This paper proposes a technique for reducing impulse noise from corrupted hyperspectral images. We exploit the spatiospectral correlation present in hyperspectral images to sparsify the datacube. Since impulse noise is sparse, denoising is framed as an -norm regularized -norm data fidelity minimization problem. We derive an efficient split Bregman-based algorithm to solve the same. Experiments on real datasets show that our proposed technique, when compared with state-of-the-art denoising algorithms, yields better results.