Target-anchored gradient integration in joint semi-supervised learning for cross-domain MRI reconstruction

Joint Supervised and Self-supervised Learning (JSSL) trains an MRI reconstruction model on a fully-sampled proxy domain and a subsampled target domain simultaneously. However, the supervised loss on the proxy domain converges quickly and produces small gradients, while the self-supervised loss on the target domain retains large, noisy gradients. This persistent magnitude imbalance allows the proxy domain, despite its smaller gradients, to dominate optimization, degrading target-domain reconstruction. The Pareto Optimization Strategy (POS) addresses gradient conflict via minimum-norm aggregation but fails in this setting because it is magnitude-sensitive. It allocates weight inversely to gradient norm, silencing the target domain when its gradients are large. A simple lower-bound constraint on the target weight recovers substantial performance, revealing that the failure stems from asymmetric gradient scaling rather than directional conflict. We propose Target-Anchored Gradient Integration (TAGI), which resolves the imbalance by operating on the unit sphere of gradient directions, decoupling direction from magnitude. TAGI anchors the target domain at unit weight, treats the proxy as a tunable regularizer, and applies conflict-aware projection to neutralize opposing gradient components. We establish a formal equivalence between TAGI and constrained POS, showing that constrained POS implicitly performs norm-ratio-adaptive weighting. This reduces TAGI to a single mixing ratio c, for which we derive a data-driven adaptive scheduler. Across six cross-domain configurations at 4× and 8× acceleration, TAGI attains the highest PSNR on ten of twelve settings, with a peak gain of ＋4.12 dB over JSSL, and the best SSIM on seven of twelve settings. Ablation studies confirm that the norm-ratio-adaptive trust coefficient provides the largest individual contribution, while conflict projection and the data-driven scheduler each yield measurable improvements, and the method is robust to the choice of the mixing ratio.