Q1: While the application ... innovative.

A1: While our work builds upon the established principles of Eq-CNN, its application to the BISR task is both novel and non-trivial. Importantly, we reveal that present alignment strategies adopted in BISR lack theoretical grounding and, in some cases, may be theoretically invalid as demonstrated in Figure 1 of the manuscript, leading to less accurate feature alignment (Table 1, Figure 2 of the manuscript). Furthermore, our theoretical analysis not only guide the design of our alignment framework but also advances the understanding of Eq-CNNs more broadly.

Q2: The reconstruction module ... work.

A2: INR is essential for multi-scale SR, without which we can only handle single-scale SR, making it irreplaceable. MDTA introduces channel-wise self-attention via cross-covariance, effectively capturing global context and enhancing reference-source feature integration. To verify the necessity of MDTA, we added ablation experiments by removing MDTA while keeping INR. As shown in Table 1, replacing MDTA with a CNN results in a 0.15 drop in PSNR, highlighting its importance.

Table 1. Ablation Study on MDTA

Q3: Among the contributions ... limited.

A3: As addressed in A1, our main contributions include a novel application of Eq-CNN to learn alignment in the image domain and transfer it to the feature domain, which is theoretically sound and previously unexplored in BISR. We also design a reconstruction module that combines this alignment with advanced upsampling and fusion techniques, as demonstrated in A2. Furthermore, our theoretical analysis advances the understanding of Eq-CNNs.

As for the final point on empirical performance gains, while it may not be a technical novelty, it is crucial for validating the effectiveness of our method. Notably, prior works [2,3] also present performance improvements as a key contribution, particularly when achieving new SOTA. Nevertheless, we appreciate the suggestion and will revise the writing to better summarize and clarify our contributions.

Q4: In Equation (1) ... needed.

A4: While our method may not capture all transformations, assuming rotation and translation is practical for BISR, as burst frames are typically captured in a short time, and this assumption aligns with common benchmarks [1].

Table 4 in A8 demonstrates the effectiveness of our alignment under real conditions. We also compare our method with optical flow, used in SOTA methods like BurstM [3], in both image and feature domains (see Table 1 and Figure 2 of the manuscript). Our method better handles misalignment, supporting the validity of our design. Besides, this limitation is discussed in the Limitation section of the manuscript.

Q5: The paper lacks ... tasks.

A5: As suggested, we added LPIPS evaluation. For fairness, all methods were tested using their released ×4 pre-trained models. As shown in Table 2, our method achieves consistently lower scores on both synthetic and real datasets. On BurstSR, it obtains the lowest score. On SyntheticBurst, it ranks second only behind BSRT-Large, a much larger and more computationally expensive model. Compared to the SOTA method BurstM, our method achieves a 0.004 lower LPIPS. These results further show the strength of our method in perceptual fidelity.

Table 2. Comparison of LPIPS

Q6: While the proposed ... zoomed in.

A6: We first want to clarify that, in the image super-resolution tasks, fine-grained detail recovery is one of the primary goals, with improvements often apparent only in zoomed-in high-frequency regions. Therefore, zoom-in visualization is a standard practice in recent SOTA methods [2,3]. Following this, we adopted the same strategy to enable fair and meaningful comparison. As shown in Figures 4–6 of the manuscript, our method better preserves textures and reduces artifacts, demonstrating superior detail recovery.

Q7: Given that alignment ... module.

A7: As suggested, we have added the GMSD metric to assess the alignment quality. As shown in Table 3, our method achieves the best scores across all compared methods, which highlights the effectiveness of our alignment module.

Table 3. Comparison of GMSD

Q8: Impact of Frame ... occlusion.

A8: We want to clarify that, in BISR, frames are typically captured under random motion, with no fixed temporal order or consistent correlation between frame index and motion magnitude (see Table 4 Input). Therefore, the concern by the reviewer will not be a practical issue in applications. In fact, it can be observed from Table 4 that our alignment remains consistently effective and stable across all frames.

Table 4. Frame-wise Comparison of GMSD

Q9: Effect of Number ... cost.

A9: We follow the standard setting of using 14 input frames (N = 14) as adopted in previous studies on SyntheticBurst and BurstSR for fair comparison. Prior studies [4] show that performance improves with more frames when N < 14. However, the use of more than 14 frames remains unexplored. Incorporating additional frames may introduce challenges such as more complex alignment and increased computational cost as mentioned by the reviewer. We leave this for future investigation by possibly collecting real burst sequences with more frames.

Q10: While the proposed ... sequences.

A10: As addressed in A4, modeling BISR transformation with rotation and translation is reasonable and aligned with the benchmark [1]. Although rolling shutter effects may occur in real scenarios, such degradations are not emphasized in this task and are typically addressed in a specific way [5], which is out of the domain of BISR. The effectiveness of our assumption is supported by the results in Table 4 of A8 and the comparisons in Figure 2 and Table 1 of the manuscript. We have indeed discussed the limitation of transformation modeling in the Limitation section of the manuscript.

Reference

[1] Goutam Bhat, Martin Danelljan, and Radu Timofte. Ntire 2021 challenge on burst super-resolution: Methods and results. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, pages 613–626, 2021.

[2] Di X, Peng L, Xia P, et al. Qmambabsr: Burst image super-resolution with query state space model[C]//Proceedings of the Computer Vision and Pattern Recognition Conference. 2025: 23080-23090.

[3] Kang E G, Lee B, Im S, et al. Burstm: Deep burst multi-scale sr using fourier space with optical flow[C]//European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2024: 459-477.

[4] Wei P, Sun Y, Guo X, et al. Towards real-world burst image super-resolution: Benchmark and method[C]//Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023: 13233-13242.

[5] Yang Z, Li H, Cheng S, et al. Multi-Frame Rolling Shutter Correction with Diffusion Models[J]. IEEE Transactions on Circuits and Systems for Video Technology, 2025.

We want to emphasize again that our main contribution, which has been been motivated and discussed in detail the introduction part of the manuscript, is the theoretically sound feature alignment, but NOT the application existing MDTA or INR. Such a theretically sound feature alignment is the main focus of the paper, and has been thoroughly discussed and justified both theoretically and empirically justified. Specifically, we have proven that the alignment is theoretically solid, and empirically demonstrated its superiority over existing alignment.

We know that assessing the contribution of a paper is sometimes subjuctive, but we kindly hope that you would be willing to check our paper again to verify our clarifications.

Q1: The visualizations are not very informative—in several examples, it is difficult to perceive meaningful differences in image quality, which limits the interpretability of the visual comparisons.

A1: For interpretability, we have indeed zoomed in or highlighted local regions for each example, and provided textual descriptions in Lines 250–253, 264–266, and 288–289 of the manuscript. For instance, in Figure 4 of the manuscript, we zoom into local details to illustrate improvements in texture (Rows 1–3) and color (Row 4). In revision, we will further revise the figures to make the advantages of our method more visually apparent.

Q2: The comparative baseline methods are relatively outdated, with most published before 2023. Including one or two more recent state-of-the-art BISR methods would strengthen the experimental validation.

A2: Considering that BISR is relatively a less hot research topic in image restoration, there are not many methods developed after 2023. In particular, to our knowledge, there are only two papers have been published in top conferences, i.e., BurstM in ECCV 2024 and QMambaBSR in CVPR 2025. We have indeed included BurstM in exmperiments. For QMambaBSR, since it has not released official code, we did not include it in our manuscript, while based on its reported metrics, our method still achieves better results (e.g., PSNR on SyntheticBurst with the x4 setting: 43.18 dB for our method vs. 43.12 dB for QMambaBSR). We will include comparisons with new methods as they become public.

Q3: While the paper reports FLOPs as a measure of efficiency, it would be more convincing to also provide real inference speed (e.g., runtime on GPU) to better reflect practical performance.

A3: We have provided inference time for additional measurement of efficiency in Table 1. It can be observed that, compared to the SOTA method BurstM, our model achieves lower FLOPs and faster inference speed. Furthermore, in comparison with large-scale model BSRT-Large (BSRT_L), our approach shows an apparent advantage in efficiency.

Table 1 Comparison of Efficiency

Q1: Though the approach is theoretically well-founded, the quantitative improvements reported in Table 2 over state-of-the-art methods (e.g., BurstM, BSRT-Large) are quite marginal, particularly on realistic benchmarks like BurstSR, where the PSNR gain is as small as 0.01 or less. Specifically, in Figure 5, the visual enhancement achieved by the proposed method appears limited, and there remains a noticeable color deviation compared to the ground truth, similar to other competing approaches.

A1: We want to clarify that the PSNR improvement on the BurstSR dataset is 0.10 dB, rather than 0.01, which can be regarded significant enough in image restoration and enhancement studies.

Moreover, to quantify the color deviation noticed by the reviewer, we additionally report the Delta E (ΔE*) metric [1], which directly measures perceptual color differences, in Table 1. It can be seen that our method consistently achieves lower ΔE* values compared to prior methods, indicating its better color preservation. Regarding the color deviation in Figure 5, this might be partly attributable to inherent limitations in the RAW-to-sRGB conversion process used in dataset generation. Similar artifacts have been noted in prior studies such as [2] on the BurstSR dataset. Another possible reason is that, due to the limited amount of real-world aligned data, existing methods, including ours, are primarily first trained on SyntheticBurst and then fine-tuned on BurstSR, which may not sufficiently capture the complex color statistics in real-world scenes. In particular, as shown in Table 1, all methods exhibit relatively more severe color shifts on BurstSR than on SyntheticBurst. Nonetheless, we acknowledge this color deviation issue should be emphasized for the BusrSR task and will further investigate it.

Table 1. Comparison of ΔE* on SyntheticBurst and BurstSR

Q2: The content of Proposition 1 largely overlaps with Section 3.3 "Theoretical Results," making it redundant. It is recommended to remove one of them to improve conciseness and avoid repetition.

A2: Thanks for the suggestion, and we will revise the manuscript accordingly to improve the conciseness.

Q3: The ablation studies (Table 3, Figures 6/7) are primarily on SyntheticBurst, not the real BurstSR data, making it unclear how robust the alignment strategy is under real-world acquisition artifacts.

A3: We want to clarify that our alignment strategy has indeed been evaluated on the real BurstSR data in the main experiments. Specifically, as shown in Table 1 and Figure 2 of the manuscript, our method demonstrates clear advantages over flow-based alignment on the real BurstSR dataset in both of the image domain and the feature domain. These results provide evidence of the robustness of our alignment module under real-world conditions.

As for the ablation studies, we followed the same experimental settings as prior studies, which all conducted ablations on SyntheticBurst. Moreover, since models for BurstSR are typically first trained on SyntheticBurst and then fine-tuned (due to the limited availability of well-aligned real bursts), ablation on SyntheticBurst offers a more stable and interpretable evaluation framework.

Q4: It is suggested to compare with more recent burst super resolution methods such as QMambaBSR.

A4: As QMambaBSR has not released official code so far, a direct comparison was not feasible. Nevertheless, based on the reported results in its paper, our method achieves comparable or even better performance (e.g., PSNR on SyntheticBurst with the x4 setting: 43.18 dB for our method vs. 43.12 dB for QMambaBSR). We will add a direct comparison once the official code become publicly available.

Reference

[1] Backhaus, Werner GK, Reinhold Kliegl, and John S. Werner, eds. Color vision: Perspectives from different disciplines. Walter de Gruyter, 2011.

[2] EungGu Kang, Byeonghun Lee, Sunghoon Im, and Kyong Hwan Jin. Burstm: Deep burst multi-scale sr using fourier space with optical flow. In European Conference on Computer Vision, pages 459–477.Springer, 2025.

Thanks for your reply.

Firstly, we want to kindly clarify that in addition to the results on the BurstSR dataset, the PSNR improvement of our method over BurstM on the SyntheticBurst dataset with the x4 setting, which is a widely used setting in the burst SR studies, is 0.31dB. In addition, the 0.1dB improvement is indeed non-trivial for the burst SR task. Specifically, in the original BurstM paper, the PSNR improvement of BurstM over Burstormer on the SyntheticBurst dataset with the x4 setting is only 0.04 dB. Comprehensively considering all the results across all the datasets and settings in Table 2 of our paper, we believe the performance improvement of our method should not be considered as marginal.

Secondly, in addition to the performance improvement, we want to kindly emphasize that the proposed theoretically sound feature alignment method, which has been recognized as a strength in the initial comments, is of more significance. As thoroughly discussed and justified in our paper, such a theoretically sound feature alignment method and corresponding theoretical analysis not only advances the burst SR task itself but also contributes to Eq-CNN theories, and these contributions could be more important to the related research areas.

Q1: Limited Transformation Modeling: The framework only models rotation and translation transformations due to the constraints of existing Eq-CNNs. This may not capture complex real-world motions (e.g., non-rigid deformations), limiting applicability in scenarios with intricate misalignments.

A1: Though might not be perfect, we believe that our assumption is practical due to the nature of the burst super-resolution task, i.e., the burst frames are captured in a very short time, and the widely used benchmark has adopted the similar assumption [1]. In addition, we also compare our alignment results both in the image and feature domains with optical flow, which is stated as an effective alignment method in the SOTA method BurstM [2], as shown in Table 1 and Figure 2 of the main text. The results suggest that our method can indeed better deal with the misalignment issue than optical flow in real-world scenarios. Indeed, we have discussed this limitation in the manuscript (see Section 5) for future exploration.

Q2: Dependence on Eq-CNN Capabilities: Performance is bounded by the equivariance of Eq-CNNs, which currently lack support for more general transformations (e.g., affine or projective transformations).

A2: We agree that the current design leverages Eq-CNNs primarily for their rotation and translation equivariance. As noted in A1, this transformation group already provides a sufficient modeling capacity for typical misalignments encountered in burst image sequences. At the same time, we have explicitly discussed this limitation in our manuscript (see Section 5) and consider the extension to broader transformation groups (e.g., affine or projective) a promising direction for future research.

Q3: Potential Overhead in Feature Extraction: Eq-CNNs may introduce additional computational complexity compared to vanilla CNNs, though experiments show the model remains efficient relative to SOTA methods (Table 2).

A3: We want to clarify that Eq-CNNs do not introduce extra computational cost compared to vanilla CNNs during inference. The reason is that the convolution operations are exactly the same between the Eq-CNN and vanilla CNN in implementation during inference. Therefore, if the total numbers of channels are same in each layer between the two kinds of networks, the computational complexity will be theoretically of no difference (more details can be found in [3] and the corresponding code implementation). Such a theoretical property leads to the efficiency of the proposed method shown in Table 2 as noted by the reviewer.

Q4: Limited Generalization to Extreme Degradations: While effective on benchmark datasets, the method’s performance on highly noisy or severely blurred burst frames is not explicitly evaluated, leaving room for further validation.

A4: Our current experiments are conducted on existing benchmark datasets, which are designed to provide fair and standardized comparisons for burst super-resolution. It is worth noting that these datasets already include realistic noise degradations, and our method demonstrates strong performance under such conditions. Scenarios involving other degradations, such as severe blur or intense noise, are typically studied under separate tasks (e.g., burst denoising or deblurring [4,5]) and often require task-specific architectures or loss functions, which is beyond of the scope of this work. Nevertheless, we acknowledge this as a valuable direction and will consider extending our framework to handle such challenging conditions in future work.

Q5: Will results be better with sub-pixel alignment?

A5: Our framework already supports sub-pixel alignment through the feature transformation modeling inherent in the learned sub-pixel alignment and interpolation module. Nonetheless, integrating explicit sub-pixel alignment strategies could potentially yield further improvements, and would be an interesting direction of future work.

Q6: What will be the improvements if the movements are small in different burst images ?

A6: It should be noted that the degree of motion naturally varies across different burst sequences, and our method is designed to handle both small and large motions effectively. In cases of smaller movements, the learning of precise alignment becomes easier, often leading to improved reconstruction quality.

Reference

[1] Goutam Bhat, Martin Danelljan, and Radu Timofte. Ntire 2021 challenge on burst super-resolution: Methods and results. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, pages 613–626, 2021.

[2] Eunggu Kang, Byeonghun Lee, Sunghoon Im, and Kyong Hwan Jin. Burstm: Deep burst multi-scale sr using fourier space with optical flow. In European Conference on Computer Vision, pages 459–477.Springer, 2025.

[3] Qi Xie, Qian Zhao, Zongben Xu, et al. Fourier series expansion based filter parametrization for equivariant convolutions[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022, 45(4): 4537-4551.

[4] Marius Tico. Multi-frame image denoising and stabilization[C]//2008 16th European Signal Processing Conference. IEEE, 2008: 1-4.

[5] Jianfeng Cai, Hui Ji, Chaoqiang Liu, et al. Blind motion deblurring using multiple images[J]. Journal of computational physics, 2009, 228(14): 5057-5071.