  One of the major science cases of the MUSE integral field spectrograph is the
detection of Lyman-alpha emitters at high redshifts. The on-going and planned
deep fields observations will allow for one large sample of these sources. An
efficient tool to perform blind detection of faint emitters in MUSE datacubes
is a prerequisite of such an endeavor.
  Several line detection algorithms exist but their performance during the
deepest MUSE exposures is hard to quantify, in particular with respect to their
actual false detection rate, or purity. {The aim of this work is to design and
validate} an algorithm that efficiently detects faint spatial-spectral emission
signatures, while allowing for a stable false detection rate over the data cube
and providing in the same time an automated and reliable estimation of the
purity.
  Results on simulated data cubes providing ground truth show that the method
reaches its aims in terms of purity and completeness. When applied to the deep
30-hour exposure MUSE datacube in the Hubble Ultra Deep Field, the algorithms
allows for the confirmed detection of 133 intermediate redshifts galaxies and
248 Lyman Alpha Emitters, including 86 sources with no HST counterpart.
  The algorithm fulfills its aims in terms of detection power and reliability.
It is consequently implemented as a Python package whose code and documentation
are available on GitHub and readthedocs.
