Adaptive SVD Denoising in Time Domain and Frequency Domain

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

in attached file

Comments for author File: Comments.pdf

Author Response

Comments1: The introduction must add all recent research about this field. 
Response1: Thank you for pointing this out. We agree with this comment. Therefore, We have add recent research in line 53.

Comment 2: What specific gap in the state of the art does your method fill, and how doexisting CWT/curvelet/EMD/SVD approaches fail quantitatively (e.g.,parameter sensitivity, SVD rank, aliasing, complexity)

Response2: ASTF  fills two key gaps in existing technologies: firstly, by combining time-domain and frequency-domain SVD, it overcomes the limitations of single-domain processing for complex seismic structures (such as dipping or curved events); secondly, it introduces adaptive rank selection based on the second-order difference spectrum of singular values and ternary search-based weight fusion, significantly reducing the dependence of traditional SVD on manually set parameters and achieving fully automatic, data-driven noise suppression. Existing methods like CWT adapt poorly to complex events; curvelet transform, while multi-directional, requires complex parameter tuning; EMD lacks theoretical foundation and suffers from mode aliasing; traditional SVD heavily relies on manual singular value selection, struggles with rank determination—often leading to signal loss or noise residue—and faces issues of high computational complexity and poor generalization.

Comment 3：What exactly is new about ASTF compared to local SVDs and published time frequency fusions: formal rank selection criterion (order 2 difference), fusion  scheme (ternary search), and guarantees/principles (theoretical intuition, 
complexity, robustness) 

Response3:  Thank you for pointing this out. We agree with this comment. Therefore, We have add recent research in line 91.

Comment 4: In part of the Results, the authors should consider applying EEMD. Compared with EMD, EEMD is more recent and effectively overcomes the well-known mode-mixing problem, yielding more reliable decompositions. A brief 
description of EEMD is provided below. 

Response4: In this paper, we chose to compare with the classical EMD method primarily for the following reasons: the main objective of this study is to validate the effectiveness of the proposed ASTF framework—focusing on its core components of adaptive SVD and domain fusion—rather than to conduct a comprehensive evaluation of the EMD family of algorithms. The classical EMD method is widely recognized and established as a benchmark in signal processing, and its computational efficiency is higher than that of EEMD. This facilitates more efficient large-scale comparative experiments on both synthetic and field data under controlled conditions. Using established classical algorithms as baselines allows for a clearer demonstration of the performance improvement offered by the novel ASTF method compared to traditional, mature solutions. We fully acknowledge that EEMD is a valuable enhanced technique, and it represents an important direction for future comparative studies.

Comment 5:  Are your gains significant across multiple noise realizations (seeds) and multiple metrics (PSNR, SSIM/FSIM, phase error)? Can you provide the mean ± standard deviation and significance tests? 

Response 5: We thank the reviewer for this rigorous suggestion. We fully appreciate the value of multiple noise realizations and statistical tests for verifying methodological robustness. However, as this study focuses on introducing the core ASTF framework and providing the first validation of its feasibility on both synthetic and field data, conducting such a large-scale systematic test (e.g., with >20 noise seeds) falls outside the current scope, and the computational resources allocated for this methodological development have been utilized. Nonetheless, the consistently superior performance of ASTF across different SNRs (1dB, 3dB, 5dB) and multiple synthetic datasets (as shown in Table 2) provides preliminary yet solid evidence of its effectiveness. We would like to emphasize that this will be a high-priority task in our immediate future work, where we will design dedicated experiments and perform comprehensive statistical analyses to further solidify the robustness of our method.

Comment 6: What is the contribution of time alone, frequency alone, and fusion? What is the sensitivity to Hankel sizes and SVD rank? 

Response 6: Thank you for pointing this out. Regarding module contribution, our preliminary ablation studies observed that time-domain processing better preserves signal energy but may leave residual noise in complex structures, while frequency-domain processing yields smoother results but may attenuate some valid signals. The fusion effectively balances these strengths. We will quantitatively present the contribution of each module in the revision. Concerning parameter sensitivity, a key advantage of our method is the adaptive selection of the SVD rank via the second-order difference spectrum, minimizing manual tuning. For the Hankel size, we followed a common heuristic (l = ⌊n/2⌋ + 1) in the field. We will include a discussion on the sensitivity analysis of this parameter within a reasonable range in the revised manuscript to demonstrate the stability of our approach.

Comment 7: How did you set DMSSA/EMD/SVMF (detailed parameters), and why not add recent baselines? 

Response 7: For the parameter settings of the baseline methods, our principle was a fair comparison. Thus, we employed the default parameters or standard implementations recommended by the original authors wherever possible and conducted grid searches for parameters requiring adjustment to ensure their optimal performance. We will detail these parameter settings in the revised manuscript. Regarding recent baselines, we appreciate this valuable suggestion. In the initial manuscript, we selected DMSSA, EMD, and SVMF as they are well-established and widely recognized classic benchmarks, facilitating the positioning of our method within a known frame of reference. We fully agree on the importance of comparison with state-of-the-art methods and will endeavor to include 1-2 recently published high-impact methods in the revised manuscript (we would be grateful for any specific recommendations), to make the comparison more comprehensive.

 

Reviewer 2 Report

Comments and Suggestions for Authors

My main comments concern the theoretical validity of the proposed methods. All new results and proposals are empirically substantiated using simulation data and field experiment data. For the simulation data, the authors obtained PSNR estimates (dB). No formal estimates are available for the experimental data. Visual comparison of results is subjective.

Comments for author File: Comments.pdf

Author Response

Comment 1: For the simulated data, the authors obtained PSNR (dB) estimates. For the experimental data, there are no formal estimates. Visual comparison of results is subjective. In the introduction, I didn't find any criticism of existing methods or the research problem statement. The text on lines 64-84 is better placed in another section. 

Response 1: We thank the reviewer for these valuable comments. We will address them in the revised manuscript with the following key improvements:Regarding quantitative estimates for experimental data: We fully agree that visual comparison can be subjective. However, for field data, obtaining an absolute "clean" reference (i.e., ground truth) to calculate metrics like PSNR is inherently impossible, a well-known challenge in seismic denoising. To provide more objective evidence, we will supplement our analysis in the revised manuscript by computing the local signal-to-noise ratio or analyzing the spectral characteristics of the removed "noise section" (obtained by subtracting the denoised result from the original noisy data, as shown in Figure 10). This will serve as strong, data-driven, and indirect quantitative support that ASTF primarily suppresses uncorrelated random noise rather than the valid signal. Regarding criticism and problem statement in the Introduction: This is a very valid point. We will significantly revise the Introduction to explicitly critique the key shortcomings of existing methods (e.g., CWT, EMD, SVD) after reviewing them. We will highlight issues such as the high sensitivity of traditional SVD to singular value selection, the limitations of single-domain (time or frequency) processing for complex structures, and the need for heavy manual parameter tuning in many methods. This will create a clear foundation for stating our research objective: to propose an adaptive SVD method that fuses time and frequency domains to overcome these drawbacks. Regarding lines 64-84: 

We thank the reviewer for their attention to the manuscript's structure. Regarding the placement of the ASTF workflow at the end of the introduction, this was a deliberate choice, following a common writing convention in many scholarly articles where the introduction provides a "roadmap" for the paper.

Our rationale is as follows: After outlining the limitations of existing methods and the research gap in the introduction, we immediately present our proposed overall solution with a clear flowchart (Figure 1) and three key steps. This provides the reader with a "roadmap" to understand the subsequent detailed theory and experiments. We believe this structure helps readers, especially those not deeply specialized in the field, to quickly grasp the core idea and innovations of our method before delving into details, understanding why and how we address the problem, thereby making the introduction's logic more complete.

We fully appreciate the reviewer's concern that the introduction should focus on the problem rather than methodological details. To address this, we will make the following revisions:

1. In the opening of the introduction, we will more explicitly and forcefully emphasize the three core shortcomings of traditional SVD methods (sensitivity to singular value selection, limitations of single-domain processing, and reliance on manual tuning) to strengthen the statement of the research problem.

2. We will ensure that the content in the Methodology/Theory section provides a significantly deeper and more theoretical elaboration of these three steps, creating a clear distinction in depth between the two sections.

We are confident that with these textual refinements, the current structure will most effectively communicate the value of our work.

Comment 2:Lines 171, 174. In my opinion, the ASTF method execution algorithm is missing as a sequence of steps. How is the omega coefficient determination block included in the algorithm? If it depends on the data, then on which sample should it be estimated? Furthermore, a theoretical explanation is needed for better understanding. Why can results in the time and frequency domains be combined, and how are time and frequency scales combined? 

Response 2：The combination of time-domain and frequency-domain results in the ASTF method is theoretically grounded in their complementary nature in signal representation: time-domain SVD effectively preserves the instantaneous amplitude and phase information of the signal, particularly protecting strong-amplitude events better, while frequency-domain SVD is more advantageous in suppressing random noise with specific frequency distributions and handles dipping or curved events more effectively. The fusion is not performed by directly combining time samples and frequency bins. Instead, the complete processed seismic traces from each domain are fused via linear weighting. Specifically, the algorithm employs a ternary search to find a single, globally optimal weight ω for the entire data trace (not local samples) that maximizes the Peak Signal-to-Noise Ratio (PSNR) of the fused result TFN = ω * TN + (1-ω) * FN. This weight ω is determined based on the entire noisy trace, estimated by minimizing the global error metric (MSE) between the fusion result and the desired signal (known for synthetic data, implicit for field data), thereby achieving an overall balance between the fidelity of the time-domain result and the smoothness of the frequency-domain result. We also add the pseudocode of ASTF in line 216.

Comment 3:Images are subject to convolution. Should an inverse filter be used for deconvolution?

Response 3：Your point regarding deconvolution is very pertinent. Indeed, raw seismic data results from the convolution of subsurface reflectivity with a seismic wavelet. However, the focus of this paper is additive random noise suppression, which is a distinct signal processing task from deconvolution (which addresses the multiplicative wavelet effect). In standard processing workflows, random noise attenuation typically precedes deconvolution. Therefore, not incorporating deconvolution in this study is justified, as it allows our research to remain focused on evaluating the core denoising effectiveness of the ASTF method.

Comment 4:Lines 197-213. The author used a Gaussian noise model. Is this accurate? What other noise is present in the data, and what are its distributions?

Response 4：We acknowledge that using a Gaussian white noise model is a simplification of complex reality, serving primarily as a controlled benchmark for initial validation of the algorithm's core capability. Real seismic data contains more complex noises, such as spatially coherent ground rolls (non-Gaussian), spike-like outliers (heavy-tailed distribution), and colored noise. Incorporating these complex noise models for testing is crucial for a comprehensive evaluation of ASTF's robustness and is planned as a key focus of our future work.

Comment 5:Line 164. In the Fourier frequency domain, the image signal (two-dimensional signal) is 
redundant. How was this fact exploited?

Response 5：We exploit the redundancy in the frequency domain through the construction of the Hankel matrix. For a specific frequency slice, the potentially low-rank nature of its corresponding Hankel matrix reflects the spatial coherence of the signal. Our adaptive SVD denoising operates on this matrix by retaining the dominant singular values to reconstruct a low-rank approximation. This process essentially leverages the structural redundancy of the frequency-domain signal to estimate and recover the coherent signal from noise-contaminated data, thereby effectively suppressing random noise that lacks such structure.

Comment 6: Lines 98-109. What is the uncertainty of sensors? How was systematic uncertainty, if any, 
considered? 

Response 6：Regarding sensor uncertainty (including systematic and random errors), in this study, we treat it collectively with other noise sources as the overall random noise component to be attenuated in the data. The ASTF method, as a data-driven post-processing tool, is designed to recover the useful signal from the final observed data without explicitly distinguishing the specific origins of the noise. The method's strength lies in its adaptive capability: it functions effectively provided the useful signal is structured and the noise is not, regardless of whether the uncertainty originates from sensors or other environmental factors.

Reviewer 3 Report

Comments and Suggestions for Authors

This paper presents a practical and well-motivated denoising framework (ASTF) that adaptively couples time-domain and frequency-domain SVD via Hankelization, automatic rank selection using a second-order difference spectrum, and a simple ternary-search fusion on PSNR. The idea of exploiting complementary domains with data-driven singular-value selection is appealing, and the experiments on both synthetic and field data indicate consistent gains over DMSSA, EMD, and SVMF, especially at low SNR. The manuscript is easy to follow at the high level, Figure 1 communicates the pipeline clearly, and the method’s reliance on classical, resource-friendly linear algebra will be attractive to seismic practitioners who need robustness and portability. Overall, the contribution is incremental but useful; with several clarifications and polish, it can make a solid addition to the applied denoising literature.

That said, a number of details should be strengthened before publication. (i) Method clarity & rigor: Please formalize the adaptive thresholding used to locate the “critical point” in the second-order difference spectrum (window length, percentile/constant, sensitivity), and justify the convexity claim underlying the ternary search for the fusion weight ω; a short proof or counterexamples/limitations would help. (ii) Complexity & resources: Report runtime (CPU/GPU), memory footprint, Hankel sizes, and randomized/partial SVD settings; include scaling with trace count and sample length. (iii) Evaluation depth: Provide confidence intervals or statistical tests over multiple noise realizations; add ablations (time-only, frequency-only, fusion without adaptivity) and robustness to coherent noise (multiples), dipping/bending events, irregular sampling, and missing traces. For the field data, complement visuals with quantitative proxies (e.g., local coherency, semblance, f-x residual energy) since ground truth PSNR is unavailable. (iv) Reproducibility & presentation: Share code/data splits (or a minimal script), fix typos (e.g., “ASFT” vs “ASTF”), clean up duplicated sentences and table formatting, and standardize references (several placeholders and incomplete entries). Clearly state whether the token “peak signal” in PSNR uses per-trace dynamic range or a fixed scale.

Suggestions for future work (constructive): Explore principled rank selection (e.g., Gavish–Donoho optimal hard threshold, SURE/GCV) and compare to your second-difference heuristic; assess tensorized/3D extensions (block-Hankel, multi-channel SSA) and robust low-rank variants (RPCA) to better handle coherent noise. Investigate frequency-dependent or trace-adaptive fusion (learning a small regressor for ω from features such as local dip and bandwidth) and accelerate with randomized/incremental SVD for large surveys. Finally, consider uncertainty estimates (e.g., bootstrap on windows), blind SNR estimation for parameter-free operation, and applications beyond post-stack (e.g., microseismic, marine streamer), reporting impacts on downstream tasks like velocity analysis and migration image quality. With these refinements, the work would move from a strong engineering solution to a more broadly generalizable and well-founded denoising approach.

Author Response

Comment1 : Method clarity & rigor: Please formalize the adaptive thresholding used to locate the “critical point” in the second-order difference spectrum (window length, percentile/constant, sensitivity), and justify the convexity claim underlying the ternary search for the fusion weight ω; a short proof or counterexamples/limitations would help. 

Response 1:We thank the reviewer for these crucial questions that will significantly enhance the clarity of our method.

1. Formalizing Adaptive Thresholding: We set a proportional range (e.g., beginTime=0.01 to endTime=0.25), which is equivalent to sliding a time window along the sequence of singular values. The threshold for judging the critical value is set as a fixed percentage of the average value in the initial window (controlled by the beginTime and endTime parameters). When the average value of the singular values within the sliding window falls below this threshold, the search stops and the truncation point is determined.This parameter (the multiplier) was determined via grid search on synthetic data and kept fixed for all experiments, providing data-driven adaptivity and showing low sensitivity to variations between 1.2x and 1.8x.

2. Convexity Justification & Ternary Search: Our claim regarding the convexity of PSNR with respect to the weight ω is primarily based on empirical observation across extensive synthetic data experiments, as suggested by Figure 2. A rigorous theoretical proof can be constructed for a linear mixing model with additive noise, but the complexity of real seismic data may introduce non-convexity. We acknowledge this as a limitation. While ternary search proved robust in practice, we will explicitly state its empirical basis in the manuscript and discuss potential failure modes under extremely low SNR or significant model mismatch.

Comment 2 : Complexity & resources: Report runtime (CPU/GPU), memory footprint, Hankel sizes, and randomized/partial SVD settings; include scaling with trace count and sample length. 

Response 2: 

We appreciate the focus on scalability and will add the following details to the revised manuscript:

• Runtime & Environment: Experiments were conducted in MATLAB on a workstation with an Intel Xeon CPU and 128GB RAM, without GPU acceleration. The average runtime for processing a single shot gather (200 traces, 1501 samples) with ASTF was approximately 0.6 seconds (specific data to be added).

• Hankel Sizes & SVD Settings: For n=200 traces, the Hankel matrices Ht and Hf had dimensions l x k, where l = floor(n/2)+1=101 and k = n - l + 1 = 100. We used MATLAB's full SVD (svd function), not randomized or partial SVD.

• Scaling: The computational complexity is dominated by the SVD of the Hankel matrices. For data with m samples and n traces, Hankel construction is O(mn), while SVD complexity is roughly O(min(l,k) * l * k). Thus, ASTF scales cubically with the number of traces n and linearly with sample length m. Memory footprint is primarily proportional to the Hankel matrix sizes.

Comment 3 : Evaluation depth: Provide confidence intervals or statistical tests over multiple noise realizations; add ablations (time-only, frequency-only, fusion without adaptivity) and robustness to coherent noise (multiples), dipping/bending events, irregular sampling, and missing traces. For the field data, complement visuals with quantitative proxies (e.g., local coherency, semblance, f-x residual energy) since ground truth PSNR is unavailable.

Response 3: We thank the reviewer for this rigorous suggestion. We fully appreciate the value of multiple noise realizations and statistical tests for verifying methodological robustness. However, as this study focuses on introducing the core ASTF framework and providing the first validation of its feasibility on both synthetic and field data, conducting such a large-scale systematic test (e.g., with >20 noise seeds) falls outside the current scope, and the computational resources allocated for this methodological development have been utilized. Nonetheless, the consistently superior performance of ASTF across different SNRs (1dB, 3dB, 5dB) and multiple synthetic datasets (as shown in Table 2) provides preliminary yet solid evidence of its effectiveness. We would like to emphasize that this will be a high-priority task in our immediate future work, where we will design dedicated experiments and perform comprehensive statistical analyses to further solidify the robustness of our method.

 We will add an ablation study subsection to quantitatively compare the performance of Time-only, Frequency-only, Fusion with fixed ω=0.5, and the full ASTF (adaptive fusion). This will clearly delineate the contribution of each component.

In the absence of ground truth, we will complement the visual results on field data with quantitative analysis of local coherency , comparing them with other methods to objectively demonstrate ASTF's superiority in enhancing event continuity and suppressing random noise.

Comment 4 : Reproducibility & presentation: Share code/data splits (or a minimal script), fix typos (e.g., “ASFT” vs “ASTF”), clean up duplicated sentences and table formatting, and standardize references (several placeholders and incomplete entries). Clearly state whether the token “peak signal” in PSNR uses per-trace dynamic range or a fixed scale.

Response 4: We thank the reviewer for raising the important point of reproducibility. We fully value the verifiability of academic research.Regarding the sharing of code and data, we are currently unable to publicly provide the full algorithm codebase and the raw field seismic data due to intellectual property protection and corporate data policy restrictions.

We will uniformly use the method name "ASTF", correct typos (e.g., "ASFT"), remove duplicated sentences, reformat tables, and standardize all references according to the journal's style, completing all placeholder entries.

We clarify that the "peak signal" value in our PSNR calculation uses the per-trace dynamic range, i.e., max(trace) - min(trace). This definition will be explicitly stated in the methodology section.

Reviewer 4 Report

Comments and Suggestions for Authors

This paper proposes the adaptive SVD denoising in both time and frequency domains (ASTF) method with three steps. Two Hankel matrices are constructed in the time domain and frequency domain, then the parameters of the reconstruction matrix are adaptively selected using the SV second‐order difference spectrum. Finally, the weights of these two matrices are learned through ternary search. Experiments carried out on synthetic data and field data justify the efficiency of the proposed denoising framework.

Comments:

• In section I, the authors presented a related work subsection where several methods are revised. This reviewer noticed that most of the referred papers are so old (2, 4-11, 13, 15-17, 24). Please provide the revision of the SOTA methods using recently published studies (not more 5-7 years) that can be compared with the proposed framework. Also, please redact Ref. 1 where there are two papers presented with number 1.
• The authors in lines 73-73, 84-91 presented some advantages of the proposed approach. This reviewer recommends exposing the principal contributions in the form of highlighting phrases for novel framework justifying their better performance against SOTA methods.
• The authors used PSNR measure that is log₁₀ [S_max/SQRT(MSE)] to characterize denoising quality but for the noise intensity, the authors employed SNR measure. Please explain why you use PSNR not SNR criterion.
• In subsect.3.1, the authors wrote “The four synthetic seismic datasets are generated by changing seismic wave speed, stratum and other conditions. Table 1 lists shot points, traces, samples, sampling intervals and source information of these datasets.” Denoising results in figs. 3-5 and table 2 show that there are differences between these four datasets. This reviewer proposes to discuss the differences between these four synthetic and field datasets permitting a potential reader better understanding filtering results.
• Please explain how you obtained the results exposed in fig.10 where the noise is suppressed using different algorithms. As this reviewer understood, the field dataset does not provide clear signal (reference signal). In this case, to characterize quality results in denoising there can be used non-reference criteria.

Author Response

Comment 1 : In section I, the authors presented a related work subsection where several methods are revised. This reviewer noticed that most of the referred papers are so old (2, 4-11, 13, 15-17, 24). Please provide the revision of the SOTA methods using recently published studies (not more 5-7 years) that can be compared with the proposed framework. Also, please redact Ref. 1 where there are two papers presented with number 1.

Response 1 :We thank the reviewer for this valuable suggestion. In the revised manuscript, we will correct the formatting of Reference 1 by removing the duplicate entry. Furthermore, we will update the literature review to specifically highlight recent works already cited in our introduction section.

Comment 2 : The authors in lines 73-73, 84-91 presented some advantages of the proposed approach. This reviewer recommends exposing the principal contributions in the form of highlighting phrases for novel framework justifying their better performance against SOTA methods.

Response 2 : Thank you for pointing this out. We agree with this comment. Therefore, We have addit in line 107.

Comment 3 : The authors used PSNR measure that is log₁₀ [S_max/SQRT(MSE)] to characterize denoising quality but for the noise intensity, the authors employed SNR measure. Please explain why you use PSNR not SNR criterion.

Response 3 :We selected PSNR over SNR as the primary evaluation metric based on the characteristics of seismic data and the inherent differences between the two metrics. PSNR uses the signal's dynamic range (peak-to-peak) as the normalization benchmark, providing a more stable assessment of amplitude fidelity for seismic traces, which is particularly important for complex seismic data with non-uniform energy distribution in the effective signal. In contrast, SNR relies on the total signal power, and its evaluation can be easily skewed by uneven energy distribution when significant energy differences exist between strong and weak reflectors in the seismic signal. By fixing the maximum dynamic range of each trace as the reference, PSNR offers a more consistent and reliable quality measure for denoising performance across different data traces.

Comment 4 : In subsect.3.1, the authors wrote “The four synthetic seismic datasets are generated by changing seismic wave speed, stratum and other conditions. Table 1 lists shot points, traces, samples, sampling intervals and source information of these datasets.” Denoising results in figs. 3-5 and table 2 show that there are differences between these four datasets. This reviewer proposes to discuss the differences between these four synthetic and field datasets permitting a potential reader better understanding filtering results.

Response 4 : We thank the reviewer for this valuable suggestion. We will add a detailed discussion in the revised manuscript regarding the differences between the four synthetic datasets and the field dataset to facilitate a better understanding of the filtering results in line 228.

Comment 5 : Please explain how you obtained the results exposed in fig.10 where the noise is suppressed using different algorithms. As this reviewer understood, the field dataset does not provide clear signal (reference signal). In this case, to characterize quality results in denoising there can be used non-reference criteria.

Response 5 :

We appreciate the reviewer's question regarding Fig. 10. For the field data, where a true "clean signal" is unavailable, the "noise" suppressed by each method, as shown in Fig. 10, was obtained by subtracting the denoised result of each method from the original noisy field data, i.e., Noise = Original Field Data - Denoised Data. This process is based on the reasonable assumption that the denoising aims to decompose the data into "signal" and "noise" components. Thus, the resulting residual can be interpreted as the noise component identified and removed by the algorithm.

We fully concur with the reviewer that using non-reference criteria is essential in the absence of a ground-truth signal. This is precisely one of the key purposes of presenting Fig. 10. Visual inspection of these "noise" sections is itself a powerful and widely accepted non-reference assessment method. If the "noise" removed by a method contains visually obvious, spatially coherent events (i.e., valid signal), it indicates over-processing or signal leakage by that method. Conversely, if the residual noise appears truly random, it suggests better denoising performance. In the revised manuscript, we will clarify this generation process and analytical logic more explicitly and commit to further complementing the visual analysis by employing quantitative non-reference metrics such as local coherency  to provide a more comprehensive evaluation of the denoising quality.

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

IN ATTACHED FILE

Comments for author File: Comments.pdf

Author Response

Comment 1：We encourage the authors to evaluate Ensemble Empirical Mode Decomposition (EEMD) in the Results section. As a more recent extension of EMD, EEMD mitigates mode mixing, improving IMF stability and the robustness of downstream measurements. Including comparative tables contrasting EEMD with EMD and alternative techniques would further enhance the paper’s rigor.

Response 1：

Thank you very much for your thoughtful comments regarding our experimental design and the selection of baseline methods.

We fully appreciate that the EEMD method you mentioned is a significant technique for alleviating mode mixing. When designing the experiments for this study, we aimed to include classical and mainstream methods representing diverse principles. The final selection—DMSSA for low-rank approximation, SVMF for non-linear filtering, and EMD for adaptive time-frequency analysis—was intended to validate the effectiveness of the ASTF framework against a diverse set of benchmarks.

We understand that including EEMD could add another valuable dimension to the comparison. As the primary goal of this paper is to introduce and provide initial validation for the feasibility of the time-frequency SVD fusion framework, our current experiments were focused on a concentrated comparison with the selected methods. We sincerely accept your suggestion, and incorporating EEMD in a comparative analysis will be a crucial part of our follow-up work to more comprehensively assess the performance boundaries of our proposed method.

We greatly appreciate your insightful comments, which are highly valuable for guiding the improvement of our work.

Reviewer 4 Report

Comments and Suggestions for Authors

The authors have attended all comments of this reviewer.

Author Response

Thank you for your positive comments .