Spectral images contain a large volume of data and place considerable demands on computer hardware and software compared with standard trichromatic image storage and processing. Although the imformation of reflectance spectra may be represented efficiently using linear models a key task is to answer how many basis functions of a linear model are necessary for a given accuracy of representation. Because the most common application of spectral images is the reproduction of color and images, it is highly important to study the tolerance of human perceptions over spectral images represented by low-dimensional linear models. In this study several data sets and psychophysical studies have been used to investigate how many basis functions are necessary to represent a spectral image to be indistinguishable from the original image. The raw objective experiment datas are analysed by a comprehensive probit analysis based on the bootstrap method, and results show that the perceptual tolerance for spectral images reconsctucted by variouse number of basis functions is highly image dependent.