We present a new method for region of interest (ROI) reconstruction from high-resolution, nontruncated data in parallel-ray X-ray computed tomography (CT). Many of the approaches to ROI CT reconstruction in the literature rely on a costly forward projection step to form an ROI-only sinogram. Our approach instead relies on a digital filtering implementation of the normal operator ((HH)-H-T) to compute a back projected version of the ROI-only sinogram that can be used directly for reconstruction, thus eliminating the forward projection step altogether. Results on three synthetic datasets with a variety of experimental conditions show that the method provides accuracy on par with a full reconstruction at a fraction of the time and memory cost.