Effective compression of hyperspectral (HS) images is essential due to their large data volume. Since these images are high dimensional, processing them is also another challenging issue. In this work, an efficient lossy HS image compression method based on enhanced multivariance products representation (EMPR) is proposed. As an efficient data decomposition method, EMPR enables us to represent the given multidimensional data with lower-dimensional entities. EMPR, as a finite expansion with relevant approximations, can be acquired by truncating this expansion at certain levels. Thus, EMPR can be utilized as a highly effective lossy compression algorithm for hyper spectral images. In addition to these, an efficient variety of EMPR is also introduced in this article, in order to increase the compression efficiency. The results are benchmarked with several state-of-the-art lossy compression methods. It is observed that both higher peak signal-to-noise ratio values and improved classification accuracy are achieved from EMPR-based methods.