The reconstruction of artifact-free images from truncated datasets poses a challenging problem in any medical imaging modality. Such a problem occurs in Projection Reconstruction MRI when the object is not fully encompassed within the FOV. This is always the case for coronal and sagittal planes in extremity imaging. Introduced recently in CT and SPECT, the derivative back projection-finite Hilbert inverse (DBP-FHI) algorithm has been proven useful to accurately reconstruct from truncated datasets within regions-of-interest. Here, we propose an adaptation of the DBP-FHI algorithm to handle PR-MRI data. Details of the underlying theory and its discrete implementation are explained. Numerical simulations show that shading artifacts present when the image is reconstructed with filtered back projection (FBP) disappear with this new algorithm. In vivo phantom and knee scans demonstrate that truncation artifacts resulting from the FBP algorithm are mitigated by the DBP-FHI algorithm. Within geometric constraints, the proposed algorithm always outperforms the FBP algorithm by its ability to reconstruct truncated datasets.