  Compton scattering is a well-established technique that can provide detailed
information about electronic states in solids. Making use of the principle of
tomography, it is possible to determine the Fermi surface from sets of
Compton-scattering data with different scattering axes. Practical applications,
however, are limited due to long acquisition time required for measuring along
enough number of scattering directions. Here, we propose to overcome this
difficulty using compressed sensing. Taking advantage of a hidden sparsity in
the momentum distribution, we are able to reconstruct the three-dimensional
momentum distribution of bcc-Li, and identify the Fermi surface with as little
as 14 directions of scattering data with unprecedented accuracy. This
compressed-sensing approach will permit further wider applications of the
Compton scattering experiments.
