
\section{Conclusion and Discussion}

% This work introduced E2E-ADS-Recon, an end-to-end framework that jointly learns adaptive dynamic subsampling and reconstruction applied and tested on multi-coil cardiac MRI. By coupling an Adaptive Dynamic Sampler with a state-of-the-art dynamic reconstruction network, the method generates case-specific sampling patterns-either frame-specific or unified-while supporting varying accelerations. Across both 1D and 2D sampling settings, E2E-ADS-Recon consistently outperformed non-adaptive baselines, with the largest improvements observed at higher accelerations. These findings demonstrate that tailoring the sampling strategy to each individual case can enhance the fidelity of dynamic MRI reconstruction and underscore the potential of joint sampling–reconstruction optimization for accelerated imaging. A broader reflection on methodological considerations, limitations, and future directions is provided as an extended discussion in \Appendix{appendix5}.


In this work, we introduced E2E-ADS-Recon, integrating a deep learning-based adaptive sampler for dynamic MRI accelerated acquisition with state-of-the-art reconstruction networks for dynamic reconstruction. E2E-ADS-Recon is trained end-to-end to generate adaptive, case-specific dynamic acquisition patterns for any given acceleration factor,  followed by dynamic image reconstruction, with the aim of exploiting temporal correlations between temporal frames.


We evaluated E2E-ADS-Recon using 4D fully-sampled cine cardiac MRI data under two sampling settings: frame-specific (distinct subsampling patterns per time frame to exploit inter-frame correlations) and unified (the same pattern applied across all frames). We also considered two sampling dimensions: 1D (line) and 2D (point). Our approach was benchmarked against equivalent pipelines that replaced the adaptive sampler of E2E-ADS-Recon with other various non-adaptive sampling schemes, including common 1D or 2D schemes (random, equispaced, Gaussian, radial), as well as data-optimized approaches.


Visualization of the sampling patterns (see \Figure{masks} and \Appendix{appendix4-qualitative-results}) generated by E2E-ADS-Recon revealed that the ADS component consistently produced adaptive patterns with denser sampling in the lower frequency regions (closer to the $k$-space center) which contain a structural information and image contrast information,  while occasionally sampling higher frequencies. In addition, the visualizations show that in frame-specific sampling experiments, the ADS module learned to generate distinct patterns for each temporal frame. As a result, this allowed the reconstruction model to effectively leverage complementary information across frames and produce better reconstructions in comparison to the unified setting.


Even though the performance improvements observed with E2E-ADS-Recon may appear incremental, they are statistically significant. Reporting such improvements is a common practice in MRI literature, where the focus often lies on incremental yet meaningful enhancements (e.g., close performance of top teams in CMRxRecon Challenge 2023 \cite{lyu2024state}). The relatively modest gains in reconstruction quality are partially attributed to the powerful vSHARP model used, which inherently minimizes the impact of different sampling patterns. Nonetheless, the consistent performance gains across experiments highlight the potential of adaptive sampling, particularly at higher accelerations.

Additionally, we replaced the vSHARP model with another state-of-the-art method (MEDL-Net) to assess the reconstruction model’s robustness. The results remained consistent, with adaptive sampling configurations continuing to outperform non-adaptive approaches across sampling dimensions and acceleration factors.


Despite the promising results of E2E-ADS-Recon, its supervised training requires fully-sampled data, similar to other data-optimized or adaptive sampling approaches, limiting its applicability to the availability of such data. Non-learned sampling methods, on the other hand, can leverage subsampled datasets for self-supervised learning of reconstruction models without requiring fully-sampled data. Recent studies have shown that joint supervised and self-supervised training of reconstruction models can enhance self-supervised results \cite{yiasemis2024jssljointsupervisedselfsupervised}. Future work could explore such direction to extend the applicability of E2E-ADS-Recon to datasets without fully-sampled $k$-spaces.

In addition, since all data were acquired at a single site using the same scanner and protocol, the model was evaluated under in-distribution conditions. As a result, its robustness to out-of-distribution variations-such as differences in scanner vendors, acquisition protocols, or patient populations-remains untested. Future work should assess generalization under more heterogeneous, clinically representative conditions.

Another factor to consider is the use of initial data (e.g., ACS) in E2E-ADS-Recon. The ADS module relies on this initialization to generate adapted, case-specific acquisition, unlike optimized sampling methods that do not require pre-sampled data. This dependency on the initial sampling pattern is a limitation shared with methods requiring initial data for calibration, such as GRAPPA or RAKI, where the quantity and size of the initial data significantly affect downstream reconstruction \cite{knoll2020deep}. Similarly, in learned adaptive sampling in static imaging scenarios, initialization with low-frequency (ACS) data is common, as seen in approaches employing reinforcement learning \cite{pineda2020, bakker2020experimental} or deep learning \cite{yin2021end}. Additionally, the influence of different sampling patterns on reconstruction performance has been well-documented in prior studies \cite{YIASEMIS202433, hammernik2017influence}. In E2E-ADS-Recon, using ACS-reconstructed images for initialization is a natural choice, as these data are already required for sensitivity profile estimation in DL-based reconstruction methods \cite{Yiasemis_2022_CVPR}.

While our retrospective study demonstrates the conceptual potential of E2E-ADS-Recon, practical implementation within an MRI scanner remains untested and is beyond the scope of this work. Implementing such an end-to-end framework on a scanner would require substantial engineering and integration efforts; however, this study serves as an initial step toward investigating how sampling and reconstruction might be co-optimized. Importantly, the observed improvements, though small and evaluated retrospectively, suggest that adaptive sampling  may offer meaningful gains if effectively translated into prospective clinical settings.

Although the runtime overhead introduced by adaptive sampling was modest (see \Table{times}), real-time deployment would impose additional constraints. In particular, frame-specific adaptive methods require generating a new sampling pattern for each frame–slice combination within a limited temporal window. The dataset used in this study was acquired with a temporal resolution of 50 milliseconds per cardiac frame (see \Appendix{appendix2-dataset}). As reported in \Section{sec5}, the estimated upper bound on per-frame overhead is approximately 27 milliseconds, suggesting that our current implementation is compatible with this timescale under retrospective conditions. However, actual deployment would introduce additional sources of latency, including scanner–module communication and real-time synchronization, which remain to be addressed in future work.

Our results underscore the advantages of frame-specific sampling over unified strategies. Frame-specific methods, which employ distinct patterns per time frame, more effectively leveraged temporal correlations, resulting in higher reconstruction quality. However, practical challenges such as large gradient switches and eddy currents might arise with frame-specific schemes, whereas unified approaches are less likely to encounter these issues. Additionally, the implementation of frame-specific sampling requires knowledge of the anatomical phase at each moment to apply the correct sampling pattern. Finally, while our results indicate that 2D sampling outperforms 1D sampling consistently with previous studies \cite{yin2021end,YIASEMIS202433}, future studies should investigate the physical implementation and application of 2D sampling in a clinical setting.

Overall, while our study illustrates the potential benefits of adaptive sampling in deep learning–based dynamic MRI reconstruction, future work is needed to evaluate its feasibility in prospective, real-time acquisition settings.