Hyperspectral Data Processing: Algorithm Design and Analysis

29.1 Introduction

Wavelet analysis has been well studied and used successfully in many areas in signal and image processing (Daubechies, 1992; Akansu and Haddad, 1992; Vetterli and Kovacevic, 1995; Strang and Nguyen, 1996; Mallat, 1999). This chapter explores a new application of wavelet analysis in hyperspectral signature characterization by taking advantage of its multiple-scale (multiscale) representation. Two specific functions resulting from wavelet analysis, called “wavelet function” and “scaling function,” are used to decompose a hyperspectral signature vector in multiscale representation for characterization. In other words, an original hyperspectral signature vector can be decomposed into detail signature component and approximation signature component via wavelet function and scaling function whose shifted and scaled versions span two orthogonal vector spaces. The wavelet function is effective in capturing details of a signature that correspond to the high-frequency domain information of the original signature, while the scaling function preserves the low-frequency domain information inherited in the original signature. Generally, such wavelet transform can be discrete or continuous depending upon the scalars used to translate and also dilate both the wavelet and scaling functions. In this chapter, only discrete orthonormal bases of wavelets are of interest and a specific algorithm, called Mallat's algorithm considered in Mallat (1989), is used to construct a high-pass ...