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Hyperspectral Imagery Denoising via Reweighed Sparse Low-Rank Nonnegative Tensor Factorization

Hyperspectral imagery (HSI) denoising is an important preprocessing step for real-world applications. Recently, sparse representation and low-rank representation based methods are proven effective in HSI denoising. However, most of these approaches only consider the low-rankness in the spectral domain and the sparsity in coding matrix. They have ignored the property that the coding matrix of each atom is also low-rank, i.e., low-rankness also exists in the spatial domain. In this paper, a reweighed sparse low-rank nonnegative tensor factorization (RSLRNTF) method is proposed to restore an HSI. It takes an HSI as a third-order tensor and factorizes it into the combination of a few component tensors where each one is the outer product of a low-rank matrix (coding matrix) and a vector (atom). Additionally, a reweighed L1 norm is added to coding matrices to enforce their sparsity. The low-rankness in both the spatial domain and the spectral domain as well as sparsity in the spatial domain improve the denoising performance. Furthermore, the nonnegativity in both coding matrices and dictionary leads to parts-based representation of HSI, which facilitates preserving local fine structure information. Experimental results on synthetic data and real-world data demonstrate the superiority of proposed method.