The circum-galactic medium consists in gas orbiting around galaxies, whose faintness prevents any complete and easy detection. A powerful tool to detect such pattern can be found in using hyperspectral imaging. Nevertheless, detection in hyperspectral datacubes faces various problems, including well-fitted signal and noise descriptions to ensure further discrimination. A specificity of astronomical images resides in dealing with faint and very noisy signals. In this paper, we introduce a new constrained generalized likelihood ratio test adapted to the problem and a compound test to exploit most of the available information. We also investigate the use of both spatial information and multiple observations on a single scene, to enhance robustness. Numerical experiments on synthetic data are performed to quantify the gain of the different approaches. Finally, results on real hyperspectral astronomical data are presented, which may map for the first time observation of the circum-galactic medium around faint and distant galaxies.