Hyperspectral Anomaly Detection Based on Wasserstein Distance and Spatial Filtering

Round 1

Reviewer 1 Report

the authors addressed  the concerns raised in the previous submission

Author Response

Thank you for your contribution to improving our manuscript.

Reviewer 2 Report

Authors did not answer satisfactorily to my previous remarks. When you propose a method depending on two parameters alpha and beta, where the originality of the method relies on the non zero value of the beta parameter, and when all experimental data (Fig 9) show that the results are better with smaller value of beta (as stated line 300), it would be fair to test the zero value also and if no real benefits are observed with the use of this new parameter to admit it in the conclusion, even if it is a negative result.

Author Response

Thank you for your comment. We apologize that we didn’t provide a satisfactory answer to your previous remarks. According to our understanding, the two parameters alpha and beta can’t be set to zero values, because the metric has its roots in Wasserstein distance. If one of the parameters set to zero, the metric can’t be used to evaluate the dissimilarity between target and background distributions. What’s more, the parameters are generally greater than zero, which has added into the updated manuscript. In other words, although the smaller beta value achieves better detection performance, the beta can’t be set to zero value. Hence, we don’t take the zero values into account in our experiments and discuss these parameters in the conclusion.

Round 2

Reviewer 2 Report

I don't see why beta has to be different of zero, it leaves only the part 

(µ1 - µ2)2

which is simpler to compute that the other part, but is perfectly usable in this context.

The fact that choosing  beta very small or zero give better results proves precisely that the Wasserstein distance might not be the best choice for the problem. It is an interesting conclusion, even if negative, and you have demonstrated it by the smart idea to introduce your coefficients alpha and beta. I don't understand why you don't see that it is an important contribution of your work, and don't want to mention it in the conclusion.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

The paper presents a novel method to detect anomalies in hyperspectral images, based on the Wasserstein distance.

The paper is clear and well written, and the research thorough.

The only problem I see is with the conclusions. We see from the 3.4 on the effects of α and β that smaller values of β work better in general. But the 0 value is not tested while it could be good also, leading to a distance that would not be the Wasserstein distance anymore, and would be easier to compute. That would be an interesting conclusion to add.

I noted some typos:

in Fig 1 : combation ? is it combination ?

The line numbering is incomplete near line 197.

On line 148 : text -> test ?

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

The paper proposes a hyper-spectral anomaly detection method based on Wasserstein distance and spatial filtering.

First of all, the proposed method is evaluated on few dataset so the results are questionable.

On page 6, the authors argued that the response values of anomaly targets are usually larger than those of background, but they did not provide sufficient evidence. What if this assumption is violated?

In Equation (4), [v1^i v2^i] may need to be [v1^i v2^i]^T. Please check it again.

On page 5, line 170: “in a descend order” should be “in a descending order.”

Table 1, Table II, Table 2, and Table 3 are used throughout the text. Please be consistent.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

The paper proposes a new algorithm for anomaly detection in hyperspectal images. 

 

I believe the paper needs a major revision before to be considered for publication. Below the concerns that the authors should address in the revised version.

 

1) The introduction should be completely rewritten. Indeed, the introduction does not well contextualize the Wasserstein distance in our field. First of all, it is important to point out that such a distance arises from  the optimal transport problem between Gaussian random vectors. Furthermore, it is also important that the optimal transport problem (and thus the corresponding distance) has been also extended to the case of Gaussian Stationary Processes as well as Gaussian random field.

 

2) This method can be also modified by using different definitions of distances or divergences between Gaussian random vector. For instance, one could use the tau-divergence. The author should discuss on that and also compare their results with the ones obtained using the tau-divergence. 

 

3) Since the parameter setting in this method is empirica, then it is more relevant, as  suggested in 2), to understand whether it is possible to obtain better calibrations using different divergence indexes.

 

4) The authors should also discuss about the possible impact of the results available in the literature on the optimal transport problem between  Gaussian Stationary Processes in this framework. Indeed, in this case it is possible to have a fault detection approach for the time evolution of the hyperspectal image

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The manuscript has been improved and can be accepted in present form.

Reviewer 3 Report

The revised version has not been improved.

First, in my previous report I have highlighted that 

 

"Furthermore, it is also important that the optimal transport problem (and thus the corresponding distance) has been also extended to the case of Gaussian Stationary Processes as well as Gaussian random field."

 

No mention, about this important extension as well as the corresponding literature in the revised version. The authors simply said that it is possible to do that in the case of Gaussian r.ve. that it is actually too restrictive. Especially in view of point 4.

 

Point 2: the authors said that "However, it is not reaonable to conduct the log and non-integer power operations on negative. ". I want to point out that in formula (2) there is a non-integer power operation, i.e. the term (\Sigma_1\Simga_2)^1/2. So, the limitation that the authors mentioned then it also applies to the distance in (2). So, at this point it seems that the proposed distance does not make sense. Indeed, the Wasserstein distance and the tau-divergence have the same domain of definition. 

 

Point 3: it would be interesting to compare the proposed algorithm with the modification using the tau-divergence proviso that the authors fix the issue popped out in point 2.