Reducing x-ray dose in computed tomography (CT) is essential for improving patient safety; however, low-dose acquisitions introduce noise and artifacts that degrade diagnostic image quality. Most existing physics-informed reconstruction methods rely on raw projection-domain measurements to enforce data consistency, although such sinogram data are rarely retained in routine clinical workflows. This study addresses this limitation by developing a reconstruction framework that incorporates physical imaging priors without requiring access to projection measurements.We propose the unrolled radon consistency network (URCN), a reconstruction framework that encodes approximate projection-domain structure as a differentiable spatial regularizer within a learned optimization architecture. At each unrolling stage, a parallel-beam Radon surrogate functioning as a geometry-approximate regularizer rather than an exact forward model computes a projection residual between the current reconstruction estimate and the low-dose input. The backprojected residual generates a spatially structured gradient that guides iterative image updates. Critically, this gradient operates as a structured image-domain regularizer whose spatial support is determined by Radon-domain geometry, rather than as a data-consistency constraint in the classical inverse-problem sense.Across 30 held-out Mayo Clinic patients, URCN achieved a peak signal-to-noise ratio (PSNR) of39.4±0.4dB, structural similarity index of0.929±0.013, RMSE of0.035±0.003, and LPIPS of0.098±0.011using the VGG backbone. Compared with the strongest sinogram-free baseline, SwinIR-CT, URCN demonstrated a statistically significant improvement in PSNR of 0.7 dB at the patient level (p<0.01, paired Wilcoxon signed-rank test; Cohen'sd=1.1). Task-based analysis revealed that URCN achieved the lowest noise magnitude among all learning-based approaches evaluated (noise power spectrum peak:72±11HU2⋅mm2) while preserving spatial resolution close to the filtered back-projection reference (modulation transfer functionf50=0.39±0.03lp mm-1), thereby overcoming the typical resolution-smoothing trade-off observed in CNN-based denoisers. When directly applied to the AAPM dataset without retraining, URCN maintained a 0.6 dB performance advantage and preserved relative ranking trends, indicating robustness to acquisition-domain shift.The findings demonstrate that reconstruction quality is influenced not merely by the inclusion of physical constraints, but by the manner in which such constraints are embedded within the optimization process. Spatially structured differentiable gradient injection consistently outperformed scalar penalization strategies. Because URCN operates directly on reconstructed DICOM images rather than raw projection data, it is applicable to large-scale retrospective clinical datasets where sinograms are unavailable, overcoming a major practical limitation of existing physics-informed methods. The proposed framework provides a reproducible and computationally tractable pathway toward clinically deployable low-dose CT reconstruction while preserving physically meaningful image characteristics that purely data-driven approaches often fail to maintain.