QSMnet-INR: Single-Orientation Quantitative Susceptibility Mapping via Implicit Neural Representation in k-Space

Quantitative Susceptibility Mapping (QSM) reconstructs tissue magnetic susceptibility from MR phase data but remains highly ill-posed in the single-orientation setting due to the cone-null region of the dipole kernel in the Fourier domain. To address this challenge, we propose QSMnet-INR, a physics informed framework that integrates an implicit neural representation (INR) into k-space modeling. The INR learns a continuous dipole response to improve stability in ill-conditioned regions, while a frequency-aware dipole loss enforces consistency with the physical model. Experiments on the 2016 QSM Reconstruction Challenge, a multi-orientation GRE dataset, and clinical data demonstrate improved reconstruction quality and reduced artifacts compared with existing methods, particularly under single orientation settings. Ablation and sensitivity analyses further support the complementary roles of INR-based modeling and frequency-aware regularization. While performance under more extreme susceptibility conditions or unseen acquisition settings warrants further investigation, the results indicate that integrating implicit representations with physics-informed constraints provides an effective approach for stabilizing ill-posed QSM reconstruction.