An important outcome of radar signal processing is the detection of the presence or absence of target reflections at each pixel location in a radar image. In this paper, we propose a technique based on extreme value theory for characterizing target detection in the context of compressive sensing. In order to accurately characterize target detection in radar systems, we need to relate detection thresholds and probabilities of false alarm. However, when convex optimization algorithms are used for compressive radar imaging, the recovered signal may have unknown and arbitrary probability distributions. In such cases, we resort to Monte Carlo simulations to construct empirical distributions. Computationally, this approach is impractical for computing thresholds for low probabilities of false alarm. We propose to circumvent this problem by using results from extreme-value theory.