  IceCube is a neutrino observatory deployed in the glacial ice at the
geographic South Pole. The $\nu_\mu$ energy unfolding described in this paper
is based on data taken with IceCube in its 79-string configuration.
  A sample of muon neutrino charged-current interactions with a purity of
99.5\% was selected by means of a multivariate classification process based on
machine learning. The subsequent unfolding was performed using the software
\truee. The resulting spectrum covers an E$_\nu$-range of more than four orders
of magnitude from 125 GeV to 3.2 PeV. Compared to the Honda atmospheric
neutrino flux model, the energy spectrum shows an excess of more than
$1.9\,\sigma$ in four adjacent bins for neutrino energies
$E_\nu\geq177.8$\,TeV. The obtained spectrum is fully compatible with previous
measurements of the atmospheric neutrino flux and recent IceCube measurements
of a flux of high-energy astrophysical neutrinos.
