Imaging spectrometer, such as MAIS produces a tremendous volume of image data with up to 5.12 Mbps raw data rate, which needs urgently a real-time, efficient and reversible compression implementation. Between the lossy scheme with high compression ratio and the lossless scheme with high fidelity, we must make our choice based on the particular information content analysis of each imaging spectrometer's image data. In this paper, we present a careful analysis of information-preserving compression of imaging spectrometer MAIS with an entropy and autocorrelation study on the hyperspectral images. First, the statistical information in an actual MAIS image, captured in Marble Bar Australia, is measured with its entropy, conditional entropy, mutual information and autocorrelation coefficients on both spatial dimensions and spectral dimension. With these careful analyses, it is shown that there is high redundancy existing in the spatial dimensions, but the correlation in spectral dimension of the raw images is smaller than expected. The main reason of the nonstationarity on spectral dimension is attributed to the instruments's discrepancy on detector's response and channel's amplification in different spectral bands. To restore its natural correlation, we preprocess the signal in advance. There are two methods to accomplish this requirement: onboard radiation calibration and normalization. A better result can be achieved by the former one. After preprocessing, the spectral correlation increases so high that it contributes much redundancy in addition to spatial correlation. At last, an on-board hardware implementation for the lossless compression is presented with an ideal result.