Cauchy sparse NMF with manifold regularization: A robust method for hyperspectral unmixing

Abstract

Recently, nonnegative matrix factorization (NMF) has achieved a great success in hyperspectral image (HSI) unmixing tasks. However, existing NMF based unmixing methods commonly suffer from two main drawbacks: 1) the lack of robustness, which leads to the failure when dealing with the noise contamination in practical HSI data; and 2) the neglect of manifold preservation, resulting in the corruption of the intrinsic structure of HSI data. Accordingly, to address these two issues, we propose a robust hyperspectral unmixing model called Cauchy Sparse NMF with manifold regularization (MCSNMF), which incorporates the prior geometric structure into robust subspace learning. More specifically, in order to filter out the outliers when extracting endmembers, we measure the reconstruction error via the sparse Truncated Cauchy function. Meanwhile, to preserve the manifold structure of original HSI data, we incorporate the graph regularization over the abundances into MCSNMF. Furthermore, from the optimization viewpoint, we conduct a theoretical analysis to confirm the robustness of the proposed method. Optimized by an efficient half-quadratic based algorithm, MCSNMF outperforms the state-of-the-art NMF based unmixing methods on both simulated datasets and real scene images.