The objective of magnetic detection electrical impedance tomography (MD-EIT) is to reconstruct in vivo images of conductivity from magnetic field measurements taken around the body. MD-EIT is performed by applying an alternating current, at one of a range of frequencies, to a conducting object through a pair of electrodes fixed to the surface of the object. Magnetic field measurements recorded by search coils at a number of positions around the object are used to determine the current distribution that is generating the magnetic field. From this distribution, a conductivity map of a cross-section of the object can be reconstructed. This paper describes the development of an MD-EIT data acquisition system and discusses the related image reconstruction issues. The ill-conditioned nature of the inverse problem is examined and a number of image reconstruction methods are compared. The technical feasibility of MD-EIT data collection and image reconstruction is demonstrated with example images of current density from both phantom and human data.