Hyperspectral Anomaly Detection via S1/2 Regularized Low Rank Representation

Anomaly detection has been drawing a great deal of attention by virtue of its practicability among the hyperspectral research area. Low-rank representation (LRR) has been widely employed to detect anomalies from hyperspectral imagery (HSI) effectively while a great number of methods derived from LRR replace rank function with a nuclear norm, which gives rise to a certain amount of error. In this letter, we propose a Schatten 1/2 quasi-norm (
$S_{1/2}$
) regularized LRR (SRLRR) method with an improved algorithm of establishing the dictionary for hyperspectral anomaly detection. First,
$S_{1/2}$
regularization is proposed to substitute the initial nuclear norm to approximate the rank function. Second, an improved dictionary construction algorithm based on K-Means++ clustering is presented to integrate the model and improve the performance. Finally, the optimization algorithm through alternating direction multiplier method (ADMM) incorporating a half threshold operator is introduced to attain the eventual results. Our method has been testified on three typical data sets and demonstrates the eminent performance.