## 4 Recent Improvements to the Free-Running Framework  
In 2021, [PERSON] et al. further improved the FRF by introducing focused navigation (fNAV) for 3D non-rigid respiratory motion correction [30]. Instead of only sorting data into multiple respiratory states and reconstructing respiratory resolved images using XD-GRASP, 3D non-rigid intra-bin motion correction of the data is performed. Using an autofocusing-based algorithm [31] that converts a 1D unitless respiratory signal derived from the SI spokes into displacement fields along all three spatial dimensions with physical units, a final 3D image is obtained that is regionally corrected for intra-bin respiratory motion. More recently, [PERSON] et al. extended the use of fNAV to an FRF adapted for visualizing and measuring blood flow [32].  
Also in 2021, [PERSON] et al. introduced a similarity-driven multi-dimensional binning algorithm (SIMBA) as an alternative reconstruction technique [33]. By leveraging intrinsic similarities in the data instead of relying on physiological assumptions and targeting specific motion states, the continuously acquired data can be clustered to find a motion-consistent subset that enables a simple and much faster reconstruction of a single anatomical 3D image. This novel whole-heart image reconstruction method enables the reconstruction of a motion-suppressed image in less than a minute, compared to fully motion-resolved compressed-sensing reconstructions that may last several hours. More recently, SIMBA was further optimized by sharing redundant information in the clustering dimension and by incorporating inter-cluster motion compensation into the CS reconstruction [34].  
In 2022, [PERSON] et al. proposed to integrate an alternative navigation system, called pilot tone (PT), into the FRF for MR image-independent motion detection [35]. This PT navigation system, which comes integrated into the chest coil array, transmits a continuous-wave radiofrequency signal into the magnet bore [36; 37]. This signal, with a frequency outside that of the frequency band of the MR imaging signal, is then captured by the receiver coils after having been modulated by the underlying physiological motion of the subject. Similarly to the aforementioned MR data-driven SG approach of the FRF, both respiratory and cardiac signature curves can be extracted from this signal, but now completely independently from the image acquisition and with a much higher sampling rate. This offers the opportunity to decouple the k-space trajectory from SG signal reception and provides the freedom to explore alternative k-space trajectories.  
Most recently, in 2024, [PERSON] et al. presented the use of non-rigid deformation fields, also referred to as'motion fields' for inter-bin compensation of respiratory motion in the FRF [38]. Given the substantial undersampling of the individual bins (for each cardiac phase and respiratory motion state), direct estimation of deformation fields between these bins from the motion-resolved data is not feasible. However, after collapsing the cardiac dimension and performing intra-bin motion correction using the aforementioned fNAV approach, 3D inter-bin motion between the individual respiratory motion states can be estimated using non-rigid image registration [39]. Simultaneously, the fNAV-corrected data are binned by the cardiac phase. Combined, intra-bin _corrected_ 5D cardiac and respiratory motion-resolved data with inter-bin _compensation_ are obtained. The inclusion of these non-rigid 3D deformation fields enables larger regularization weights during reconstruction [24], which reduces artefacts without incurring motion blur and may be exploited for higher resolution or shortened scan durations. Although this work investigated the use of motion fields for inter-bin correction of respiratory motion only, similar work, albeit unpublished yet, has been performed for inter-bin compensation of cardiac motion.