Anatomy Is the Manifold: Learning Intrinsic Metrics Instead of Images for Prior-Guided MRI Reconstruction

Prior-guided multi-contrast MRI uses a fully sampled companion scan to reconstruct an undersampled target contrast. Networks that predict target intensities from the companion can transfer structures absent from the target and lose accuracy under distribution shift. We train a network to predict edge conductivities on an anatomy graph. These conductivities define a quadratic prior, and reconstruction solves a convex problem driven by target measurements. The formulation returns zero for zero measurements and provides an explicit expression for the effect of companion changes. We use held-out k-space to select among hand-crafted, learned and randomised metrics, supported by a risk-estimation result under uniform random sampling. In synthetic lesion experiments, learned metrics reduce the response to companion-only lesions while recovering more of target-only lesions than intensity priors. Learned geometry remains sensitive to companion appearance and registration. Randomising both during training reduces the PSNR loss from a one-pixel misalignment to 2.0 dB, compared with 3.6–5.0 dB for intensity priors trained with the same augmentation. Geometry selection remains within 0.6 dB of intensity selection in distribution and improves PSNR by 0.6–2.3 dB over the strongest intensity baseline on each cohort with a scanner, pathology, contrast or anatomy shift. On raw four-coil 0.3 T M4Raw data, the learned metric achieves higher PSNR than U-Net, MoDL and TGVN.