Efficient Computer-Generated Holography Based on Mixed Linear Convolutional Neural Networks
Round 1
Reviewer 1 Report
The topic is relevant.
The text of the article requires serious correction, espeсially in terms of a more understandable description of the method.
Below are more inaccuracies that need to be corrected.
In Line 16 (abstract), it is necessary to specify more clearly what “can decrease the parameters by 69%” means. Apparently, the authors wanted to say – “can reduce the number of network parameters, needed for network training”?
Line 102-103: “However, some optical problems are difficult to describe using linearly separable functions…”. What problems do you mean?
According to Line 225 «Compared with traditional iterative methods, our method can achieve faster computation speed». But in section 3, a comparison (in terms of optimization, not computation speed) is presented with the only U-net method. And also it is not clearly indicated how much MLCNN is faster than U-net, it is only indicated that “The curves show that the MLCNN network has faster optimization speed and higher accuracy than the U-net network.” - Line 170.
Figure 5 uses Rule instead of ReLu
Author Response
Response to Reviewer 1
(Manuscript ID: applsci-1678602，Title: Efficient Computational Holographic Based on Mixed Linear Convolutional Neural Networks)
Dear Reviewer:
Thank you for your positive and professional comments, which is useful for the improvement of the quality of the manuscript. In accordance with your comment, we revised the manuscript to eliminate the inaccuracies in description of the method as the followings:
Comment1: In Line 16 (abstract), it is necessary to specify more clearly what “can decrease the parameters by 69%” means. Apparently, the authors wanted to say – “can reduce the number of network parameters, needed for network training”?
Response: Thank you for this comment, the expression in line 16 referred is really inaccurate. For clear and accurate description, the sentence is revised into “Compared with traditional computed holography by deep learning, the method here can reduce about two thirds of the number of network parameters, needed for network training, but obtain high quality image in reconstruction, and the network structure has the potential to solve various image reconstruction problems.”
Comment2: Line 102-103: “However, some optical problems are difficult to describe using linearly separable functions…”. What problems do you mean?
Response: Here the optical problems are mostly used optical operations, including image encoding, holographic encryption, frequency analysis and so on. To describe the problems more specially, the sentence is corrected into “However, problems such as image encoding, holographic encryption, and frequency analysis are difficult to describe with linearly separable functions”.
Comment3: According to Line 225 «Compared with traditional iterative methods, our method can achieve faster computation speed». But in section 3, a comparison (in terms of optimization, not computation speed) is presented with the only U-net method. And also it is not clearly indicated how much MLCNN is faster than U-net, it is only indicated that - Line 170.
Response: Thank you very much for this helpful indication, which reveals a significant problem in this manuscript. After our investigation, the computation speeds of these methods are compared and the corresponding results are given in several sentences before table 2. The sentence “The curves show that the MLCNN network has faster optimization speed and higher accuracy than the U-net network.” is corrected at the same time. Please see “To investigate the computing efficiency of MLCNN network, a common computer with CPU processer (Intel i5) and GPU (Nvidia GTX 1060) is employed to compete the training work and the result show that 38ms and 9.8ms are needed to finish the work of MLCNN network training and phase-only holographic image generation for one frame respectively. For comparison, similar works are also conducted by both U-net network and GS iterative method. Corresponding computing times used for phase-only holographic image gener-ation are 13.5ms and 0.62s respectively for one frame. The results show that the MLCNN network has faster optimization speed and higher accuracy than either the U-net network or GS algorithm.”
Simultaneously, the sentence “Compared with traditional iterative methods, our method can achieve faster computation speed.” is corrected as “Compared with traditional U-net network [21, 22] and GS algorithm [17], our method can achieve faster computation speed in hologram generation.”
Comment 4: Figure 5 uses Rule instead of ReLu
Response: Thank you for your reminding. We have amended the expression in Figure 5.
Thank you very much again for your time and kind suggestions. We have tried our best to revise the manuscript according to your comments, which made surely a substantial improvement in this presentation of the work, and hope that this revised manuscript now is suitable for publication in AS.
Sincerely,
Dr. X. F. Xu
Reviewer 2 Report
The article "Efficient Computer-generated Holography Based on Mixed Linear Convolutional Neural Networks" is devoted to the creation of a network "Mixed linear convolutional neural networks (MLCNN)". Using the simplest example of a 48x48 dot object, the authors show that it works better than the well-known "U-net", judging by the smaller standard deviation of a flat two-dimensional image of handwritten digits from 0 to 9 restored by a synthesized phase hologram. The result of this work is undoubtedly of interest, although it is not possible to check the data obtained by the authors, since the trained networks are very difficult to control. It's just good that the authors guessed to bring some of their findings into the structure of the network, as it seems to me, for example, the bridge structure and some other elements. However, the text of the article shows some shortcomings:
- It is difficult to understand what the authors mean when they write (102) that "... simple convolution and deconvolution are always limited to a certain area". How and what is limited? I can always take any size for these operations.
- The abbreviation MNIST (145) is not deciphered anywhere. Apparently, abbreviation MNIST is not needed in the text.
- I belong to the old school, so instead of "Loss" (166) I would prefer to use "deviation".
- And as a holographer, I declare that it's just a disaster when both the holographic object and the hologram contain the same number of pixels, because in real holographic experiments, the hologram contains much more information than the holographic object. The authors are excused only by the fact that their experiments are exclusively model in nature. Indeed, a 48x48 pixel object and a 48x48 pixel hologram are too small to get practically meaningful results. Moreover, holograms of flat objects are extremely uninteresting for holography. The word holography itself refers to the recording of complete information about an object, meaning not a mathematical abstraction in the form of an image projection onto a flat surface, but real material objects that are always three-dimensional.
- And finally, the authors, with a very modest size of the hologram, say that they wanted to reduce the computation time (144), but nowhere do they give how much time was required for such a modest 48x48 hologram. After all, this time must be compared with the calculation time for other algorithms. This is one of the most important characteristics in the hologram synthesis. It definitely needs to be reported.
Author Response
Response to Reviewer 2
(Manuscript ID: applsci-1678602，Title: Efficient Computational Holographic Based on Mixed Linear Convolutional Neural Networks)
Dear Reviewer:
Thank you for your positive and professional comments, which is useful for the improvement of the quality of the manuscript. In accordance with your comment, we revised the manuscript correspondently as the followings:
Comment 1：It is difficult to understand what the authors mean when they write (102) that "... simple convolution and deconvolution are always limited to a certain area". How and what is limited? I can always take any size for these operations.
Response: We think this comment is reasonable here. The area size should be controlled to improve the operating efficiency. So the sentence is changed into “…simple convolution and deconvolution are always limited to a certain area size to improve the operation efficiency.”
Comment 2：The (145) is not deciphered anywhere. Apparently, abbreviation MNIST is not needed in the text.
Response: We agree with you on this comment. Considering that the abbreviation MNIST is used many times in the manuscript, to save page space, it is explained in the end paragraph of the introduction section. Please see the phrase “Mixed National Institute of Standards and Technology database (MNIST)”.
Comment 3：I belong to the old school, so instead of "Loss" (166) I would prefer to use "deviation".
Response: We also think the word "deviation" is better. So it is added in the sentence.
Comment 4：And as a holographer, I declare that it's just a disaster when both the holographic object and the hologram contain the same number of pixels, because in real holographic experiments, the hologram contains much more information than the holographic object. The authors are excused only by the fact that their experiments are exclusively model in nature. Indeed, a 48x48 pixel object and a 48x48 pixel hologram are too small to get practically meaningful results. Moreover, holograms of flat objects are extremely uninteresting for holography. The word holography itself refers to the recording of complete information about an object, meaning not a mathematical abstraction in the form of an image projection onto a flat surface, but real material objects that are always three-dimensional.
Response: Thank you for your professional understanding of holography. Really, neither a 48x48 pixel object nor a hologram with the same size is big enough to get practically meaningful results and real material objects with three-dimensional distribution should be considered in holography configuration. Here we provide an alternative concept to improve the computing efficiency. Like other researchers, the 48x48 pixel object or holograms is chosen for testing on common computing resources. In the future work, more complicated objects and holograms will used by this MLCNN network.
Comment 5：And finally, the authors, with a very modest size of the hologram, say that they wanted to reduce the computation time (144), but nowhere do they give how much time was required for such a modest 48x48 hologram. After all, this time must be compared with the calculation time for other algorithms. This is one of the most important characteristics in the hologram synthesis. It definitely needs to be reported.
Response: We understand your concerns in this comment and corresponding studied have been conducted on the computation time. The computing results with comparisons are added in this new version. Please see the sentences before Table 2 “To investigate the computing efficiency of MLCNN network, a common computer with CPU processer (Intel i5) and GPU (Nvidia GTX 1060) is employed to compete the training work and the result show that 38ms and 9.8ms are needed to finish the work of MLCNN network training and phase-only holographic image generation for one frame respectively. For comparison, similar works are also conducted by both U-net network and GS iterative method. Corresponding computing times used for phase-only holographic image gener-ation are 13.5ms and 0.62s respectively for one frame. The results show that the MLCNN network has faster optimization speed and higher accuracy than either the U-net network or GS algorithm.”
Thank you very much again for your time and comments. We have tried our best to improve the manuscript quality according to your suggestions. Your comments made surely a substantial improvement in this presentation of the work, and We hope that this revised manuscript now is suitable for publication in AS.
Sincerely,
Dr. X. F. Xu
Author Response File: 
Author Response.docx
Reviewer 3 Report
In the presented paper, the authors suggested a non-iterative deep learning model, titled Mixed Linear Convolutional Neural Networks (MLCNN), for generating Efficient Computer-generated Holography (ECGH) images.
The paper is well written, and its organization is excellent. However:
- In the last part of the introduction, it is recommended to organize the main contributions in the form of points.
- Paper’s organization should be added at the end of the introduction.
- Authors should add some perspectives in the last part of the conclusion.
- Lines 75-77: correct the paragraph into: “…the corresponding principle of the computational holography, the real amplitude, and the normalized intensity of the target image are denoted as”.
- Line 84: the numbering of this section is 3.
- Line 143: the numbering of this section is 4.
- Line 194: the numbering of this section is 5.
- Line 223: the numbering of this section is 6.
- Authors should add more details about the dataset (number of images, splitting…) and the employed evaluation protocol.
- Authors should compare their findings to some recently related papers.
Author Response
Response to Reviewer 3
(Manuscript ID: applsci-1678602，Title: Efficient Computational Holographic Based on Mixed Linear Convolutional Neural Networks)
Dear Reviewer:
Thank you for your positive and helpful comments, which is instrumental for us to improve the quality of the manuscript. According to your comment, we revised the manuscript as the followings:
Comment 1: In the last part of the introduction, it is recommended to organize the main contributions in the form of points.
Response: Thank you for your suggestion, which can high light the advantages of the method proposed. Several sentences are added to the end of the introduction. They are “The merits of the proposed method lie in the following three aspects. Firstly, the mixed linear convolutional neural networks structure can reduce the number of the used parameters by about two thirds so that the computing loads can be alleviated correspondently. Secondly, the method can save half the computing time when compared with conventional U-net structure [21, 22]. Compared to GS algorithm [17], MLCNN method can reduce much more computing time. Lastly, the mixed linear convolutional neural networks structure is introduced in ECGH to improve the image quality.”
Comment 2: Paper’s organization should be added at the end of the introduction.
Response: This is a good comment to make the manuscript structure more clear. Several sentences are also added to the end of the introduction. Please see “In the following sections, the reconstructed optical configuration of the comput-er-generated holography is given first and then the design for the MLCNN network structure and the network training logic are introduced. Subsequently the network training results are shown in Section 4 and the stability of the method is analyzed in Sec-tion 5 followed by the conclusions at last.”
Comment 3: Authors should add some perspectives in the last part of the conclusion.
Response: We think this comment remind us to exhibit the future application of the method. So a paragraph is added to the end of the conclusion. Please see “Virtual reality (VR) and augmented reality (AR) are currently hot spots in display technology and application. However, conventional technologies in VR and AR employ micro-displays to load images, which can cause visual fatigue when used for extended periods of time. Benefiting from the ability of reproducing three-dimensional scenes perfectly, computational holography can avoid the appearance of visual fatigue. This ECGH method is expected to ease the huge CGH computing load and to improve the quality of the computational holography images”
Comment 4: Lines 75-77: correct the paragraph into: “…the corresponding principle of the computational holography, the real amplitude, and the normalized intensity of the target image are denoted as”.
Response: Yes，the sentence has been changed into “Through the optical realization setup shown in Figure 1, the corresponding principle of the computational holography, the real amplitude, and the normalized intensity of the target image are denoted as”. (Line 81-83)
Comment 5-8:
Line 84: the numbering of this section is 3.
Line 143: the numbering of this section is 4.
Line 194: the numbering of this section is 5.
Line 223: the numbering of this section is 6.
Response: Yes, these section numbering is wrong in the original version. We have modified the corresponding numbers into “3,4,5,6”.
Comment 9: Authors should add more details about the dataset (number of images, splitting…) and the employed evaluation protocol.
Response: To add more details of the dataset and the evaluation protocol, one sentence “In this work, 6000 MNIST images are used and split into training set and test set according to the ratio of 5:1.” is added in the first paragraph of section 4 in the new version. (Line 152-154) and one more sentence is also added. Please see “In order to evaluate the quality of the generated images more objectively, the intensity value for all pixels in images are normalized to [0, 1], and MATLAB software is used to calculate each group of images.”
Comment 10: Authors should compare their findings to some recently related papers.
Response: we think this comment is reasonable to show the improvement of our work. The sentence “Compared with traditional iterative methods, our method can achieve faster computation speed.” In conclusion section is corrected as “Compared with traditional U-net network [21, 22] and GS algorithm [17], our method can achieve faster computation speed in hologram generation.”.
Thank you very much again for your time and comments. We have tried our best to revise the manuscript according to your suggestions. Your comments made surely a substantial improvement in this presentation of the work, and We hope that this revised manuscript now is suitable for publication in AS.
Sincerely,
Dr. X. F. Xu
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Authors revised the manuscript according to the comments.
Reviewer 3 Report
- The paper has been vastly improved.
- The authors have considered all my suggested remarks.
- For all these reasons, I recommend accepting the manuscript in the current form for publication.
