\section{Experiments}
\label{sec:experiment}
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\subsection{Experimental Settings}
\subsubsection{Datasets}
We evaluate our method on two widely used benchmark datasets, i.e., CAVE and Harvard. CAVE consists of 32 indoor hyperspectral images, each with a spatial resolution of 512$\times$512 pixels and 31 spectral bands ranging from 400 nm to 700 nm. The Harvard dataset contains 50 outdoor hyperspectral images, each with a resolution of 1392$\times$1040 pixels and 31 spectral bands covering the 420 nm to 720 nm wavelength range. For training and testing, we randomly split approximately 80\% of the images from each dataset for training and use the remaining 20\% for testing. To construct the training set, we randomly crop 64 patches from each training image in the CAVE dataset and 30 patches from each image in the Harvard dataset. To accommodate the scaling factors of $\times$4, $\times$8, and $\times$12, we extract the top-left regions of the test images, with sizes of 480$\times$480$\times$31 for CAVE and 576×576×31 for Harvard, as the evaluation areas.
% We evaluate the proposed method on two widely used hyperspectral benchmarks: CAVE and Harvard. CAVE contains 32 indoor images at 512×512 resolution with 31 bands spanning 400–700 nm, while Harvard includes 50 outdoor images at 1392×1040 resolution with 31 bands covering 420–720 nm. For each dataset, 80\% of the images are used for training and 20\% for testing. We randomly extract 64 patches per training image for CAVE and 30 for Harvard. To support scaling factors of ×4, ×8, and ×12, we crop the top-left regions of the tested images—480×480×31 for CAVE and 576×576×31 for Harvard—for evaluation.

% Data augmentation on the training set includes rolling, rotations (90°, 180°, 270°), and flipping. To simulate diverse degradations, isotropic or anisotropic Gaussian kernels of five sizes are randomly generated and convolved with HR images, alone or combined with downsampling, to produce LR images. For testing, LR inputs are generated via bicubic downsampling.

Data augmentation techniques applied to the training set, including rolling, rotations (90°, 180°, and 270°), and flipping operations. To simulate diverse degradation patterns, isotropic or anisotropic Gaussian functions are randomly used to generate sampling kernels of five different sizes. These kernels are then applied to the HR training images via convolution or a combination of convolution and downsampling to produce the corresponding LR versions. For testing samples, bicubic downsampling is adopted to generate the LR-degraded version.

\subsubsection{Comparison methods \& Evaluation metrics}
% For comparison, we select seven state-of-the-art methods, including HySure \cite{simoes2014convex}, SSRNet \cite{zhang2020ssr}, MoG-DCN \cite{dong2021model}, IFMSR \cite{li2023rgb}, PSRT \cite{deng2023psrt}, MSST \cite{jia2023multiscale}, and KNLNet \cite{ran2024knlconv}. Among them, HySure is an unsupervised, traditional optimization-based method, while the others are deep learning-based approaches.
For comparison, we evaluate seven state-of-the-art methods: HySure \cite{simoes2014convex}, SSRNet \cite{zhang2020ssr}, MoG-DCN \cite{dong2021model}, IFMSR \cite{li2023rgb}, PSRT \cite{deng2023psrt}, MSST \cite{jia2023multiscale}, and KNLNet \cite{ran2024knlconv}. Among them, HySure is a traditional unsupervised method that formulates hyperspectral image super-resolution as a convex optimization problem without requiring paired training data. The remaining methods are all based on deep learning frameworks, designed to learn nonlinear mappings from LR inputs to HR hyperspectral outputs through data-driven training.

To quantitatively evaluate super-resolution performance, we use five standard metrics: peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), spectral angle mapper (SAM), root mean square error (RMSE), and correlation coefficient (CC). Among the five evaluation metrics, PSNR, SSIM, and CC are positively correlated with performance, meaning that higher values indicate better reconstruction quality \cite{10990127}.
\subsubsection{Implementation Details}
In this study, all convolutional layers employ 3$\times$3 kernels with 64 filters, unless otherwise specified. The network is trained using the Adam optimizer with parameters $\beta_1 = 0.9$ and $\beta_2 = 0.999$. The initial learning rate is set to 1e-4 and is halved every 40 epochs over a total of 200 epochs. The implementation is based on the PyTorch framework and conducted on an NVIDIA GeForce RTX 3090 GPU. The network is optimized using the $\mathcal{L}_1$ loss function, defined as:
\begin{equation}
	\mathcal{L}_1 = \|{\bm I}_i^{hr} -  \bm I_i^{sr}\|_1
\end{equation}
where $\bm I_i^{\text{hr}}$ and $\bm I_i^{\text{sr}}$ denote the ground-truth and reconstructed high-resolution images of the $i$-th spectral band, respectively.

\subsection{Study on the Number of Cascaded DDF Modules}
\begin{table}[htbp]
	\centering
	\caption{Study of the Number of Cascaded DDF Modules on the CAVE Dataset at the Scale Factor 4}
	\label{Tab.4}
    \renewcommand{\arraystretch}{1.1}  % 控制行高，适配半页行距
    \setlength{\tabcolsep}{1mm}       % 控制列间距，均匀分布
    %\small                             % 缩小字号，更适合论文排版
	\begin{tabular}{c|cccc}
    \hline
    Evaluation indices & 1       & 2       & 3       & 4       \\ \hline
    PSNR$\uparrow$               & 45.0548 & 45.7476 & 45.8552 & 45.6232 \\
    SSIM$\uparrow$               & 0.9917  & 0.9937  & 0.9938  & 0.9927  \\
    SAM$\downarrow$                & 3.3582  & 2.9457  & 2.9194  & 3.0224  \\
    Param.             & 1208K   & 2172K   & 3135K   & 4098K   \\ \hline
    \end{tabular}
\end{table}
To investigate the impact of the number of cascaded Dual-Domain Fusion (DDF) modules on reconstruction performance, we conduct a set of experiments on the CAVE dataset at a scale factor of $\times$4. Specifically, we vary the number of cascaded modules from 1 to 4 and evaluate the corresponding quantitative results, as summarized in Table~\ref{Tab.4}. As the number of cascaded modules increases, the model performance exhibits a general upward trend. Notably, increasing the number from 1 to 2 leads to a significant improvement: PSNR increases by 0.6928, SSIM improves by 0.0020, and SAM decreases by 0.4125, indicating enhanced capability in recovering spatial details and preserving spectral fidelity. Further increasing the number to 3 yields marginal performance gains, with PSNR reaching 45.8552 and SAM slightly decreasing to 2.9194. However, when the number of modules is increased to 4, a slight performance drop is observed. This degradation is likely attributed to overfitting, caused by the substantially increased parameter count (up to 4098K) and the limited availability of training samples. Considering both reconstruction performance and model efficiency, we adopt two cascaded DDF modules as the default configuration in our framework.



\begin{table}[htbp]
	\centering
	\caption{Study of Different Configurations of the DDFL Network on the CAVE Dataset at the Scale Factor 4}
	\label{Tab.4}
    \renewcommand{\arraystretch}{1.1}  % 控制行高，适配半页行距
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    %\small                             % 缩小字号，更适合论文排版
	\begin{tabular}{c|ccc}
        \hline
        Module & \multicolumn{3}{c}{Different combinations of modules} \\ \hline
        $\mathcal{B}_k^{\mathrm{Fre}}$ & $\surd$ & $\times$ & $\surd$ \\
        $\mathcal{B}_k^{\mathrm{Spa}}$ & $\surd$ & $\surd$ & $\times$ \\ \hline
        PSNR$\uparrow$                  & 45.7476       &    43.1123           &  43.2225       \\
        SSIM$\uparrow$                  & 0.9937        &    0.9821            &  0.9823        \\
        SAM$\downarrow$                 & 2.9457        &    4.0021            &  3.6823        \\ \hline
	\end{tabular}
\end{table}

\subsection{Ablation Studies}
To evaluate the contribution of each component in our DDLN model, we conduct ablation experiments by selectively removing the frequency domain branch ($\mathcal{B}_k^{\mathrm{Fre}}$) and the spatial domain branch ($\mathcal{B}_k^{\mathrm{Spa}}$). As shown in Table \ref{Tab.4}, removing either branch causes a noticeable performance drop, confirming their complementary roles in feature representation. Specifically, the removal of the frequency domain branch causes a significant decline in PSNR and SAM, indicating its effectiveness in capturing global frequency information. Similarly, discarding the spatial domain branch also results in degraded performance, underscoring its importance in modeling fine-grained spatial structures. These results demonstrate that both branches collaboratively enhance the overall reconstruction quality, thereby validating the effectiveness of the dual-domain exploration strategy.

\subsection{Comparison with State-of-the-Art Methods}
Table \ref{natureTab} reports the quantitative performance of different methods across six evaluation metrics, along with their model parameter sizes. The best and second-best results are highlighted in bold and underlined, respectively. It can be observed that HySure, as an unsupervised method lacking explicit supervisory signals, yields the poorest performance. SSRNet introduces spatial and spectral loss functions and exhibits high parameter efficiency. However, its relatively shallow network architecture limits its expressive power, constraining overall performance. MoG-DCN enhances hyperspectral image representations by learning affine transformation coefficients from multispectral features. Nonetheless, this strategy performs suboptimally in scenarios where spatial deformation differences are minimal. PSRT and MSST, both Transformer-based approaches, can effectively capture long-range contextual dependencies. However, such architectures typically require large-scale training datasets, leading to underperformance in hyperspectral scenarios with limited labeled samples. KNLNet explores long-range dependencies in kernel space and demonstrates superior spatial fidelity—for instance, achieving second-best PSNR across all scales ($\times 4$, $\times 8$, and $\times 12$) on the CAVE dataset. However, KNLNet does not explicitly model inter-modal interactions, which can lead to excessive noise being introduced during the fusion of complementary modalities. As a result, it suffers from severe spectral distortions; for example, on the Harvard and CAVE datasets at scale $\times 4$, the SAM values are 0.1124 and 1.0721 higher than the best-performing method, respectively.

In contrast, the proposed DDLN explicitly models interactions between modalities in both the frequency and spatial domains, enabling effective multi-domain information fusion and improving reconstruction accuracy. For instance, on the CAVE dataset at scale $\times 8$, the proposed method surpasses the second-best results by 0.6155 in PSNR, 0.0035 in SSIM, and 0.6245 in SAM.
\begin{table*}[htbp]
        \centering
	\caption{Quantitative Evaluation with Other State-of-the-art Competitors at Different Scales on Harvard and CAVE Datasets by Parameter Number and PSNR/SSIM/SAM/RMSE/CC}
	\label{natureTab} 
	%	\renewcommand\tabcolsep{5pt} 
	\renewcommand\arraystretch{1.1} %行距/
	\renewcommand\tabcolsep{1.1mm}  %列距
	%	\footnotesize 
	\begin{tabular}{rcccccccccccc}
		\toprule		\addlinespace[-1pt]
		&       &        & \multicolumn{5}{c}{\multirow{-1}[-1]{*}{Harvard}}                                   & \multicolumn{5}{c}{\multirow{-1}[-1]{*}{CAVE}}                                      \\ \cmidrule(lr){4-8} \cmidrule(lr){9-13} 
		\multicolumn{1}{c}{\multirow{-2}[1]{*}{Method}} & \multicolumn{1}{c}{\multirow{-2}[1]{*}{Scale}} & \multirow{-2}[1]{*}{Param.}& PSNR$\uparrow$    & SSIM$\uparrow$   & SAM$\downarrow$    & RMSE$\downarrow$   & CC$\uparrow$     & PSNR$\uparrow$    & SSIM$\uparrow$    & SAM$\downarrow$    & RMSE$\downarrow$   & CC$\uparrow$       \\ \hline	
		HySure\cite{simoes2014convex}                                      & $\times$4                      & /                             & 40.5967 & 0.9818 & 2.2549 & 0.0102 & 0.9954       & 33.4454 & 0.9199  & 10.3347& 0.0228 & 0.9736       \\
		SSRNet\cite{zhang2020ssr}                                     & $\times$4                      & 26K                       & 43.2856 & 0.9809 & 2.3027 & 0.0071 & 0.9966   & 42.1299 & 0.9820  & 5.5191 & 0.0085 & 0.9954  \\
		MoG-DCN\cite{dong2021model}                                     & $\times$4                      & 7071K                     & 44.5263 & 0.9821 & 2.2225 & 0.0061 & 0.9971    & 45.0414 & 0.9879  & 3.9045 & 0.0062 & 0.9971  \\
		IFMSR\cite{li2023rgb}                                       & $\times$4                      & 1725K                     & 42.7411 & 0.9820 & 2.2037 & 0.0076 & 0.9970   & 42.7529 & 0.9889  & \underline{3.1725} & 0.0079 & 0.9957  \\
		PSRT\cite{deng2023psrt}                                        & $\times$4                      & 247K                      & \underline{44.8436} & 0.9821 & \underline{2.1042} & \underline{0.0058} & 0.9969    & 42.8007 & 0.9789  & 3.6072 & 0.0081 & 0.9948  \\
		MSST\cite{jia2023multiscale}                                        & $\times$4                      & 16631K                   & 42.7181 & 0.9780 & 2.8541 & 0.0075 & 0.9965    & 43.3527 & 0.9816  & 6.1109 & 0.0074 & 0.9964  \\
	%	SFPN\cite{SFPN}                                        & $\times$4                      & 1164K                     & 44.6934 & \underline{0.9836} & \underline{2.0614} & 0.0060 & 0.9976    & 44.9178 & 0.9931  & 2.6849 & 0.0061 & 0.9976  \\
	%	MulSR\cite{MulSR}                                       & $\times$4                      & 4636K                     & \underline{44.9451} & 0.9833 & 2.1075 & \underline{0.0058} & \underline{0.9977}   & 45.2596 & \underline{0.9933}  & \underline{2.5181} & 0.0058 & \underline{0.9978}  \\
		KNLNet\cite{ran2024knlconv}                                      & $\times$4                      & 259K                      & 44.7729 & \underline{0.9832} & 2.1750 & 0.0059 & \underline{0.9974}    & \underline{45.7321} & \underline{0.9905}  & 4.0178 & \underline{0.0056} & \underline{0.9978}  \\ 
		DDLN [ours]                                       & $\times$4                      & 2172K                     & \textbf{45.1658} & \textbf{0.9839} & \textbf{2.0626} & \textbf{0.0056} & \textbf{0.9978}   & \textbf{45.7476} & \textbf{0.9937}  & \textbf{2.9457} & \textbf{0.0055} & \textbf{0.9981}  \\ \hline 
		HySure\cite{simoes2014convex}                                      & $\times$8                      & /                           & 35.9152 & 0.9655 & 3.9217 & 0.0172 & 0.9866    & 28.1364 & 0.8516  & 18.3129& 0.0442 & 0.9200  \\
		SSRNet\cite{zhang2020ssr}                                      & $\times$8                      & 26K                       & 42.6630 & 0.9806 & 2.4056 & 0.0077 & 0.9963   & 41.5099 & 0.9786  & 5.8655 & 0.0091 & 0.9944 \\
		MoG-DCN\cite{dong2021model}                                     & $\times$8                      & 7071K                     & \underline{44.2608} & 0.9817 & \underline{2.2666} & \underline{0.0063} & 0.9970    & 44.0708 & 0.9873  & \underline{3.9393} & 0.0069 & 0.9966  \\
		IFMSR\cite{li2023rgb}                                       & $\times$8                      & 1725K                     & 41.1873 & 0.9802 & 2.4600 & 0.0093 & 0.9954    & 40.0497 & 0.9844  & 4.0225 & 0.0107 & 0.9926  \\
		PSRT\cite{deng2023psrt}                                        & $\times$8                      & 247K                      & 43.6057 & 0.9807 & 2.3144 & 0.0068 & 0.9958   & 41.5527 & 0.9738  & 4.3212 & 0.0093 & 0.9931  \\
		MSST\cite{jia2023multiscale}                                        & $\times$8                      & 18404K                   & 42.3303 & 0.9779 & 3.0590 & 0.0079 & 0.9965    & 41.8637 & 0.9757  & 7.2599 & 0.0087 & 0.9951  \\
	%	SFPN\cite{SFPN}                                        & $\times$8                      & 1164K                     & 44.1819 & \underline{0.9834} & 2.1455 & 0.0064 & 0.9973    & 44.1061 & \underline{0.9932}  & 2.9963 & 0.0066 & \underline{0.9972} \\
	%	MulSR\cite{MulSR}                                       & $\times$8                      & 4636K                   & \underline{44.5628} & \underline{0.9834} & \underline{2.1417} & \underline{0.0061} & \textbf{0.9976}    & 44.3391 & 0.9931  & \textbf{2.8714} & 0.0066 & 0.9971 \\
		KNLNet\cite{ran2024knlconv}                                      & $\times$8                      & 259K                    & 44.2304 & \underline{0.9825} & 2.2698 & \underline{0.0063} & \underline{0.9974}    & \underline{44.7368} & \underline{0.9897}  & 4.5563 & \underline{0.0063} & \underline{0.9972}  \\ 
		DDLN [ours]                                       & $\times$8                      & 2172K                     & \textbf{44.8772} & \textbf{0.9838} & \textbf{2.1372} & \textbf{0.0059} & \textbf{0.9975}    & \textbf{45.3523} & \textbf{0.9932}  & \textbf{3.3148} & \textbf{0.0059} & \textbf{0.9976}  \\ \hline 
		HySure\cite{simoes2014convex}                                      & $\times$12                     & /                            & 32.7803 & 0.9475 & 5.9659 & 0.0278 & 0.9782       & 24.8233 & 0.7931  & 27.3215& 0.6320 & 0.8579  \\
		SSRNet\cite{zhang2020ssr}                                      & $\times$12                     & 26K                      & 42.5665 & 0.9805 & 2.4371 & 0.0079 & 0.9958    & 41.0082 & 0.9778  & 5.6928 & 0.0096 & 0.9937  \\
		MoG-DCN\cite{dong2021model}                                     & $\times$12                     & 7071K                    & 43.7853 & 0.9816 & \underline{2.2866} & 0.0068 & 0.9967   & 43.4875 & 0.9868  & \textbf{4.1433} & 0.0074 & 0.9962  \\
		IFMSR\cite{li2023rgb}                                       & $\times$12                     & 1725K                     & 39.9500 & 0.9781 & 2.7414 & 0.0107 & 0.9938    & 38.8197 & 0.9810  & 4.7085 & 0.0125 & 0.9902  \\
		PSRT\cite{deng2023psrt}                                        & $\times$12                     & 247K                      & 42.4168 & 0.9793 & 2.4573 & 0.0073 & 0.9939    & 42.5480 & 0.9814  & \underline{4.1869} & 0.0083 & 0.9944  \\
		MSST\cite{jia2023multiscale}                                        & $\times$12                     & 21358K                  & 42.6189& 0.9790 & 2.6255  & 0.0077 & 0.9962    & 41.5560 & 0.9792  & 5.7534 & 0.0091 & 0.9946  \\
	%	SFPN\cite{SFPN}                                        & $\times$12                     & 1164K                     & 43.7386 & \underline{0.9834} & 2.1998 & 0.0069 & 0.9970   & 43.0457 & \underline{0.9920}  & 3.5455 & 0.0077 & 0.9964  \\
	%	MulSR\cite{MulSR}                                       & $\times$12                     & 4636K                     & \underline{44.2450} & 0.9833 & \underline{2.1804} & \underline{0.0063} & \textbf{0.9975}   & 43.0722 & 0.9916  & \textbf{3.2364} & 0.0076 & 0.9963  \\
		KNLNet\cite{ran2024knlconv}                                      & $\times$12                     & 259K                     & \textbf{44.1506} & \underline{0.9827} & 2.2918 & \textbf{0.0064} & \textbf{0.9974}   & \underline{43.6919} & \underline{0.9894}  & 4.4409 & \underline{0.0071} & \underline{0.9965}  \\ 
		DDLN [ours]                                       & $\times$12                     & 2172K                     & \underline{44.0442} & \textbf{0.9835} & \textbf{2.2234} & \underline{0.0065} & \underline{0.9972}   & \textbf{43.8342} & \textbf{0.9902}  & 4.4957 & \textbf{0.0070} & \textbf{0.9973}  \\ \hline 
	\end{tabular}
\end{table*}

%In addition, to intuitively compare the reconstruction quality of different methods, we present visual results at a scale factor of $\times4$. To highlight differences between the reconstructed hyperspectral images and their corresponding high-resolution ground truth, we also provide absolute error maps. In these maps, darker blue indicates lower reconstruction error. As shown in Fig. \ref{CAVE_Harvard}, the proposed DDLN exhibits consistently lower reconstruction errors, especially around object boundaries, suggesting its superiority in restoring fine-grained details compared to other methods. Furthermore, to visually evaluate the spatial-spectral consistency and spectral fidelity of the reconstructed images, we present the average spectral error curves (left) and the spectral reflectance curves at a selected pixel (right) for one test image from each dataset, as shown in Fig. \ref{dataset_spectral}. It can be observed that the proposed method achieves lower average spectral errors overall, with reconstructed spectral curves more closely matching the ground truth. These qualitative results underscore the significant advantages of our approach in both spatial detail restoration and spectral accuracy.
In addition to quantitative metrics, visual inspection offers an intuitive and compelling means of assessing the reconstruction quality of various methods. To this end, we present representative visual comparisons at a scale factor of $\times4$ to qualitatively evaluate the spatial fidelity and spectral consistency of the reconstructed hyperspectral images. As shown in Fig.\ref{CAVE_Harvard}, the visual results include the reconstructed images generated by different competing methods as well as their corresponding absolute error maps computed against the ground-truth high-resolution hyperspectral images. In these maps, darker blue indicates lower reconstruction error, indicating a closer match to the ground truth.

\begin{figure*}[htbp]
	\centering
	\includegraphics[width=1.0\textwidth]{Multimodal Dual-domain learning for image fusion/figure/CAVE_Harvard.pdf}
	\caption{Visualization of the reconstruction images and the absolute error maps at the scale factor 4, including \textit{imgc8} in Harvard and \textit{balloons\_ms} in CAVE, where the 17-th band of each image is displayed. The PSNR and SSIM values for each image are reported at the bottom.}
	\label{CAVE_Harvard}
\end{figure*}

%As observed in Fig.\ref{CAVE_Harvard}, the proposed DDLN produces lower reconstruction errors across diverse scenes, particularly along object edges and regions with fine textures. This demonstrates its strong capability in restoring detailed spatial structures that are often blurred or lost by competing methods. The results highlight the advantage of our dual-domain fusion strategy in preserving both global consistency and local detail.

As observed in Fig.\ref{CAVE_Harvard}, the proposed DDLN demonstrates consistently lower reconstruction errors across a diverse range of scenes, particularly along object boundaries and in regions rich in fine textures. These improvements indicate that our method is highly effective in restoring detailed spatial structures, which are often blurred or lost by competing approaches. Such performance gains can be attributed to the dual-domain fusion strategy employed in DDLN, which integrates spatial- and frequency-domain features in a complementary manner. This allows the model to maintain global structural consistency while simultaneously enhancing the preservation of local details, such as edges and textures. The results clearly highlight the advantage of our approach in achieving a better balance between coarse structural information and fine-grained texture representation, leading to more accurate and visually pleasing reconstructions.

To further evaluate the spatial-spectral consistency and spectral fidelity of the reconstructed images, we provide two complementary visualizations in Fig.\ref{dataset_spectral}: the average spectral error curves across all pixels in a test image, and the spectral reflectance curves at a pixel location. The average spectral error curves help to reveal overall spectral deviations, while the reflectance curves illustrate how well individual pixel spectra are reconstructed compared to the ground truth. It is evident that KNLNet, PSRT, and the proposed DDLN achieve relatively lower average spectral errors. However, due to the lack of effective modeling of cross-modal interactions, KNLNet still exhibits noticeable deviations in spectral reconstruction compared to the ground truth.

\begin{figure}[htbp]
	\centering
	%	\hspace{-2mm}
	\begin{minipage}{0.48\linewidth}
		\label{a}
		\includegraphics[width=1\linewidth]{Multimodal Dual-domain learning for image fusion/figure/mean_DDLN_imge7.pdf}
	\end{minipage}
	\begin{minipage}{0.48\linewidth}
		\label{a}
		\includegraphics[width=1\linewidth]{Multimodal Dual-domain learning for image fusion/figure/DDLN_imge7_290_320.pdf}
	\end{minipage}

	\begin{minipage}{0.48\linewidth}
		\label{a}
		\includegraphics[width=1\linewidth]{Multimodal Dual-domain learning for image fusion/figure/mean_DDLN_oil_painting_ms.pdf}
	\end{minipage}
	\begin{minipage}{0.48\linewidth}
		\label{a}
		\includegraphics[width=1\linewidth]{Multimodal Dual-domain learning for image fusion/figure/DDLN_oil_painting_ms_130_300.pdf}
	\end{minipage}
	
	\caption{Visualization of the mean spectral difference (left) and the spectral reconstruction results (right) on the Harvard and CAVE datasets at the scale factor 4.}
	\label{dataset_spectral}
\end{figure}

In constrast, the proposed DDLN achieves the lowest average spectral error in both datasets, indicating its effectiveness in maintaining spectral consistency across wavelengths. In addition, the reflectance curves produced by DDLN show a closer alignment with the ground-truth spectra, with reduced distortion and better shape preservation. These results confirm the superior performance of our method in simultaneously enhancing spatial resolution and preserving spectral integrity.


