Learned Design of a Compressive Hyperspectral Imager for Remote Sensing by a Physics-Constrained Autoencoder

Round 1

Reviewer 1 Report

Comments to the Author：

This paper proposes a Physics Constrained Autoencoder (PyCAE) for the design and optimization of a physically realizable sensing model, which allows capturing hundreds of spectral bands with as few as four compressed measurements. Results on two datasets demostrate its outstanding performance. However, there still several problems need to be addressed.

(1) In page 5, from line 170 to 172, you said the proposed system consists of hardware with relay optics that images the light from the scene through the SpLM onto the sensor and software which is a reconstruction DNN. But, in Figure 2.1. (a) you said the encoder is also implemented by DNN. If both the encoder and decoder are implemented by DNN, if not, how the jointly training was done?

(2) Some Figures are bluring and the legends are denoted with different fonts, which should be improved. For instance, Figure 1.1 and Figure 3.4.

(3)  It may be helpful to report the running speed and the number of parameters for the proposed method. This could help readers know the complexity of the proposed method.

(4)  There are some grammar errors and typos. For example, an DNN. Please check the paper carefully.

Author Response

Reviewer 1

RECOMMENDATION: This paper proposes a Physics Constrained Autoencoder (PyCAE) for the design and optimization of a physically realizable sensing model, which allows capturing hundreds of spectral bands with as few as four compressed measurements. Results on two datasets demonstrate its outstanding performance. However, there still several problems need to be addressed.

(1) In page 5, from line 170 to 172, you said the proposed system consists of hardware with relay optics that images the light from the scene through the SpLM onto the sensor and software which is a reconstruction DNN. But, in Figure 2.1. (a) you said the encoder is also implemented by DNN. If both the encoder and decoder are implemented by DNN, if not, how the jointly training was done?

(2) Some Figures are blurring, and the legends are denoted with different fonts, which should be improved. For instance, Figure 1.1 and Figure 3.4.

(3)  It may be helpful to report the running speed and the number of parameters for the proposed method. This could help readers know the complexity of the proposed method.

(4)  There are some grammar errors and typos. For example, an DNN. Please check the paper carefully.

ANSWERS:

(1) Thank you for pointing out this misleading sentence. Line 170 to 172 was rewritten to avoid the above-mentioned confusion. Instead of 'The proposed system consists of hardware with relay optics that images the light from the scene through the SpLM onto the sensor and software which is a reconstruction DNN.', the corrected sentence reads now  'The proposed system consists of an encoder that emulates hardware with relay optics that images the light from the scene through the SpLM onto the sensor and software which is a reconstruction DNN.'

(2) The blurred scripts in figures 1.1, 3.4 and others were replaced with bigger letters, so it is much clear and readable.

(3) Following the reviewer's suggestion, a new subsection (3.3 The reconstruction DNN) was added to the manuscripts with tables containing running speed data for each configuration together with details about the trainable parameters.

(4) The whole manuscript underwent professional English proofreading. Thank you.

Reviewer 2 Report

The authors presented a wonderful idea. Unfortunately, the description of this idea no longer looks so wonderful. Figures 1.1e, 2.1 and 3.4 need to be enlarged by 2 times to read. The authors present the results quite modestly, even a twofold increase is not enough there!

Figure 3.5-3.8 needs to be modified so that they can be seen! The authors should provide 2-3 spectra, but in good quality, and they provide general data in tables. Why do the authors cite Figures 3.1 and 3.2?

The symbol 0 is missing in table 3.3.

Author Response

Reviewer 2

RECOMMENDATION: The authors presented a wonderful idea.

• Unfortunately, the description of this idea no longer looks so wonderful. Figures 1.1e, 2.1 and 3.4 need to be enlarged by 2 times to read. The authors present the results quite modestly, even a twofold increase is not enough there!
• Figure 3.5-3.8 needs to be modified so that they can be seen! The authors should provide 2-3 spectra, but in good quality, and they provide general data in tables.
• Why do the authors cite Figures 3.1 and 3.2?
• The symbol 0 is missing in table 3.3.

ANSWER:

We are pleased that the reviewer enjoyed the idea of our paper. Following the reviewer’s comments, we made several changes to improve the graphical presentation.

• Figures 1.1.e and 3.4 were enlarged, figure 3.4 was numbered correctly and is now 3.3, and in figure 2.1 the script letters were enlarged.
• Figures 3.5-3.8 were completely modified, and now they include fewer spectra graphs with large legends, ticks' numbers, and labels. Also, they were numbered correctly as 3.4-3.7.
• We chose to cite the databases in Figures 3.1 and 3.2 ( despite being well known), as is commonly done, see for example -  Cruz-Ramos, C.; Garcia-Salgado, B.P.; Reyes-Reyes, R.; Ponomaryov, V.; Sadovnychiy, S. Gabor Features Extraction and Land-Cover Classification of Urban Hyperspectral Images for Remote Sensing Applications. Remote Sens. 2021, 13, 2914..

Reviewer 3 Report

This manuscript provides the design of a compressive hyperspectral imager for remote sensing by a Physics Constrained Autoencoder. This is a very interesting and up to date paper since the design and optimization of systems by end-to-end deep learning is a recently emerging subject applied in many fields. In this particular case, the authors apply this technology to remote sensing, managing to capture hundreds of spectral bands with as few as four compressed measurements. The work is very well structured, including a good introduction followed by the sensor design. The methods followed by the authors are deeply explained and high-quality figures illustrate each step of the work. The results section is very complete as well, taking the surroundings of Pavia University to characterize the sensor performance. The manuscript is well written, includes most of the most relevant references in this field and it provides a good level of discussion and scientific soundness, so that it can be followed also by the non-expert public interested in these advances. All in all, this is a nice piece of work and an excellent match for Remote Sensing. Therefore, I recommend its acceptance for publication in the present form.

Author Response

Reviewer 3

RECOMMENDATION: This manuscript provides the design of a compressive hyperspectral imager for remote sensing by a Physics Constrained Autoencoder. This is a very interesting and up to date paper since the design and optimization of systems by end-to-end deep learning is a recently emerging subject applied in many fields. In this particular case, the authors apply this technology to remote sensing, managing to capture hundreds of spectral bands with as few as four compressed measurements. The work is very well structured, including a good introduction followed by the sensor design. The methods followed by the authors are deeply explained and high-quality figures illustrate each step of the work. The results section is very complete as well, taking the surroundings of Pavia University to characterize the sensor performance. The manuscript is well written, includes most of the most relevant references in this field and it provides a good level of discussion and scientific soundness, so that it can be followed also by the non-expert public interested in these advances. All in all, this is a nice piece of work and an excellent match for Remote Sensing. Therefore, I recommend its acceptance for publication in the present form.

ANSWER:

We are delighted by the positive feedback on our paper.