Kalman filtering approach to multispectral/hyperspectral image classification - Aerospace and Electronic Systems, IEEE Transactions on

0018-9251/99/$10.00 @ 1999 IEEE Remotely sensed images have been used in a broad range of applications ranging from geology, agriculture, and global change detection to defense and law enforcement [ 11. They are generally acquired by multiple-band sensors operated from either a spaceborne or an airborne platform. Examples include satellite multispectral sensors such as Landsat 7-band Thematic Mapper (TM), 4-band Multispectral Scanner (MSS), 3-band SPOT (Satellite Pour l’observation de la Terra) and airborne hyperspectral sensors such as the 224-band NASA Jet Propulsion Laboratory’s Airborne Visible/InfraRed Imaging Spectrometer (AVIRIS) and the 210-band Naval Research Laboratory’s Hyperspectral Digital Imagery Collection (HYDICE). Since the area covered by a multispectralhyperspectral image pixel is generally 20-30 m by 20-30 m (except HYDICE data which has spatial resolution ranging from 1 m to 4 m), a scene pixel usually contains more than one material and results in a mixture of these materials. One of the major challenges in remote sensing data exploitation is to discriminate, quantify, and identify multiple material constituents in a mixed pixel. In particular, when the size of a target is smaller than the ground sampling distance, detecting such a target at subpixel scale presents great difficulty because the target is embedded in only one pixel and cannot be seen from the image. Linear unmixing has been a widely used technique to unmix multicomponent mixtures [2, 3, 41. It models a pixel as a linear mixture of spectral signatures of materials within that pixel, then inverts the signature matrix formed by the spectra of the materials to identify and classify these individual material components in the pixel. Unfortunately, it works only on a pixel-by-pixel basis and does not take into account the pixel spatial correlation. Therefore, it cannot detect the change in the abundance vector from one pixel to another. Kalman filtering is a well-known technique in control, communications, and signal processing and has been used in versatile applications because it can be implemented recursively in real-time data processing as well as for nonstationary data. By taking advantage of strengths of the Kalman filtering, an approach based on a concept of combining the Kalman filtering and linear unmixing, called linear unmixing Kalman filtering (LUKF) is introduced for subpixel detection and classification for remotely sensed images. The LUKF can be also be viewed as a hybrid of the linear unmixing and the Kalman filtering which implements the linear unmixing in a Kalman filtering fashion. More specifically, the measurement (also referred to as observation, output or process) equation required for the Kalman filter is governed by the linear mixture model while the state equation of the Kalman filter is used as an ancillary equation for