Constrained least squares spectral unmixing for subpixel target detection, classification and quantification in hyperspectral and multispectral imagery

Detection, classification and quantification of targets in hyperspectral and multispectral imagery present a challenge for image analysis since the targets of interest are sometimes smaller than the ground sampling distance and traditional spatial-based image processing techniques may not be effective or applicable. Under this circumstance, target detection, classification and quantification must be performed at subpixel level and spectral analysis offers a valuable alternative. A classical approach is linear spectral mixture analysis (LSMA) which models an image pixel as a linear mixture of material substances in the image data. In order for this approach to produce accurate abundance estimates, two constraints on the model are generally required. The first constraint requires the sum of the abundance fractions of targets present in an image pixel to be one and the second imposes the constraint that these abundance fractions be nonnegative. While the first constraint is easy to deal with, the latter constraint is difficult to implement since it results in a set of inequalities that can only be solved by numerical methods. Consequently, most LSMA-based methods are unconstrained and produce solutions that do not necessarily reflect the true abundance fractions of targets. This dissertation addresses constrained LSMA by imposing these two constraints on the linear mixture model. Two new and efficient numerical algorithms are developed for imposing these constraints. One is referred to as the nonnegatively constrained least squares (NCLS) method, which can be used for subpixel target detection and classification. The second, called the fully constrained least squares (FCLS) method can be used for target or material quantification.; A common drawback of LSMA-based methods is the requirement for complete prior target knowledge. To resolve this issue, three unsupervised constrained least squares error-based methods are proposed for inclusion with the designed algorithms so that they can be applied to unknown image scenes. In order to further extend the utility of the algorithms, real-time processing techniques are further developed for on-line implementation. Finally, a comprehensive study using computer simulations and real hyperspectral and multispectral data experiments is conducted to substantiate detection, classification and quantification performance of the proposed constrained least squares LSMA methods.