Joint weighted nuclear norm and total variation regularization for hyperspectral image denoising

A hyperspectral image is typically corrupted by multiple types of noise including Gaussian noise and impulse noise. On the other hand, a hyperspectral image possesses a high correlation in its spectral dimensions, and its Casorati matrix has a very low rank. Inspired by the recent development of robust principal component analysis, which can be used to remove sparse and arbitrarily large noise from a low-rank matrix, we propose a joint weighted nuclear norm and total variation regularization method to denoise a hyperspectral image data. First, weighted nuclear norm regularization is constructed for sparse noise removal. Total variation regularization is then imposed on each band of the hyperspectral image to further remove the Gaussian noise. A concrete optimization algorithm is developed to implement the two-stage regularization. The combined approach is expected to effectively denoise hyperspectral images even with varying data structures and under varying imaging conditions. Extensive experiments on both simulated and real data sets validate the performance of our proposed method.