Recent developments in optical sensors enable a wide range of applications for multispectral imaging, e.g., in surveillance, optical sorting, and life-science instrumentation. Increasing spatial and spectral resolution allows creating higher quality products, however, it poses challenges in handling such large amounts of data. Consequently, specialized compression techniques for multispectral images are required. High Efficiency Video Coding (HEVC) is known to be the state of the art in efficiency for both video coding and still image coding. In this paper, we propose a cross-spectral compression scheme for efficiently coding multispectral data based on HEVC. Extending intra picture prediction by a novel inter-band predictor, spectral as well as spatial redundancies can be effectively exploited. Dependencies among the current band and further spectral references are considered jointly by adaptive linear regression modeling. The proposed backward prediction scheme does not require additional side information for decoding. We show that our novel approach is able to outperform state-of-the-art lossy compression techniques in terms of rate-distortion performance. On different data sets, average Bj{\o}ntegaard delta rate savings of 82 % and 55 % compared to HEVC and a reference method from literature are achieved, respectively.