With the rapid development of remote sensing techniques, the quantity of remotely sensed data generated by remote sensors increases fast. A large amount of remotely sensed data provide valuable information for researches on earth resources, but it is hard to be stored and transmitted. Therefore, there is a critical need of data compression for remote sensing applications. In the case of MSI data, there are two types of redundancy: spatial redundancy and spectral redundancy. Usually, the prediction technique is used in spatial and spectral decorrelation in lossless compression. In this paper we construct integer wavelet transform by using lift scheme, which is used for spatial decorrelation, and construct a spectral predictor by using classification that is used for spectral decorrelation. This combined technique could improve the compression ratio.