Hyperspectral subpixel target detection using the linear mixing model

Relative to multispectral sensing, hyperspectral sensing can increase the detectability of pixel and subpixel size targets by exploiting finer detail in the spectral signatures of targets and natural backgrounds. Over the past several years, different algorithms for the detection of full-pixel or subpixel targets with known spectral signature have been developed. The authors take a closer and more in-depth look at the class of subpixel target detection algorithms that explore the linear mixing model (LMM) to characterize the targets and the interfering background. Sensor noise is modeled as a Gaussian random vector with uncorrelated components of equal variance. The paper makes three key contributions. First, it provides a complete and self-contained theoretical derivation of a subpixel target detector using the generalized likelihood ratio test (GLRT) approach and the LMM. Some other widely used algorithms are obtained as byproducts. The performance of the resulting detector, under the postulated model, is discussed in great detail to illustrate the effects of the various operational factors. Second, it introduces a systematic approach to investigate how well the adopted model characterizes the data, and how robust the detection algorithm is to model-data mismatches. Finally, it compares the derived algorithms with regard to two desirable properties: capacity to operate in constant false alarm rate mode and ability to increase the separation between target and background.