A Kalman filtering approach to multispectral image classification and detection of changes in signature abundance

Subpixel detection and classification are important in identification and quantification of multicomponent mixtures in remotely sensed data, such as multispectral/hyperspectral images. A recently proposed orthogonal subspace projection (OSP) has shown some success in Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and Hyperspectral Digital Imagery Collection Experiment (HYDICE) data. However, like most techniques, OSP has its own constraints. One inherent limitation is that the number of signatures to be classified cannot be greater than that of spectral bands. Owing to this limitation, OSP may not perform well for multispectral imagery as it does for hyperspectral imagery. This phenomenon is observed by three-band Satellite Pour l'Observation de la Terra (SPOT) data because of an insufficient number of spectral bands compared to the number of materials to be classified. Further, most approaches proposed for multispectral and hyperspectral image analysis, including OSP, operate on a pixel by pixel basis. In this case, a general assumption is made on the fact that the image data are stationary and pixel independent. Unfortunately, this may be true for laboratory data, but not for real data, due to varying atmospheric and scattering effects. In this paper, a Kalman filtering approach is presented that overcomes the aforementioned problems. In addition to the observation process described by a linear mixture model, a Kalman filter utilizes an abundance state equation to model the nonstationary nature in signature abundance. As a result, the signature abundance can be estimated and updated recursively by the Kalman filter and an abrupt change in signature abundance can be detected via the abundance state equation.