Hyperspectral Anomaly Detection Based on Regularized Background Abundance Tensor Decomposition

Round 1

Reviewer 1 Report

 

In this paper, the authors consider a regularized tensor decomposition technique for hyperspectral anomaly detection. More precisely, the authors combine several state-of-the-art penalization terms (i.e., low-rankness, sparsity, and TV regularization) to provide a high-performance anomaly detection in hyperspectral images. The proposed method is shown to outperform SotA methods. Overall, the paper is interesting and easy to follow. Still, it can be improved.

 

1) Investigation of the effects of the parameters lambda_i and beta.

The authors introduce a high number of parameters to fix (lambda_1, lambda_2, beta) and they propose to investigate their individual effects while fixing the others. Firstly, when they fix some parameters to investigate the free parameter, we do not know which values they choose. Secondly, the conclusions they derive from their experiments might significantly change if the fixed parameters are set differently. Actually, the considered penalized tensor decomposition is an instance of a multi-objective optimization problem and it might be interesting to check the reached performance of the proposed method with all the tested parameters in order to define a Pareto front [a].

 

2) Investigation of the Dm methods.

The authors also compare their proposed methods with two degradation models (named Dm-1 and Dm-2). The latter consider a portion of the objective functions of the proposed ATLSS method. However, I found unfortunate that the TV regularization term was not investigated as a degradation model. In particular, it would be interesting to investigate the performance of Dm-3 and Dm-4 methods which would replace the sparsity penalization term of Dm-1 and Dm-2 (penalized by lambda_1) with the TV regularization term (penalized by lambda_2)

 

3) Minor comments and typos.

- p2: “most recently, [2]” should be replaced by “more recently”

- p2: missing space between “multidimensional structure” and “[31]”

- p3, item 2 of the enumeration: “charaterized” should be written in the present form (as the other verbs of the paragraph)

- p7: the tensor l_{1,1,2} norm is introduced 6 lines before Eq. (6) but is defined after this equation. Please define it once you first introduce the notation.

- p8: Eq. (11) is introduced as a TV-based extension of (10) but the low-rankness penalization term is not present in the former. It is back in Eq. (14).

- p15, first paragraph of Section 3.3: add an S at the end of “Figure” in “are shown in Figure 7-11”

- p15, last paragraph of Subsect. 3.3.1: I guess the authors mean that lambda_2 is in the interval [0.0001, 0.05] (and not 0.005)

 

References:

[a] Ngatchou, P., Zarei, A., & El-Sharkawi, A. (2005, November). Pareto multi objective optimization. In Proceedings of the 13th international conference on, intelligent systems application to power systems (pp. 84-91). IEEE.

 

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper proposed a hyperspectral anomaly detection method based on low-rank linear mixing model. In particular, it designed a blind tensor-based model using abundance tensor and endmember matrix, and characterized abundance maps by tensor regularization with imposed low rankness, smoothness and sparsity. The proposed method achieved good performance. However, there are following problems in this work.

1. The innovation of this paper is not prominent enough. Compared with other similar tensor-based methods, the innovation and effectiveness of this work need to be further expounded.

2. In the experiment part, the used competitors are not representative enough, and the methods based on deep learning and tensor seem to be lacking. It is better to supplement the comparative experiments and make analysis in depth.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors took into consideration all the reviewers' comments.

Reviewer 2 Report

Thank you. All the questions have been answered well. The reviewer has no more questions.