  Exoplanet detections and characterizations via direct imaging require high
contrast and high angular resolution. These requirements typically require (i)
cutting-edge instrumental facilities, (ii) optimized differential imaging to
introduce a diversity in the signals of the sought-for objects, and (iii)
dedicated processing algorithms to further eliminate the residual stellar
leakages.
  Substantial efforts have been undertaken on the design of more efficient
post-processing algorithms but their performance remains upper-bounded at
shorter angular separations due to the the lack of diversity induced by the
processing of each epoch of observations individually. We propose a new
algorithm that is able to combine several observations of the same star by
accounting for the Keplerian orbital motion across epochs of the sought-for
sources in order to constructively co-add their weak signals.
  The proposed algorithm, PACOME, integrates an exploration of the plausible
orbits within a statistical detection and estimation formalism. It is extended
to a multi-epoch combination of the maximum likelihood framework of PACO, which
is a mono-epoch post-processing algorithm. We derive a reliable multi-epoch
detection criterion, interpretable both in terms of probability of detection
and of false alarm.
  We tested the proposed algorithm on several datasets obtained from the
VLT/SPHERE instrument with IRDIS and IFS. By resorting to injections of
synthetic exoplanets, we show that PACOME is able to detect sources remaining
undetectable in mono-epoch frameworks. The gain in detection sensitivity scales
as high as the square root of the number of epochs. We also applied PACOME on a
set of observations from the HR 8799 star hosting four known exoplanets, which
are detected with very high signal-to-noise ratios. In addition, its
implementation is efficient, fast, and fully automatized.
