Hyperspectral Data Processing: Algorithm Design and Analysis

20.7 Conclusions

This chapter introduces a new concept of DP that has never been explored in the literature in the past. Its idea arises from recognition of several issues in implementing DR. One is that the number of data dimensions required to be retained, q, after DR must be known in advance. In a case that the value of q is inaccurate, the entire process of DR must be reimplemented again for a new value of q. This leads to an issue, “Can the data dimensions previously obtained by a smaller value of q be used without re-running DR for a new larger value of q?” In addition, once DR is performed, how can these DR-transformed dimensions be represented in terms of information contained in these new spectral dimensions? Despite that PCA resolves the above issues by solving eigenvalues from the characteristic polynomial equation, it is unfortunate that the same approach cannot be extended or generalized to any linear transformation. For example, ICA does not have such nice properties. The PIPP and DP presented in this chapter provide a feasible solution to resolving this dilemma where PI plays a twofold role in producing projection vectors and prioritizing projection vector-generated PICs. However, it should be noted that the used PIs for both cases are not necessarily the same and can be different. In other words, when PIPP is implemented in conjunction with DP, a pair of two different PIs must be used, one for projection vector generation and the other for PIC prioritization. This ...