We propose a compression framework for four-channel images, composed of color (RGB) and near-infrared (NIR) channels, which exploits the correlation between the visible and the NIR information. The high-frequency components of both visible and NIR scene representations are strongly correlated. By encoding only the DCT components that differ above a chosen threshold, we significantly improve compression ratios for a given quality level. To evaluate our proposed method, we compare our results with standard JPEG compression, as well as PCA-based approaches that are often employed to compress multispectral images. Our experiments show that applying our proposed method yields the same quality at a lower bit-rate, compared to conventional JPEG and PCA-based algorithms.