arXiv:2610.19120v1 Announce Type: new Abstract: Purpose: Free-breathing abdominal MRI is limited by respiratory motion, which introduces image artifacts and k-space inconsistencies. Existing reconstruction approaches often depend on pre-estimated motion fields or external respiratory surrogate signals. We propose a coupled reconstruction-motion estimation algorithm for self-navigated free-breathing acquisition, in which motion is represented by compact Gaussian primitives and jointly refined with the image estimates during iterative reconstruction. Methods: An iterative reconstruction that alternates between data consistency updates and motion modelling was proposed. Respiratory motion was represented using Gaussian primitives. A Gaussian splatting was integrated into the reconstruction algorithm. The method was evaluated on self-navigated free-breathing Cartesian gradient-echo (GRE) acquisition in four healthy volunteers, including retrospective scan shortening experiments, and was compared with regularized compressed sensing (CS) reconstruction. Results: Respiratory motion states were reconstructed in approximately 1.5 min. Compared with CS, the proposed method improved visual image quality, particularly in coronal liver views, and better preserved anatomical structures in retrospectively shortened acquisitions. These findings provide proof of concept for the proposed method. Conclusion: The proposed coupled reconstruction-motion estimation algorithm improved visual image quality compared with CS alone. Gaussian primitives provided a compact and sufficiently flexible representation of nonrigid respiratory motion with practical runtime, supporting further scanner integration and validation in larger cohorts.