Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper tackles the inverse problem of "seismic deblending" by using the well known "Plug-And-Play" (PnP) framework together with a recently proposed self-supervised denoiser, which is adapted to follow the noise structure of the particular problem at hand. Experiments on a real dataset artificially blended by the authors show that the approach outperforms a state-of-the-art method based on a Fourier sparsity prior, and an ablation study show that the proposed combination of PnP with a carefully trained self-supervised denoiser is efficient.
strengths_and_weaknesses: ## Strengths
- The paper is generally very didactic. Quite unusually, 5 out of 9 pages are devoted to the introduction, background and related work sections. In that sense, the paper can almost be regarded as a "tutorial" paper, giving a subsequent overview of the field of seismic deblending and of recently proposed self-supervised denoising techniques to non-expert readers.
- The proposed approach is sound and seem to outperform a more conventional technique on a real dataset

## Weaknesses
- While 5 pages are devoted to introductory materials, only half a page is devoted to presenting the methodology. On the one hand this seems short, on the other hand, this can be explained by the fact that the proposed methodological contribution is very incremental: two relatively well-known existing techniques are straight-forwardly combined and applied to a known problem in the field.
- The experiments are relatively limited, eventhough this may be justified by the lack of available real data for this problem. Still, more detailed quantitative results could have been provided.
- No detail is given on the key "StructBS" step of the method (the self-supervised denoising), not the paper nor in the supplementary material. The reader is entirely referred to the recent reference [47] for this (in fact, the reference to [47] is implicit, and the acronym StructBS is never made explicit). This makes the methodological part of paper not self-contained, which is not good for research reproducibility and transmission.
- A lot of important implementation details are scattered across the experimental section or in the appendix, which would make the proposed method very hard to reimplement
- In the ablation study, not using the PnP iterations and using only self-supervised denoising seem to be equivalent to what is done in [47], but this is not explicitly stated by the authors. More details should be given on these results than a single number, since according to the authors themselves, [47] is the closest work to what they propose.


questions: The main question I have is: Is the proposed method without the PnP steps the same as [47] ? If so, this should be made very explicit in the method section and in the experimental results.

I noted the following minor typos:
- L136 : "to to"
- L172 a image -> an image
limitations: The limitations and societal impact of the work are adequately addressed by the authors in section 6.
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: The paper introduces the problem of seismic deblending and provide a state-of-the art result in this problem using denoising network in the PnP setup. Denoising model is learned as a part of PnP. 
strengths_and_weaknesses: [strengths]
1. Introduces Seismic Deblending to ML community. Seismic problems are generally less explored in ML community and this paper introduces a good problem. 
2. Good results with learned denoiser.

[weaknesses]
1. Writing : The paper devotes very less space to the main algorithm. PnP + denoiser. Also, for people who are not familiar with the ADMM algorithm like me, the section 4 reads very difficult with a lot of terms introduced but not explained like y_k , x-update, y-update, LSQR, StuctBS, theta. These details are provided partially in the supplementary. However more discussion space should be provided to the algorithmic part.

2. Novelty: I am not sure if paper provides enough novelty for this conference. It uses denoiser architecture in a seismic setting and shows good results. However, it is not clear what the contributions are apart from applying existing denoiser in seismic PnP.

3.  Experimental validation is limited. The experiments are performed on a single dataset. More empirical validation is needed.


questions: 1. Please consider weaknesses above as questions. 
limitations: Limitations are adequately addressed.
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: This paper combines a self-supervised deep image denoising method and PnP framework to improve seismic deblending. The problem is interesting and significant. However, the rationale of the proposed algorithm is unclear. It seems like a combination of existing techniques and the technical contribution seems limited. 
strengths_and_weaknesses: Strength:
1. This paper aims to improve the performance of seismic deblending, which is a significant problem and can benefit geophysical studies.
2. The authors explore to improve the conventional deblending problem with deep image denoising technology.
3. The proposed method can outperform a conventional method according to the experiment.

Weakness:
1. This paper is poorly organized and the meanings of many symbols in formulas and figures are not well introduced (see Questions for detail). This makes it difficult to understand the background and the problem formulation. The reader needs to spend a long time reading this paper before understanding the problem.
2. The authors introduced their algorithm very briefly in “Method”. The motivation of the proposed algorithm is unclear because the authors only provide the resulting update rules instead of showing the original optimization problem and the regularization term. Especially, the biggest modification to the algorithm in this paper seems to be using a self-supervised denoiser for y-update. However, the rationale behind it is confusing. I wonder how this update rule is derived. Indeed, too much essential information has been omitted. 
3. Partly because the authors did not give any theoretical illustrations for their algorithm, the technical contribution seems limited. According to the paper, the authors (1) follow the conventional optimization problem formulation of seismic blending/denoising; (2) use PnP framework to solve this optimization problem; (3) change a term for y-update (without properly explaining the rationale) based on the self-supervised image denoiser. Then, this paper seems like a combination of existing techniques. The inspiration it can bring to the community is limited.
4. The experiments are not sound. The authors have mentioned in the related work that there are other seismic deblending/denoising methods. However, only one conventional method is used as the baseline. The authors should report their performance to better demonstrate the effectiveness of the proposed algorithm in comparison to SOTA. Otherwise, the authors should explain why the other methods are not applicable. 

questions: 1. How is the blending operator decided? Why does it have the property of B^TB=I? Maybe a proper citation is needed here for the reader to better understand the background.
2. What do t(s), x_R(m), and \bar{\bar{x}}_R(m) mean in Figure 1 b)? Also, why does the y-axis x_s(m) instead of x_R(m) in Figure 1 c)? What does m represent here?
4. According to Figure 1 b), the input seems like an image. However, it is confusing how it is generated. What are the white curves and the horizontal dash line mean?
5. What is the regularization term in the proposed optimization problem? How is y-update derived as StructBS(x+u)？
7. How will the model perform if only adopting PnP framework but does not use the self-supervised denoiser? 

limitations: The authors have adequately addressed the limitations and social impact of their work.
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: This paper proposed a plug-and-play (PnP) algorithm for reflection seismology (RS). The key concept of PnP is to leverage an image denoiser as an implicit regularizer to impose prior within an iterative optimization algorithm. By using deep image denoisers, PnP combines the physical constraints and trainable priors. Proposed algorithm in this paper combines PnP with self-supervised deep image denoisers to solve the RS problem.
strengths_and_weaknesses: **Strength:**
- New application of PnP to reflection seismology (RS).

**Weakness:**
- The proposed method is not novel. The claimed novelty is the inclusion of self-supervised image denoiser in the PnP framework. However, this has been done in [1] for medical imaging.
- The presentation of the work is not well organized. The introduction and background is too long while the method section is too short.

[1] RARE: Image Reconstruction using Deep Priors Learned without Ground Truth
questions: 1. Besides the apparent benefits of self-supervised deep image denoiser, that is, no use of ground-truth data, what else motivates you to use such image denoiser? Why this is denoiser is necessary.

2. Apart from the deep image denoiser, what else can be considered as contributions of the work?
limitations: Not applicable.
review_title: null

Meta-review: metareview: The paper studies a seismic deblending problem. This is a problem in reflection seismology, in which multiple excitations are applied simultaneously, and then an underdetermined inverse problem is solved to recover the underlying composition of the earth. Existing approaches to this problem are mostly based on regularization — e.g., frequency domain sparsity. The paper proposes an alternative method based on plug-and-play-ADMM, with a self-supervised regularizer. The regularizer here is a “blind spot” network, which tries to predict a pixel based on its surroundings. In simulation studies (based on synthetic blending of real seismic data), the proposed algorithm outperforms the regularization approach. 

 Reviews of the paper were mixed: reviewers all recognized careful, pedagogical manner in which the paper lays out its problem of interest. At the same time, several reviewers raised concerns that the exposition was overly focused on background material, at the expense of explaining the paper’s technical contributions. Exposition aside, much of the discussion in the reviews and authors’ response centers on the novelty and depth of the paper’s technical contributions. The reviewers note that the application of self-supervised denoising within a plug-n-play framework is not a novelty of the paper (nor is it argued as one). Rather the technical contribution lies in a combination of existing ideas (self-supervised denoising ala struct BS, plug-n-play) which is well suited to the reflection seismology application. Reviewers generally felt that the paper would be stronger if it focused more on this methodology and on the technical justification of the approach. While the paper introduces a method that has value for reflection seismology, it is current form, the concerns are significant enough to place it below the bar for acceptance. 
confidence: Less certain
Decision: Reject