A refined energy constrained minimization method is developed for target detection in hyperspectral remote sensing images captured by unmanned aerial vehicles (UAVs) during their surveillance missions, which has been tested in the experiment under this paper. The experiment result proves, in the detection process, this method can effectively restrain noises so far as the spectral characteristics of any potential target are known, and find sub-pixel targets out effectively from the hyperspectral remote sensing image in unknown background spectrum.