An instrument is demonstrated whereby radiographic images of a sample's electron density are compiled from the information encoded in the energy spectra of gamma rays backscattered from one side of the sample. Nondestructive inspection of aluminum airframes is the application of interest, so it is assumed that access is restricted to only one surface of the object under inspection. Use of energy coding allows imaging in a fan beamrather than independent interrogation of individual volume elements. The Multiplexed Compton ScatterTomograph (MCST) instrument consists of an array of planar high-purity germanium detectors, a set of fan beamcollimators, and a Cd109 radionuclide source. Instrument signals are converted to electron density images using a penalized weighted least squares image reconstruction algorithm coupled with a deterministic system model that includes effects of finite source and detector size, detector resolution and efficiency, attenuation, and Doppler broadening. The Doppler broadening, resulting from the momentum distribution of bound electrons, is significant at the energies used here. The proof-of-principle instrument is demonstrated on some aluminum samples. In an 8-mm thick sample with a 4 mm void in its center, contrast recovery of 90% is achieved. In a 10-mm thick sample with a 3 rum void at the back, about 85% of the contrast is recovered.