  The performance demands of future particle-physics experiments investigating
the high-energy frontier pose a number of new challenges, forcing us to find
new solutions for the detection, identification, and measurement of final-state
particles in subnuclear collisions. One such challenge is the precise
measurement of muon momenta at very high energy, where the curvature provided
by conceivable magnetic fields in realistic detectors proves insufficient to
achieve the desired resolution.
  In this work we show the feasibility of an entirely new avenue for the
measurement of the energy of muons based on their radiative losses in a dense,
finely segmented calorimeter. This is made possible by the use of the spatial
information of the clusters of deposited photon energy in the regression task.
Using a homogeneous lead-tungstate calorimeter as a benchmark, we show how
energy losses may provide significant complementary information for the
estimate of muon energies above 1 TeV.
