Hyperspectral Data Processing: Algorithm Design and Analysis

29.3 Wavelet-Based Signature Characterization Algorithm

In this section, WSCA is developed for hyperspectral signal processing, which can perform signature self-tuning (SST) and signature self-correction (SSC), referred to as WSCA-SST and WSCA-SSC, respectively.

29.3.1 Wavelet-Based Signature Characterization Algorithm for Signature Self-Tuning

The SST ability of WSCA arises from the fact that a signature can be wavelet-decomposed into two orthogonal signature components, called details signature and approximation signature, an idea borrowed from the innovations process used in the Kalman filtering. Mallet's algorithm (1989) demonstrated that the wavelet decomposition and reconstruction of a signal f(x) could be related to each other by the two flow diagrams depicted in Figure 29.3.

Figure 29.3 Flow diagrams for both wavelet decomposition and reconstruction.

The signal function f(x) represents the original hyperspectral signature, which will be later used as a reference signature. The two signature components of f(x), D^df(x) and A^df(x), are referred to as its details and approximation signatures, respectively. The G and H in Figure 29.3 denote the high-pass and low-pass filters derived from the wavelet function and scaling function, respectively, as described in Section 29.2, where and are the corresponding mirror filters of G and H. Assume that the detail signature of the original ...