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 proposes to use a bessel basis and a post-processing neural network for modeling the optical transmission through a multi-mode optical fiber. The key idea is that multi-mode fiber outputs are band-limited with respect to the bessel functions of different modes. Applying this representation for the multi-mode fiber output allows us to reduce the number of parameters significantly, reducing the computational burden of inverse estimation: from a speckle image to a target natural image.

strengths_and_weaknesses: Strengths
- For the first time, a 256x256 image is reconstructed from a speckle image, thanks to the efficient parameterization.
- Using the bessel representation is a neat idea for the neural modeling of the multi-mode fiber outputs.
- The paper is well written.

Weaknesses
- The authors show that the bessel representation is effective in modeling the MM fiber output. However, there is no analysis on it's representation capability with respect to the number of bases. 

questions: My concern mainly lies in the analysis of the representation capability of the bessel basis. How accurate the basis is for modeling the MM fiber outputs, especially w.r.t. the number of bases used? What are the remaining components that cannot be modeled? Probably visualizing the full weight matrix might be useful to answer these questions.

Second, many works using MM fibers for display applications modulate incident wavefront to generate high-fidelity images directly out of the fiber. Could the proposed method be also used for this application?
limitations: The authors adequately described the limitations.
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: This paper assumes that the transmission matrices (TMs) associated with multimodal fibers (MMF) are diagonizable using a Bessel Function Basis. Using this assumption, the authors propose a new learning-based technique for imaging through MMFs. The speckle image is first multiplied by the learned diagonal inverse TM and is then denoised by a post-processing CNN. The proposed method is tested on low-resolution toy (MNIST and FMNIST) experimentally captured data from (Mora et al. 2018). It is also tested on simulated TM data on higher-res image-net data.
strengths_and_weaknesses: ## Strengths 

The diagonal assumption massively reduced the number of parameters that need to be learned and could make imaging through MMF much easier. 

## Weaknesses

The paper makes extremely strong assumptions on the structure of the TM which are not adequately justified. The only experimental validation is on (F)MNIST which isn't convincing. The paper provides no evidence that Bessel functions accurately describe the structure of higher-dimensional TMs. The simulated speckle data (Fig 6) looks considerably more structured than the experimental data (Fig 5), suggesting the adopted model is inaccurate.

Some details are missing. It seems the paper is considering only "incoherent" fiber bundles.

There's no evidence the proposed method generalizes across MMFs.

There are minor inaccuracies in the paper: Line 270 states reducing the calibration dataset size minimizes how long cells have to be imaged; cells are involved in the calibration of a TM.


questions: How would fitting a low rank approximation of the TM (or its inverse) compare to the proposed method?
limitations: Not discussed. Method is specific to a particular MMF. Moreover, if that fiber bends (like it would in endoscopy) that fibers TM is likely to change.
review_title: null

final_score: rating: 8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.
review_content: summary: The paper reports on a novel NN architecture for image transmission through a multimode fiber. The approach is physics based, and rely on modeling a NN using bessel modes, that mimicks the pre-existing modes in a MMF. the main advantage is to reduce strongly the number of parameters to train (compared to a complex-valued fully connected layer, the current SoTA) and  the required number of examples, while maintaining similar performances and generalization ability. The concept is validated numerically and experimentally, at scale (256*256) previously unattainable. 
strengths_and_weaknesses: The paper is overall clearly written, the results are sound, and the comparison to the previous litterature is qualitatively and quantitatively appropriate. The main advantage of the technique (less parameters) meaning less memory usage and less examples needed, means that it can scale to complex and large scale images, which is demonstrated. 

A minor criticism is that the authors could have cited a recent paper (Cite: Li, Shuhui, et al. "Compressively sampling the optical transmission matrix of a multimode fibre." Light: Science & Applications 10.1 (2021): 1-15.) that also exploit the sparsity of the transmission matrix of a multimode fiber.  The paper in my opinion should be cited and properly put in perspective with their result.
questions: -Modes of MMF are usually denoted LP modes in the literature, can the authors comments if they are the same as their Bessels? is it a different terminology, or is there a real difference? 

limitations: I think it really doesn't apply here.
review_title: null

Meta-review: metareview: This paper proposes a new learning-based technique for imaging through multimodal fibers (MMF). A key idea of this work is to exploit the property that the transmission matrices associated with MMFs are approximately diagonalizable by Bessel basis. This idea then allows one to significantly reduce the number of parameters, which in turn reduces the memory usage and computational burden of the inverse problem of recovering a natural image from speckle patterns. The authors demonstrated the effectiveness of their proposed algorithm on low-resolution experimentally captured data as well as on higher-resolution simulated dataset.

confidence: Certain
Decision: Accept