Total Variation Regularized Collaborative Representation Clustering With a Locally Adaptive Dictionary for Hyperspectral Imagery

Abstract

Clustering is a very challenging task for hyperspectral imagery (HSI) because of the complex spectral–spatial structures found in such data. Recently, the sparse recovery-based approaches have been introduced to deal with hyperspectral clustering, and have achieved state-of-the-art performances. Several recent works have shown that it is the collaborative representation mechanism over all the dictionary atoms, rather than the sparse constraint that determines the recognition performance. Based on this fact, in this paper, we focus on the working mechanism of collaborative representation to explore its potential in HSI clustering. However, directly introducing collaborative representation clustering (CRC) to HSIs results in several problems, i.e., the high redundancy of the global dictionary atoms and the absence of spatial information, which greatly limit the clustering performance. In view of this, we propose a novel total variation regularized CRC with a locally adaptive dictionary (TV-CRC-LAD) algorithm for HSI. First, the LAD construction strategy is introduced instead of the global dictionary to relieve the high redundancy and the interference of unrelated atoms in the representation process, to more precisely represent each pixel only with the highly correlated atoms. Second, TV regularization is integrated to better account for the rich spatial-contextual information and promotes the piecewise smoothness of the HSI clustering result. The proposed algorithm was tested on three widely used hyperspectral data sets, and the experimental results clearly illustrate that the proposed algorithm outperforms the corresponding sparsity-based clustering methods and the other state-of-the-art methods.