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Wavelet Representation for Hyperspectral Signals
Wavelet analysis has been used successfully in many areas in signal and image processing. Its applications to remote sensing have also been evidenced by many publications. This chapter presents a new application of wavelets in hyperspectral signature representation for spectral characterization. In particular, a new algorithm, called wavelet-based signature characterization algorithm (WSCA), is developed for hyperspectral signature discrimination, classification, and identification. The key idea of WSCA is to decompose a hyperspectral signature vector into two signature components, referred to as detail and approximation signatures, respectively, via the discrete wavelet transform (DWT) specified by Mallet's algorithm where two types of filters, high-pass and low-pass filters, are constructed to generate these two components. Two specific functions, called “wavelet function,” and “scaling function,” are used for DWT to span two orthogonal vector spaces. Since the wavelet function is effective in capturing the details of a signature vector that corresponds to the high-frequency domain information of the original signature vector, it can be used to generate signature details. On the other hand, the scaling function represents the low-frequency domain information inherited in the original signature vector to retain majority of the signature vector; thus, it can be used to produce the signature approximation. By means of these two ...
