Reweighted Nuclear Norm and Total Variation Regularization With Sparse Dictionary Construction for Hyperspectral Anomaly Detection

Abstract

Hyperspectral anomaly detection is an important technique in the field of remote sensing image processing. Over the last few years, low rank and sparse matrix decomposition (LRSMD) has played an increasingly significant role in hyperspectral anomaly detection. The detection performance of the LRSMD-based anomaly detectors is primarily determined by prior constraints and the background dictionary construction method. To increase the detection accuracy, we proposed the reWeighted Nuclear Norm and total variation regularization with Sparse Dictionary construction for hyperspectral Anomaly Detection (WNNSDAD), which incorporated reweighted nuclear norm and total variation regularizations as the prior constraints into the LRSMD model, and constructed a sparse background dictionary without the need of clustering. Compared to the standard nuclear norm, the reweighted nuclear norm helped to overcome the challenge of an unbalanced penalty for a singular value and ensure a more effective low rank approximation. Simultaneously, total variation regularization was introduced as a piecewise smoothing constraint, which helped to maintain the spatial correlation of the hyperspectral image. Additionally, we proposed a background dictionary construction method, by which a relatively complete background dictionary could be obtained without clustering, and the background part could be represented more reliably. The experiments on seven real-world hyperspectral datasets show that in comparison to eight state-of-the-art anomaly detection methods, the proposed WNNSDAD method demonstrated greater accuracy.