  A recent re-determination of the non-thermal component of the hard X-ray to
soft gamma-ray emission from the Galactic ridge, using the SPI instrument on
the INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) Observatory, is
shown to be well reproduced as inverse-Compton emission from the interstellar
medium. Both cosmic-ray primary electrons and secondary electrons and positrons
contribute to the emission. The prediction uses the GALPROP model and includes
a new calculation of the interstellar radiation field. This may solve a
long-standing mystery of the origin of this emission, and potentially opens a
new window on Galactic cosmic rays.
