Nonlinear Orthogonal NMF on the Stiefel Manifold With Graph-Based Total Variation Regularization

This letter proposes a novel Nonlinear Orthogonal NMF model with Graph-based Total Variation regularization (GTV) for Multispectral document images decomposition. In this model, a GTV regularization is incorporated to preserve the intrinsic geometrical structure of document content lost by the vectorization of spectral images. A spatial orthogonality constraint over the Stiefel manifold is imposed to ensure the uniqueness of the solution and improve its sparsity. The kernel trick is involved to account for the non-linear correlation inherent to spectral data. We devised an efficient algorithm to solve the formulated problem using the Alternating Direction Method of Multipliers (ADMM). The experimental results on real-world data show that the proposed model achieves better decomposition performance than recent competitive methods and outperforms some traditional state-of-the-art methods.