved.