Constrained weighted least squares approaches for target detection and classification in hyperspectral imagery

Least squares unmixing methods are widely used to solve linear mixture problems for endmember abundance estimation in hyperspectral imagery. In this paper, a weighted least squares method is introduced as a generalization. When different weight matrix is used, a certain detector or classifier will be resulted. For accurate abundance fraction estimation, a constrained weighted least squares approach is developed by combining sum-to-one and nonnegativity constraints. The experimental results show that when a meaningful weight matrix is applied as a data pre-processing operator, the weighted least squares method will outperform ordinary least squares solution and the constrained methods will outperform unconstrained ones.