The task of gradient magnitude image construction for hyperspectral images (HSI) is currently under-explored, with most approaches in use being naive extensions of gradients, originally proposed for color images. But HSI showcase principal differences from color or multispectral images in that their pixels register consecutive narrow bands of the electromagnetic spectrum, thus approximating a continuous signal, instead of a few wide discrete bands. We propose three novel gradient calculation approaches for HSI. Using a new comparative experimental setup, we benchmark the new approaches against twelve gradient calculation methods. Experimental results show that our MorphL1 algorithm is the best across multiple HSI. We further provide parallel CUDA implementations of eleven (existing and new) HSI gradient approaches for GPU execution. The range of average speedup factor is 12.5-1142.4 over CPU execution. Our MorphArea algorithm proves the fastest on most HSI. The CUDA implementations are available at GitHub-link-to-appear-here.