A Content-Aware Non-Local Means Method for Image Denoising

Round 1

Reviewer 1 Report

This research proposes an image denoising method by improving non-local means. It is applicable to images with similar patches in themselves. Experimental results demonstrate the effectiveness. However, there are several issues:

- The authors propose a fast search approach, but the fastness is not verified by experiments.

- Eq (1) is not a denoising model, but a descriptive model.

- References needed for Eq (1-3).

- The term "local patches" above Eq (3) needs to be defined.

- The motivation of Eq (8) needs to be improved.

- In Eq (10), how to determine edge regions? How sensitive to edge selection methods and hyper-parameter 0.6? It is not clear whether \hat{h} here is the same as the h in Eq. (3).

- In addition, the sensitivity of parameters needs to be discussed, such as the 10 in Eq (16). Choices of hyper-parameters may be declared in the experiment section.

- The experimental data set seems to be very limited.

- H in Eq 14 the same as H in Eq 5?

- In Eq 15, what is the search result, the index?

- How the Hessian matrix is calculated from neighborhood pixels may be described. 

Author Response

Response to Reviewer 1 Comments

 

Point 1: The authors propose a fast search approach, but the fastness is not verified by experiments.

 

Response 1: We have added the comparison of the execution times of several algorithms in Section 6.3.

 

Point 2: Eq (1) is not a denoising model, but a descriptive model.

 

Response 2: We have re-understood the concept of both and revised the model formulation. We claimed that this is an additive noise model in my revised edition.

 

Point 3: References needed for Eq (1-3).

 

Response 3: Eq (1-3) is from the NLM method, and we have added the reference.

 

Point 4: The term "local patches" above Eq (3) needs to be defined.

 

Response 4: We realized that “local patches” above Eq (3) means “patches,” then deleted the word “local.”

 

Point 5: The motivation of Eq (8) needs to be improved.

 

Response 5: Eq (4) “” is an original formulation in the NLM method, where  is a recommendation factor. Thus, we combine “0.7” into Eq (8). And we claimed that “the filtering parameter should be larger on smooth region and smaller on texture regions” before introducing Eq (7) in Section 3.

The eigenvalues are close to smooth or corner regions. The eigenvalues are small on smooth regions; and large on corner ones. According to Eqs (7-9), the filtering parameter is adaptive to three regions. The above is the motivation of Eq(8), and we describe it more clearly in the article.

 

Point 6: In Eq (10), how to determine edge regions? How sensitive to edge selection methods and hyper-parameter 0.6? It is not clear whether \hat{h} here is the same as the h in Eq. (3).

 

Response 6: In Eq (10), we introduced the Canny operator to determine edge regions and added the description in Section 3.

The sensitivity to edge selection depends on the Canny operator. The hyper-parameter 0.6 is an empirical value, and we declared it in the experimental results in Section 6.

\hat{h} is a new filtering parameter, and it is the same in a physical sense as Eq (3).

 

Point 7: In addition, the sensitivity of parameters needs to be discussed, such as the 10 in Eq (16). Choices of hyper-parameters may be declared in the experiment section.

 

Response 7: We revised the parameter formulation in Eq (16) and other hyper-parameters. We declared all the choices of hyper-parameters in Section 6. These hyper-parameters are empirical values.

 

Point 8: The experimental data set seems to be very limited.

 

Response 8: We added ten classic test images for denoising in the experimental datasets and updated the experimental results. Because these 30 images are from different datasets, we did not mark out the sources.

 

Point 9: H in Eq 14 the same as H in Eq 5?

 

Response 9: H in Eq (14) is not the same as H in Eq (5), and we rephrased H as  in Eq (14).

 

Point 10: In Eq 15, what is the search result, the index?

 

Response 10: The search result in Eq (15) is the number of searched similar patches according to the 2-D histogram in Section 5.1. A 2-D histogram also recorded the coordinates of each patch in the image. As a result, the index in Eq (15) also contained each patch's statistical features and center coordinates. We described it in Section 5.2.

 

Point 11: How the Hessian matrix is calculated from neighborhood pixels may be described.

 

Response 11: We added more description about the Hessian matrix in Section 3. Hessian matrix is based on a pixel region and calculated within second-order derivatives. The mathematical formulation is shown in eq (5).

 

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors introduced a new factor based on the Hessian matrix to adapt the smoothing parameter. Then a strategy is proposed to implement the NLM by representing patches in terms of features, which uses the 2D histogram and summed-area table. Overall, the topic of this paper is convincing and the problem is hot.

Please give more mathematical explanations of Eqs. 5-10. Tell us more details about Hessian Matrix Analysis.

Please edit the English language and check the grammatical mistakes. There are some online tools to do it.

Please compare with

Cai, Shuting, et al. "Image denoising via improved dictionary learning with global structure and local similarity preservations." Symmetry 10.5 (2018): 167.

 

Cai, Shuting, et al. "A new development of non-local image denoising using fixed-point iteration for non-convex ℓp sparse optimization." PloS one 13.12 (2018): e0208503.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

- Language issues need to be fixed, for example, noisy additive image -> noisy image.

 

- Point 3: References needed for Eq (1-3).

Response 3: Eq (1-3) is from the NLM method, and we have added the reference.

Only Eq 2 is noted.

 

- Again language issues, some are difficult to understand, for example,

the similarity between patches centered at positions u and v (why are two patches centered at a certain position?)

Thus, a new term k, which measures local content (which content? The motivation is not mentioned)

Line 5 is difficult to understand.

Line 71 and 72 is difficult to understand: approximate -> approximately the same? the ones are large, -> the differences is large?

 

Point 6: For sensitivity analysis, the authors should try different values and see experimental results.

 

Point 8: source should be marked, and 30 images seem to be quite limited. How other approaches are measured in their research papers?

 

Point 10: Eq 15 is still difficult to understand. What is L1234? Pixel indices?

 

Point 11: Details are still missing. For example, what is the window size? How the first derivative and the second derivative are computed in terms of pixels?

 

- The best result should be highlighted (bold) in tables.

 

- It should be inequality in Eq. 10?

 

The authors should better highlight (in red for example) their changes in the manuscript. 

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

It can be published.

Author Response

We have improved language style.

Round 3

Reviewer 1 Report

I think experiments should be expanded as well. I checked this reference, and I don't think they have used 30 images only to justify an algorithm:
Frosio, I.; Kautz, J. Statistical nearest neighbors for image denoising.Ieee T. Image Process. 2018,28, 723-738
We test the effectiveness of the SNN schema on the Kodak image dataset [17].

Author Response

Please see the attachment.

Author Response File: Author Response.pdf