Abstract
The low-rank and sparse decomposition model has been favored by the majority of hyperspectral image anomaly detection personnel, especially the robust principal component analysis(RPCA) model, over recent years. However, in the RPCA model, ℓ0 operator minimization is an NP-hard problem, which is applicable in both low-rank and sparse items. A general approach is to relax the ℓ0 operator to ℓ1-norm in the traditional RPCA model, so as to approximately transform it to the convex optimization field. However, the solution obtained by convex optimization approximation often brings the problem of excessive punishment and inaccuracy. On this basis, we propose a non-convex regularized approximation model based on low-rank and sparse matrix decomposition (LRSNCR), which is closer to the original problem than RPCA. The WNNM and Capped ℓ2,1-norm are used to replace the low-rank item and sparse item of the matrix, respectively. Based on the proposed model, an effective optimization algorithm is then given. Finally, the experimental results on four real hyperspectral image datasets show that the proposed LRSNCR has better detection performance.
Highlights
The Hyperspectral sensing image (HSI) integrates spectrum and spatial information and is a kind of three-dimensional image data [1–3]
The proposed method adopts improved Robust Principal Component Analysis (RPCA) models to detect anomalies, anomalies are modeled by the sparse component, and background is modeled by the low-rank component
The availability of the LRSNCR model for hyperspectral anomaly detection (HAD) is expounded by the analysis and discussion of the experimental results
Summary
The Hyperspectral sensing image (HSI) integrates spectrum and spatial information and is a kind of three-dimensional image data [1–3]. In 1990, the linear RX method was proposed by Reed [13] et al, it is a pioneering algorithm for hyperspectral anomaly detection [14] This algorithm divides the HSI into a background information part and binary classification problem to be detected, which solves the problem of anomaly detection. Due to its complete theoretical knowledge and operability, the method derived from low-rank sparse matrix decomposition (LRaSMD) [19–21] has attracted increasing attention in the field of HSIs anomaly detection. The original RPCA-RX [27] algorithm treats hyperspectral remote sensing image data as a two-dimensional matrix A and uses matrix decomposition to decompose it as a low-rank item L and a sparse item S, the former of which is background and the latter is a non-zero element that contains the anomaly information of the image. The proposed method adopts improved RPCA models to detect anomalies, anomalies are modeled by the sparse component, and background is modeled by the low-rank component. LRSNCR method has better detection performance than other methods and can better separate the background and anomalies
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