Hyperspectral Data Processing: Algorithm Design and Analysis

28.2 Kalman Filter-Based Linear Unmixing

KF has been widely used in statistical signal processing for parameter estimation (Gleb, 1974). It makes use of a measurement equation (input/output equation) and a state equation (process equation) to recursively estimate parameters of states. When a Kalman filter is implemented for spectral unmixing as a mixed pixel classifier, the state vector x in an equation, called state equation, is specified by the abundance vector α present in an image pixel vector r, which is specified by another equation called measurement equation. With this formulation, a Kalman filter takes advantage of a linear mixing model commonly used in spectral unmixing to describe how a pixel vector r is linearly mixed via a measurement equation. Meanwhile, KFLU includes an additional equation, state equation, which is absent in spectral unmixing to estimate the abundance fractions of the abundance vector of the currently processed pixel vector in an image based on previously processed pixels. Implementing these two equations recursively, KFLU generally produces better estimates of abundance fractions than spectral unmixing methods.

This and the following sections present several new applications of KF in spectral estimation, identification, and quantification for hyperspectral signature characterization by re-deriving the measurement and state equations, which results in several techniques referred to as KFSCSP techniques. There are important and salient differences ...