Blind Hyperspectral Unmixing with Enhanced 2DTV Regularization Term
Round 1
Reviewer 1 Report (Previous Reviewer 1)
The authors have addressed my previous comments. I have only a minor comment. In Table 3, the SAM of E-gtvMBO is obvously worse than FCLSU. However, the RMSE result of E-gtvMBO is much better than FCLSU. In general, the SAM and RMSE values have relations. Why the results are inconsistent?
Author Response
Response: Thanks very much for this reviewer’s proper summary. You may be confused by the unclear description before. In fact, by observing Table 3, alternate SAM (X), nMSE (X) and RMSE (X) in FCLSU are better than that in the proposed E-gtvMBO for the quantitative index of the end matrix X, RMSE (A) and nMSE (A) for the quantitative indexes of the foundation matrix A observed by the proposed E-gtvMBO is the smallest Therefore, from the quantitative point of view, the proposed E-gtvMBO still shows the good performance.
In other words, SAM is used to calculate the endmember matrix X, and what you pointed out that the results are inconsistent with RMSE, and the inconsistent results are about abundance matrix A. So, it's not a conflict.
We have added the explanation on page 11 line 356-line 360.
Author Response File: 
Author Response.docx
Reviewer 2 Report (Previous Reviewer 2)
Most of my concerns are solved. However, the presentation of this paper is still a mass, for example, the equations.
Author Response
Response: Thanks very much for this suggestion. According to your suggestion, we further shortened the number of equations in the text of this paper. First of all, we delete the formulas of three indicators (RMSE, SAM, and nMSE) that are familiar to everyone (equations 20, 21 and 22 in the original article).
In addition, we will transfer the six sub-problems (equations 12-19 in the original article) of ADMM in the original article from the text to Appendix A. In this way, only 11 formulas appear in the text of this paper.
The relevant description is given on page 6, line 225-line 226, and on page 16 line 455-page 17 line 491.
Author Response File: Author Response.docx
Reviewer 3 Report (Previous Reviewer 3)
Many thanks to the authors for addressing my comments. I think the paper is ready for publication now.
Author Response
Response: Thanks very much for this reviewer’s proper summary.
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
(1) In the introduction, it is better to introduce some related hyperspectral unmixing methods, such as DOI: 10.1109/TGRS.2020.2996688
(2) Please check the letter, symbols and formulas in the paper, such as Eq. (4).
(3) What is “HSI distance”?
(4) “But the graph Laplacian regularization generally leads to over smoothing due to the l2-norm” Please provide some explanation.
(5) In the simulated experiments, only SNR=20 is considered. It is better to consider different SNRs.
(6) In the Algorithm 1, the algorithm can output X and A simultaneously. However, in the experiments, the authors only evaluate the performance on the abundance A, as shown in Eqs. (31)-(33).
(7) In Table 1, why there are Inf? Why the results of nMSE and SRE are not consistent. From the definition, if the nMSE is small, the SRE should be large.
(8) Please check Eq. (32), it is the F-norm.
Reviewer 2 Report
This paper introduces an enhanced 2DTV regularization for hyperspectral unmixing. Compared with traditional TV, the sparsity is calculated based on the subspace rather than the gradient map itself.
- Could the author explain more details of Eq. (14)-(16)? What does the * symbol mean？
- The total variation is imposed on the abundance map rather than the spatial and spectral domain. It is confusing that the correlations between different bands can be encoded,
- As an optimization-based method, what’s the convergence property?
- “ alternating direction method of multipliers” is generally abbreviated as ADMM.
- The introduction section should be improved to incorporate the deep learning-based unmixing such as doi: 10.1109/LGRS.2022.3199583, doi: 10.1109/TGRS.2021.3081177, doi: 10.1109/TGRS.2020.2982490.
Reviewer 3 Report
kindly see attached
Comments for author File: 
Comments.pdf
Reviewer 4 Report
This paper introduces a novel hyperspectral unmixing method, by designing an enhanced 2DTV. The proposed method, called E-gtvMBO encodes correlations and differences between spectral bands, which can better reflect the sparseness characteristics of natural hyperspectral images gradient maps.
A major issue of this work is in its contribution, which seems not clear. The contribution of the paper is on the so-called enhanced 2DTV, which is roughly a classical 2DTV with a sparsity promoting element. However, there are too many papers in the literature that have included a TV-like regularization and a sparsity regularization term.
Examples of related methods:
- Wang, Minghua, Qiang Wang, Jocelyn Chanussot, and Danfeng Hong. "L₀-l₁ hybrid total variation regularization and its applications on hyperspectral image mixed noise removal and compressed sensing." IEEE Transactions on Geoscience and Remote Sensing 59, no. 9 (2021): 7695-7710.
- Niresi, Keivan Faghih, and Chong-Yung Chi. "Unsupervised hyperspectral denoising based on deep image prior and least favorable distribution." IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 15 (2022): 5967-5983.
- Sun, Le, Tianming Zhan, Zebin Wu, and Byeungwoo Jeon. "A novel 3d anisotropic total variation regularized low rank method for hyperspectral image mixed denoising." ISPRS International Journal of Geo-Information 7, no. 10 (2018): 412.
- Yang, Yanhong, Shengyong Chen, and Jianwei Zheng. "Moreau-Enhanced Total Variation and Subspace Factorization for Hyperspectral Denoising." Remote Sensing 12, no. 2 (2020): 212.
- Bauer, Sebastian. Hyperspectral image unmixing incorporating adjacency information. Vol. 18. KIT Scientific Publishing, 2018.
- Ekanayake, E. M. M. B., H. M. H. K. Weerasooriya, D. Y. L. Ranasinghe, Sanjaya Herath, Bhathiya Rathnayake, G. M. R. I. Godaliyadda, M. P. B. Ekanayake, and H. M. V. R. Herath. "Constrained nonnegative matrix factorization for blind hyperspectral unmixing incorporating endmember independence." IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 14 (2021): 11853-11869.
- Zhang, Ge, Shaohui Mei, Bobo Xie, Mingyang Ma, Yifan Zhang, Yan Feng, and Qian Du. "Spectral Variability Augmented Sparse Unmixing of Hyperspectral Images." IEEE Transactions on Geoscience and Remote Sensing 60 (2022): 1-13.
- Sun, Baochen, and Huibin Chang. "Proximal Gradient Methods for General Smooth Graph Total Variation Model in Unsupervised Learning." Journal of Scientific Computing 93, no. 1 (2022): 1-23.
- Song, Hanjie, Xing Wu, Anqi Zou, Yang Liu, and Yongliao Zou. "Weighted Total Variation Regularized Blind Unmixing for Hyperspectral Image." IEEE Geoscience and Remote Sensing Letters 19 (2021): 1-5.
- Lee, Harlin. "Better Inference with Graph Regularization." PhD diss., Carnegie Mellon University, 2021.
- Cruz-Guerrero, Inés A., Daniel U. Campos-Delgado, and Aldo R. Mejía-Rodríguez. "Extended Blind End-member and Abundance Estimation with Spatial Total Variation for Hyperspectral Imaging." In 2021 43rd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), pp. 1957-1960. IEEE, 2021.
Experiments are not much convincing. The only experiments that show good results are on synthesized images from the USGS dataset. It is well known that synthesized images can be manipulated, by choosing the most relevant configuration for the proposed method. Experiments on reals images, namely Urban and Cuprite images, are less convincing. Moreover, the computational complexity seems to be higher that comparative methods, such as GraphL (as given in Table 5)
There are many spelling and grammatical errors, such as “HSI is often consists”, “ it needs to conform the abundance is nonnegative”, “Massively spectral unmixing methods uses”, “exploits the spectral information of different pixels has similar”, “we consider impose an”, “ can naturally encodes”, “At this section”, “ummixing results”.
Some sentences need to be rewritten, such as “For comparing all methods performance, a simulated data which selected from the United States Geological Survey (USGS) library is tested” and “The distribution map of minerals which from USGS”. In many sentences, there are missing articles (the/a)
Reviewer 5 Report
A brief summary
The article analyze a typical problem of hyperspectral image (HSI): since a single pixel include various ground objects, hyperspectral unmixing technology is proposed to reverse the various pure substance spectra existing in each pixel. To improve the results, the regularization term of the total variation of the graph (g-TV) is often introduced into the hyperspectral unmixing model. The term g-TV, however, does not adequately use the correlations and differences between the available bands. The authors propose an enhanced 2DTV (E-2DTV) regularization term and suggest a blind hyperspectral unmix method with the E-2DTV regularization term (E-gTVMBO). The E-2DTV regularization term is based on the gradient mapping of all bands of HSI. The experiments performed prove that the E-gTVMBO method is superior both qualitatively and quantitatively.
The article has many weaknesses and needs to be deeply restructured.
Suggestions
1. The abstract is not written in a clear way, it refers to complex or at least too specific concepts and not known to the basic readers of a remote sensing journal. It needs to be rewritten in a more organized way, recalling the theoretical concepts and describing the applications in a more explicit and non-encrypted way as it is currently,
2. Too many acronyms are present in the introduction: the authors claim to recall an exaggerated myriad of concepts in an introductory section. All right, there are bibliographic references and therefore the reader can deepen what is referred to in a synthetic way, but, in my opinion, an introduction cannot propose the references of many concepts all together. If what was described in the introduction serves to understand what is written later, it is better that some of these concepts are hosted in a separate paragraph. For example, I would recommend making a section or a sub-section dedicated to preliminary concepts to be inserted before (as section) or at the beginning (as subsection) of section 2, a preamble before describing the actual methodological aspects.
3. The methods section is full of formulas, thirty formulas are reported. Are the authors sure that all these formulas are needed? The reading seems heavy, perhaps the description can be summarized by quoting only some of the formulas listed in the current version.
4. The simulated dataset described in the sub-section 3.1 is no clear. Please explain better this aspect: which are the characteristics of USGS Library Dataset? In which way and based on which criteria you select your dataset?
5. The conclusions are limited and unclear. What is the advantage that your approach could generate in other situations? to what type of data can your method always be applied in an advantageous way?
Ultimately, a major revision is requested. In this form the article is not suitable for publication under Remote Sensing Journal.
