Discrete inverse theory (DIT) provides an orderly framework in which to combine measurements of total electron content (TEC) with a priori information to image the ionosphere tomographically. We have developed a DIT-based tomographic processor for use with relative TEC data. The processor's a priori information comprises the global mean of over 17,000 profiles generated from an ionospheric model, for use as a “generic background”; empirical orthogonal functions (EOFs) spanning the same model profiles, for use as vertical basis functions; and a red power-law horizontal spectrum. Relative TEC data are used to evaluate coefficients multiplying the EOFs and harmonics, thus quantifying a perturbation electron-density field. The perturbation field, which need not be small, is added to the a priori background to produce the image. We present here several images produced by employing the processor with simulated TEC data based on in situ ionospheric measurements and incoherent-scatter radar observations.©1994 John Wiley & Sons Inc