A new algorithm for subpixel target detection in hyperspectral imagery is proposed which uses the PFCM-FLICM-PCE algorithm to model and estimate the parameters of the image background. This method uses the piece-wise convex mixing model with spatial-spectral constraints, and uses possibilistic and fuzzy clustering techniques to find the piece-wise convex regions and robustly estimate the parameters. A method for integrating the elevation measurements of a co-registered LiDAR sensor is also proposed. The performance of the proposed methods is demonstrated on a real-world dataset with emplaced detection targets.