In MR-guided interventions, it is mandatory to establish a solid relationship between the imaging coordinate system and world coordinates. This is particularly important in image-guided radiotherapy (IGRT) on an MRI accelerator, as the interaction of matter with γ-radiation cannot be visualized. In conventional acquisitions, off-resonance effects cause discrepancies between coordinate systems. We propose to mitigate this by using only phase encoding and to reduce the longer acquisitions by under-sampling and regularized reconstruction. To illustrate the performance of this acquisition in the presence of off-resonance phenomena, phantom and in vivo images are acquired using spin-echo (SE) and purely phase-encoded sequences. Data are retrospectively under-sampled and reconstructed iteratively. We observe accurate geometries in purely phase-encoded images for all cases, whereas SE images of the same phantoms display image distortions. Regularized reconstruction yields accurate phantom images under high acceleration factors. In vivo images were reconstructed faithfully while using acceleration factors up to 4. With the proposed technique, inherently undistorted images with one-to-one correspondence to world coordinates can be obtained. It is a valuable tool in geometry quality assurance, treatment planning and online image guidance. Under-sampled acquisition combined with regularized reconstruction can be used to accelerate the acquisition while retaining geometrical accuracy.