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Hyperspectral images exhibit significant spectral correlation, whose exploitation is crucial for compression. In this paper, an efficient method for jointly compression and noise reduction of Hyperspectral images based on the Hierarchical Nonnegative Tucker Decomposition (HNTD) is presented. This algorithm not only exploits redundancies between bands but also uses spatial correlations of every image band. The goal is to identify the optimal lower rank-(J1 × J2 × J3) of Tucker tensor to achieve maximum compression ratio at a certain reconstruction PSNR. Genetic Algorithm (GA) is implemented as a heuristic technique to this constrained optimization problem. Simulation results applied to real Hyperspectral images demonstrate the success of the proposed approach in achieving a remarkable compression ratio and noise reduction simultaneously.