Direct robust Non-Negative Matrix Factorization and its application on image processing

In real applications of image processing, we frequently face outliers, which cannot be simply treated as Gaussian noise. Nonnegative Matrix Factorization (NMF) is a popular method in image processing for its good performance and elegant theoretical interpretation, however, traditional NMF is not robust enough to outliers. To robustify NMF algorithm, here we present Direct Robust Nonnegative Matrix Factorization (DRNMF) for image denoising based on the assumptions that the ground truth data is of low rank and the outliers are sparse. This method explictly models the outliers in the data, and the sparsity of the outliers is controlled by L0 norm. The experiments show that DRNMF can accurately localize the outliers, and outperforms traditional NMF in image denoising.