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Reviewers are satisfied with the revisions, and I concur to accept this manuscript.
[# PeerJ Staff Note - this decision was reviewed and approved by Jyotismita Chaki, a PeerJ Section Editor covering this Section #]
After reviewing the revised manuscript, I observed that the authors have diligently addressed all the comments and suggestions I provided earlier. Given the improvements and revisions made, I believe the paper is now in an acceptable state for publication.
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All the comments are answered properly, the manuscript can be published as is.
The reviewers have substantial concerns about this manuscript. The authors should provide point-to-point responses to address all the concerns and provide a revised manuscript with the revised parts being marked in different color.
[# PeerJ Staff Note: Please ensure that all review comments are addressed in a rebuttal letter and any edits or clarifications mentioned in the letter are also inserted into the revised manuscript where appropriate. It is a common mistake to address reviewer questions in the rebuttal letter but not in the revised manuscript. If a reviewer raised a question then your readers will probably have the same question so you should ensure that the manuscript can stand alone without the rebuttal letter. Directions on how to prepare a rebuttal letter can be found at: https://peerj.com/benefits/academic-rebuttal-letters/ #]
The proposed spatially variant high-order variational model (SVHOVM) introduces novelty into the field of Rician noise reduction. The use of a spatially variant TV regularizer that adjusts the smoothing strength per pixel based on its characteristics, coupled with the bounded Hessian (BH) regularizer to diminish the staircase effect, is an innovative approach to this problem. However, there are some parts to enhance whole paper quality.
1.It's crucial to maintain clarity and precision when presenting mathematical models in scientific literature. While reading through your equations, I noticed some notations that appear to be either missing or unclear. I recommend a thorough review of your equations to ensure all variables and constants are correctly defined and notated. For example, equation 13,
except figure 1 the flowchart. Here's a suggestion if you can create a graph that could demonstrate the cooperation between a spatially variant TV regularizer and bounded Hessian (BH) regularizer.
1.line 181. It's encouraging to see that SVHOVM outperformed other models on the SB dataset. However, to further strengthen the validity and generalizability of these findings, it would be beneficial to test SVHOVM on additional datasets. Specifically, the application of this method on Radiology dataset could provide valuable insight, considering the crucial role that MR imaging plays in cancer diagnosis and treatment.
2.For Figures 4 and 5, it would be informative to delve deeper into the impact of different x-axis parameter settings on y-axis outcomes. This can elucidate how varying these parameters influences the performance of the SVHOVM model. Such discussions could help in understanding the sensitivity of the model to parameter variations and the optimal settings for achieving the best performance.
3.In the conclusion section, further information about the potential usage of SVHOVM would be valuable. While it's clear that it has potential for MR imaging noise reduction, elaborating on specific scenarios, potential benefits in clinical or research settings, and its performance relative to other methods would enhance the paper's relevance and impact.
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1. Figure 6, The difference between each column is not very clear, please zoom in and make the difference to be more readable.
1. Page 3, line 91, please provide the equation for calculating gamma function.
1. Figure 3, panel f-h. Images are provided with alpha_0 = 50 which is not shown in panel c-e. Please provide more details regarding why select alpha_0 = 50 or change it to images with alpha shown in label c-e.
1. Please also provide more discussions regarding the limitations of this study and future direction.
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