Hyperspectral Data Processing: Algorithm Design and Analysis

15.6 Conclusions

This chapter introduces a kernel version of LSMA, called kernel-based LSMA (KLSMA) to perform spectral unmixing in a feature space transformed by a nonlinear kernel function. Despite that a kernel-based OSP was also proposed by Kwon and Nasrabadi (2005) the derivation for the KOSP or KLSOSP presented in this chapter is much simpler than the one in Kwon and Nasrabadi (2005). Most importantly, it can be used as a base to extend NCLS and FCLS to KNCLS and KFCLS which were not developed in Kwon and Nasrabadi (2005). The kernel versions of NCLS and FCLS derived in this chapter are independent of that developed in Broadwater et al. (2007). In particular, the details of derivations for the three kernel-based algorithms, KLSOSP, KNCLS, and KFCLS including their step-by-step algorithmic implementations provided in this chapter are by far most comprehensive and can serve as guidelines for those who are interested in their implementations. It is also worth being mentioned that since the fundamental framework of kernelizing LSMA is laid out in this chapter, extensions of FLSMA in Chapter 13 and WACLSMA in Chapter 14 to their kernel counterparts can be carried out by a treatment similar to the one in extending LSMA to KLSMA presented in this chapter, but more complicated matrix manipulations are involved in their derivations (Liu, 2011). Nevertheless, such extensions may not be as trivial as expected. In addition, to conduct quantification analysis for performance evaluation, ...