We report on tomographic measurements in the terahertz spectral range and subsequent image reconstruction of a phantom subject. At terahertz wavelengths we abandon the traditional hard-field tomography approach to use attenuation measurements for imaging, because of the strong beam steering at the periphery of objects and the existence of a substantial diffusely scattered component. Under these conditions we focus on imaging from the measurements of the terahertz pulse propagation delay, taken with a system for time-domain terahertz spectroscopy, and reconstruct the subject's optical density instead of e.g. material density as in x-ray tomography. The novelty is our experimental approach to retain, by spatial and temporal filtering, only the photons that propagate along the shortest straight paths allowing hard-field tomography, approach for the image reconstruction. We show that pulse delay measurements result in path integrals of the light's group velocity in the subject and therefore the image reconstruction yields the spatial distribution of the real part of the refractive index. Furthermore, we suggest a procedure whereby the pulse delay time is calculated from the time-domain waveform with a better precision, taking into account the physics of THz generation by ultrashort pulses in a biased-gap antenna.