Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery

Linear spectral mixture analysis (LSMA) is a widely used technique in remot e sensing to estimate abundance fractions of materials present in an image pixel. In order for an LSMA-based estimator to produce accurate amounts of material abundance, it generally requires two constraints imposed on the li near mixture model used in LSMA, which are the abundance sum-to-one constra int and the abundance nonnegativity constraint. The first constraint requir es the sum of the abundance fractions of materials present in an image pixe l to be one and the second imposes a constraint that these abundance fracti ons be nonnegative. While the first constraint is easy to deal with, the se cond constraint is difficult to implement since it results in a set of ineq ualities and can only be solved by numerical methods. Consequently, most LS MA-based methods are unconstrained and produce solutions that do not necess arily reflect the true abundance fractions of materials. In this case, they can only be used for the purposes of material detection, discrimination, a nd classification, but not for material quantification. In this paper, we p resent a fully constrained least squares (FCLS) linear spectral mixture ana lysis method for material quantification. Since no closed form can be deriv ed for this method, an efficient algorithm is developed to yield optimal so lutions. In order to further apply the designed algorithm to unknown image scenes, an unsupervised least squares error (LSE)-based method is also prop osed to extend the FCLS method in an unsupervised manner. A series of compu ter simulations and real hyperspectral data experiments were conducted to d emonstrate the performance of the proposed FCLS LSMA approach in material q uantification.