Hyperspectral Data Processing: Algorithm Design and Analysis

6.7 Dimensionality Reduction by Band Selection

Since different spectral bands provide different levels of information of interest the primary goal of DRBS is to select an appropriate band subset from the original band set to represent the original data in some sense of optimality. Therefore, the information preserved by DRBS has significant impact on data analysis because the information of un-selected bands will be completely lost after BS. So, a key success in DRBS is how to design effective criteria for the BS to meet various applications. Solving a general BS problem generally requires an exhaustive search for all possible combinations, with L and being the total number of spectral bands in Ω_BS, respectively.

More specifically, assume that J(·) is a generic objective function of Ω_BS for BS to be optimized. For a given number of selected bands, n_BS, a BS technique is to find an optimal band subset, with , that satisfies the following optimization problem:

(6.72)

Depending on how the ...