Global Overcomplete Dictionary-Based Sparse and Nonnegative Collaborative Representation for Hyperspectral Target Detection

The combined sparse and collaborative representation-based algorithm is one of the most effective methods among hyperspectral target detection methods based on representation and dictionary learning. It encourages target atoms to compete with each other and background atoms to collaborate in the representation. However, this method suffers from several drawbacks. In sparse representation, an overcomplete dictionary is necessary, whereas, in collaborative representation, non-negative coefficients are required. Besides, the local dual window approach may result in impure background dictionaries obtained from the outer window. To address these issues, we propose a novel approach for hyperspectral target detection, referred to as the global overcomplete dictionary-based sparse and nonnegative collaborative representation (GODSNCR) detector. First, a hierarchical density clustering algorithm is used to complete the dictionary atom extraction to construct a joint overcomplete dictionary to satisfy the dictionary overcompleteness problem required for sparse representation. Second, a nonnegative constraint on the coefficient matrix and a "sum to one" constraint for the joint representation are incorporated to make it more consistent with the physical meaning. Finally, the limitation of the local dual window approach is overcome by substituting the local background dictionary with a global background dictionary. Through the aforementioned strategies, we can use a joint overcomplete dictionary for achieving the sparse representation of targets and utilize a global background dictionary for the collaborative representation of background, the final detection results are obtained by calculating the residuals. The experimental results clearly demonstrate that the proposed algorithm has significant improvement in detection accuracy and strong robustness compared to other typical representation-based hyperspectral target detection methods. Our model will be available at https://github.com/Chenxing-Li/GODSNCR.