Hyperspectral (HS) images (HSI) provide a vast amount of spatial and spectral information based on the high dimensionality of the pixels in a wide range of wavelengths. A HS image usually requires massive storage capacity, which demands high compression rates to save space with preservation of data integrity. HS image can be deemed as three dimensional data cube where different wavelengths (W) form the third dimension along with X and Y dimensions. To get a better compression result, spatial redundancy of HS images can be exploited using different coders along X, Y, or W direction. This article focuses on taking maximum advantage of HS images redundancy by rearranging HS image into different 3D data cubes and proposes a directionlet based compression scheme constituted the optimal compression plane (OCP) for adaptive best approximation of geometric matrix. The OCP, calculated by the spectral correlation, is used to the prediction and determination of which reconstructed plane can reach higher compression rates while minimizing data loss of hyperspectral data. Moreover, we also rearrange the 3D data cube into different 2D image planes and investigate the compression ratio using different coders. The schema can be used for both lossless and lossy compression. Our experimental results show that the new framework optimizes the performance of the compression using a number of coding methods (inclusive of lossless/lossy HEVC, motion JPEG, JPG2K, and JPEG) for HSIs with different visual content.