This paper deals with hyperspectral detection in impulsive and/or non homogeneous background contexts. In hyperspectral imaging applications, the detection performance of the detectors (target detection or anomaly detection like Mahalanobis distance) is typically evaluated on Gaussian assumption. However, it is well known that hyperspectral imaging data exhibit spatial heterogeneity and non-Gaussian behavior leading to a poor performance for all the conventional Gaussian detectors. Many works have been already derived in the context of radar detection in non-homogeneous and non-Gaussian clutter. These works can be easily extended in the context of hyperspectral detection. The aim of this pa per is twofold. In the context of Spherically Invariant Random Vectors (SIRV) modeling for the background, we re call some properties of different non-Gaussian detectors built with a nice and robust estimate of the background Covariance Matrix. Secondly, we present some results on regulation of false alarm obtained on experimental background hyper spectral data. These results demonstrate the interest of the proposed detection scheme, and show an excellent correspondence between experimental and theoretical results.