  Direct imaging of exoplanets is a challenging task as it requires to reach a
high contrast at very close separation to the star. Today, the main limitation
in the high-contrast images is the quasi-static speckles that are created by
residual instrumental aberrations. They have the same angular size as planetary
companions and are often brighter, hence hindering our capability to detect
exoplanets. Dedicated observation strategies and signal processing techniques
are necessary to disentangle these speckles from planetary signals. The output
of these methods is a detection map in which the value of each pixel is related
to a probability of presence of a planetary signal. The detection map found in
the literature relies on the assumption that the residual noise is Gaussian.
However, this is known to lead to higher false positive rates, especially close
to the star. In this paper, we re-visit the notion of detection map by
analyzing the speckle noise distribution, namely the Modified Rician
distribution. We use non-asymptotic analysis of the sum of random variables to
show that the tail of the distribution of the residual noise decays as an
exponential distribution, hence explaining the high false detection rate
obtained with the Gaussian assumption. From this analysis, we introduce a novel
time domain detection map and we demonstrate its capabilities and the relevance
of our approach through experiments on real data. We also provide an empirical
rule to determine detection threshold providing a good trade off between true
positive and false positive rates for exoplanet detection.
