\section{Results}
\label{sec:sec5}

Quantitative analysis is presented in Figures \ref{fig:metrics}, \ref{fig:metrics_psnr} and \ref{fig:metrics_nmse}, which display the distributions of SSIM, PSNR, and NMSE metrics for the test set. Boxplots highlight the top-performing methods and their statistical significance across all configurations. 
% Detailed metric averages are provided in  Tabs \textcolor{blue}{S1} - \textcolor{blue}{S4}.

Our results consistently demonstrate that frame-specific sampling outperforms unified sampling across all tested configurations, acceleration factors, and sampling dimensions (line-1D, point-2D). Consistent trends were also observed on an unseen aortic cine dataset with different anatomy and motion patterns as illustrated in \Figure{metrics_ssim_aorta}.


Among the methods evaluated, our proposed E2E-ADS-Recon achieves the highest performance across nearly all combinations of frame-specific and unified setups, for both 1D and 2D sampling. E2E-ADS-Recon shows statistically significant results in most metrics, with the highest SSIM values achieved by variants of our approach. A similar trend is observed for PSNR and NMSE, although in frame-specific 1D sampling at $R=4$, equispaced sampling slightly outperforms our method. When evaluated at higher, unseen acceleration factors ($R=10, 12$), the same qualitative performance ordering was preserved, with adaptive sampling maintaining its advantage over non-adaptive baselines (\Figure{metrics_ssim_10x_12x}).

For 1D sampling, both frame-specific and unified setups benefit from combining our adaptive strategy with equispaced initialization and ACS $k$-space data, yielding the highest average performance. Despite this, non-adaptive equispaced sampling remains the top competitor. At high acceleration factors ($6\times, 8\times$), all ADS configurations generally outperform non-adaptive methods in both frame-specific and unified settings concerning the SSIM metric, as well as the PSNR and NMSE in most cases.

In 2D setups, E2E-ADS-Recon significantly surpasses non-adaptive methods across all metrics and acceleration factors, with optimized parameterized sampling being the closest competitor.

\begin{figure*}[!th]
    \centering
    \includegraphics[width=0.9\textwidth]{figs/fig3.jpg}
    % \vspace{-1pt}
    \caption{SSIM ($\times 100$) metrics across all experimental settings and setups. Diamonds ($\Diamond$) on the box-plot median indicate the average best methods. A star ($\star$) on the upper whisker indicates non-significance in comparison to the average best method. }
    \vspace{-5pt}
    \label{fig:metrics}
\end{figure*}


\begin{figure}[!hbt]
    \centering

    \subfigure[Frame-specific: each frame pattern represented by one row.]{
        \includegraphics[width=\textwidth]{figs/fig4a.jpg}
        \label{fig:masks_a}
    }

    \subfigure[Unified: same patterns are applied to all temporal frames.]{
        \includegraphics[width=0.9\textwidth]{figs/fig4b.jpg}
        \label{fig:masks_b}
    }
    \vspace{-5pt}
    \caption{Examples of 1D patterns across setups at $R=8$ for (a) frame-specific and (b) unified settings. Black: fixed/initial, red: learned pattern. Cyan boxes mark SSIM values.}
    \vspace{-10pt}
    \label{fig:masks}
\end{figure}

\begin{figure}[!ht]
    \centering
    \vspace{-6pt}
    \includegraphics[width=1\textwidth]{figs/fig5.jpg}
    \vspace{-18pt}
    \caption{Example of reconstructions across setups for unified 1D sampling at $R=8$.}
    \label{fig:recon}
    \vspace{-7pt}
\end{figure}


% \input{tabs/tab1}


Qualitative results are shown in \Figure{masks}, which shows examples of generated 1D sampling patterns for both setups.  Visual inspection of generated sampling patterns reveals that learned patterns tend to prioritize lower-frequency components near the $k$-space center, while occasionally incorporating higher frequencies. In \Figure{recon}, we illustrate example reconstructions from the unified experiments at a high acceleration factor ($R=8$), where adaptive methods demonstrate improved preservation of anatomical structures and reduced artifacts relative to non-adaptive approaches. Additional pattern examples and image reconstructions for all setups are available in \Appendix{appendix4-qualitative-results}. 

Inference runtime is reported in \Table{times}. Across all configurations, mean inference times remain within a narrow range of approximately 10.5–11.5 seconds per test volume. Adaptive methods introduced a small additional overhead (less than 1 second on average) relative to non-adaptive baselines, primarily due to the sampling prediction step. Unified compared to frame-specific adaptive sampling setups exhibit faster runtime overall, as expected given their shared sampling mask across frames. 

\vspace{3pt} \noindent \textbf{Reconstruction Model Robustness}
Results are provided in \Appendix{appendix3-medl}, where we replace the reconstruction model with MEDL-Net.  Figures \ref{fig:metrics_ssim_medl}, \ref{fig:metrics_psnr_medl} and \ref{fig:metrics_nmse_medl} present the corresponding SSIM, PSNR, and NMSE metrics. Across both 1D and 2D sampling, the numerical trends remain consistent with those observed using vSHARP as the reconstruction module. In nearly all acceleration-metric combinations, adaptive sampling methods outperform their non-adaptive counterparts on average, except for SSIM at $R=4$, where the $k$tEqui scheme shows a slight, though statistically insignificant, advantage. For 1D sampling, E2E-ADS-Recon with equispaced initialization continues to be the top-performing configuration in most cases. Furthermore, the benefits of adaptive sampling become more evident at higher acceleration factors (e.g., $R=8$). Additionally, while not the primary focus of this study, we observe that employing vSHARP yields overall better results than MEDL-Net.
% 

\vspace{3pt} \noindent \textbf{Ablation Studies} 
Tables \ref{tab:N1-ssim-psnr-nmse} and \ref{tab:NU-ssim-psnr-nmse} provide results from our ablation study employing single ($N=1$) ADS cascade, as well as non-uniform frame-specific adaptive sampling. Using a single cascades yields performance comparable to using two cascades, with most cases outperforming non-adaptive methods. Non-uniform sampling budget allocation did not show competitive results compared to equal budget distribution across time frames.