Constrained Energy Minimization (CEM) has been widely used for target detection in hyperspectral remote sensing imagery. It detects the desired target signal source using a unity constraint while suppressing noise and unknown signal sources by minimizing the average output power. Base on the design CEM can only detect one target source at a time. In order to simultaneously detect multiple targets in a single image, several approaches are developed, including Multiple-Target CEM (MTCEM), Sum CEM (SCEM) and Winner-Take-All CEM (WTACEM). Interestingly, the sensitivity of noise and interference seems to play a role in the detection performance. Unfortunately, this issue has not been investigated. In this paper, we take up this problem and conduct a quantitative study of the noise and interference suppression abilities of LCMV, SCEM, WTACEM for multiple-target detection.