We propose a new noise reduction algorithm for the denoising of hyperspectral images. The proposed algorithm, Genetic Kernel Tucker Decomposition (GKTD), exploits both the spectral and the spatial information in the images. With respect to a previous approach, we use the kernel trick to apply a Tucker decomposition on a higher dimensional feature space instead of the input space. A genetic algorithm is used to optimize for the lower rank Tucker tensor in the feature space. We evaluate the effect of the kernel algorithm with respect to non-kernel GTD, and also compare the results to those from principal component analysis bivarate wavelet shirinking on real images. Our results show a better performance of the proposed method.