Double-Regularized Dictionary Learning and Low-Rank Matrix Factorization for Hyperspectral Anomaly Detection

The tensor-subspace-representation-based (TSR) methods have been proposed to enhance the hyperspectral anomaly detection (HAD) performance. However, the existing TSR-based detectors only partially dig the background’s data property in the spatial or spectral dimensions. To overcome this problem, this paper proposes a double-regularized dictionary learning (DRDL) and multi-dimension low-rank matrix factorization (DRDL-LRMF) approach for HAD. Firstly, the learnable dictionary is constrained with the matrix nuclear norm and total variation (TV) regularization to dig the background’s low-rankness (LR) and piecewise-smoothness (PS) in spectral dimension. Then, LRMF is adopted to all unfolding matrices of the coefficient tensor to dig the background’s LR in spatial dimensions, and the front slice of this tensor is constrained by TV regularization to dig the background’s PS in spatial dimensions. Next, the anomaly tensor is constrained by l<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</inf> regularization to dig the anomaly’s group sparsity. Then, we adopted the alternating direction method of multipliers to solve our model. Finally, the detection results on several real datasets verify the superiority of our method.