Boltzmann Entropy-Based Unsupervised Band Selection for Hyperspectral Image Classification

Band selection for hyperspectral images helps improve the efficiency of data processing and even the accuracy of classification. It is to reduce the dimensionality of a hyperspectral image by selecting representative bands. In such a process, the quantification of band similarity is the fundamental issue, and it is usually achieved by using an information-theoretic measure, such as mutual information or relative entropy. However, these measures are incapable of quantifying similarity in terms of both composition and configuration. To solve this problem, the Boltzmann entropy (BE), which captures both configurational and compositional information, is employed in this letter. More precisely, the difference in BE between two hands is used for such quantification. The corresponding search strategy is designed for band selection. Experimental evaluation was carried out using remote sensing images for classification. The results clearly demonstrate the superiority of the proposed band selection method over traditional information-theoretic methods: an increase of up to 27% in classification accuracy was observed when using the difference in relative BE with 20 selected bands. In addition, another comparison with some state-of-theart methods was conducted. The results show that the proposed method is still very competitive; it outperformed all the others when the number of selected bands ranges from 18 to 23. This letter, the first of its kind, reveals that the BE may form a new base for information-theoretic approaches to image processing and even for spatial information science in a broad sense.