Simultaneously Counting and Extracting Endmembers in a Hyperspectral Image Based on Divergent Subsets

Abstract

Most existing endmember extraction techniques require prior knowledge about the number of endmembers in a hyperspectral image. The number of endmembers is normally estimated by a separate procedure, whose accuracy has a large influence on the endmember extraction performance. In order to bridge the two seemingly independent but, in fact, highly correlated procedures, we develop a new endmember estimation strategy that simultaneously counts and extracts endmembers. We consider a hyperspectral image as a hyperspectral pixel set and define the subset of pixels that are most different from one another as the divergent subset (DS) of the hyperspectral pixel set. The DS is characterized by the condition that any additional pixel would increase the likeness within the DS and, thus, reduce its divergent degree. We use the DS as the endmember set, with the number of endmembers being the subset cardinality. To render a practical computation scheme for identifying the DS, we reformulate it in terms of a quadratic optimization problem with a numerical solution. In addition to operating as an endmember estimation algorithm by itself, the DS method can also co-operate with existing endmember extraction techniques by transforming them into a novel and more effective schemes. Experimental results validate the effectiveness of the DS methodology in simultaneously counting and extracting endmembers not only as an individual algorithm but also as a foundation algorithm for improving existing methods. Our full code is released for public evaluation. 1 1 https://github.com/xuanwentao/DivergentSubset