Image Reconstruction in Ultrasonic Speed-of-Sound Computed Tomography Using Time of Flight Estimated by a 2D Convolutional Neural Networks

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Major Issues:

1.      The article title is misleading. Although the title mentions TOF estimation, the results and discussion sections lack detailed information on TOF estimation. Instead, they focus more on the CT image and its performance score.

 

2.      In lines 73-75 of the manuscript, ‘The waveforms measured by the speed-of-sound CT system contained sound speed data from hundreds of different paths, enabling the formation of profile data in a fan-beam manner.’ Ambiguously mentioned hundreds of different paths. The authors need to be more specific.

 

3.      In lines 79-81 of the manuscript, ‘To verify the effectiveness of the proposed method, the results were compared with those of two traditional signal-processing methods.’ In this section, the authors must mention the specific names of the signal-processing methods for the reader to understand them better.

 

4.       In lines 90-92 of the manuscript, ‘Each grid point was categorized as background, normal, or anomaly, and each category was assigned specific acoustic properties.’ In the manuscript, a description is needed for background, normal, or anomaly in this section, or the authors needs to cite Fig. 1.a here for better understanding.

 

5.      In lines 94-96 of the manuscript, ‘One of the receivers was placed at the same location as the transmitter, designated as CH0, and the receivers were numbered clockwise. The elements were arranged as uniformly as possible.’ In a scientific journal, the authors need to be specific during simulation. The arrangement of the receiving transducers needs to be specific. The authors mention that the elements are arranged as uniformly as possible, which decreases the reader's confidence in the article's acceptability.

 

6.      In lines 109-111 of the manuscript, ‘In this study, 768 simulations were conducted (6 radius positions from the center point × 64 movements of the anomaly × 2 types of anomaly radii).’ In this section, the design space of the training dataset is not specified. The six radius positions from the center point are not specified, and the two types of anomaly radii are also not specified in the manuscript.

 

7.      In Section 2.1 (Ultrasonic propagation simulation), the authors did not mention the boundary conditions of the simulation. The description of the boundary conditions of the simulation is required in the manuscript.

 

8.      Also, in Section 2.1, the authors did not provide the wave equation to understand the readers. I encourage the authors to introduce a section named “Mathematical Modeling” and mention the equations used for the wave simulation.

 

9.      In lines 156-157 of the manuscript, ‘A total of 64 profile datasets were collected for testing.’ According to the authors’s description, for the test objective, only one anomaly with a diameter of 30 mm at the center of the circle is created. Then, what is the importance of creating 64 profiles for a single anomaly?

 

10.  In Section 2.3, the authors discuss the Network design. The authors did not mention the reason behind selecting this specific model. Also, for the CNN architecture, the hyperparameter tuning is missing, which is essential for improving the prediction accuracy of the CNN framework.

 

11.  In line 210 of the manuscript, ‘The threshold method was the same as the one used to create the label data in Section 2.2.’ This statement implies that the training dataset for the CNN framework was generated using the threshold method. However, in the results section, it is mentioned that the performance of this model is lower than that of the CNN framework. Theoretically, the performance of the method used to generate the training data should not be lower than the CNN prediction accuracy, as the CNN is being trained to replicate the threshold method’s results. Can you please clarify how the CNN framework outperforms the method used to create its training labels?

 

 

Minor Issues:

 

1.      The details of ultrasonic propagation simulation are insufficient. Additional details and visual aids are needed to help readers better understand the simulation setup and data generation process.

 

2.      In lines 90-91 of the manuscript, “Each grid point was categorized as background, normal, or anomaly, and each category was assigned specific acoustic properties.” It should define what background, normal, or anomaly is here.

 

3.      In lines 135-136 of the manuscript, “The first peak that exceeded the set threshold was designated as the TOF. As shown in Figure 2(b), label data is created by assigning the value “1” at the position of the TOF and “0” elsewhere.” The label creation procedure is unclear in lines 136-137. Additional clarification is needed on what is done here.

 

4.      The presented article worked on simulated data. The simulated ultrasonic waveforms are not discussed in terms of how realistic they are compared to real-world data. Have any steps been taken to validate the simulation against experimental data?

 

 

 

Comments on the Quality of English Language

N/A

Author Response

Major Issue:

Comment 1: The article title is misleading. Although the title mentions TOF estimation, the results and discussion sections lack detailed information on TOF estimation. Instead, they focus more on the CT image and its performance score.

Response 1: Thank you for pointing this out. We decided to change the title of our paper to “Image reconstruction in ultrasonic speed-of-sound CT using time-of-flight estimated by a 2D convolutional neural networks.”

 

Comment 2: In lines 73-75 of the manuscript, ‘The waveforms measured by the speed-of-sound CT system contained sound speed data from hundreds of different paths, enabling the formation of profile data in a fan-beam manner.’ Ambiguously mentioned hundreds of different paths. The authors need to be more specific.

Response 2: Thank you for pointing this out. We have removed the ambiguous sentence from lines 73 to 75 of the original manuscript. We also changed lines 76-78 of the original manuscript to the following sentence. In line 74-76 of new manuscript, “Specifically, the ultrasonic waveform profile data were acquired through an ultrasonic propagation simulation in a 64-pass fan-beam configuration, and then several amplitudes of white noise were added.”

Comment 3: In lines 79-81 of the manuscript, ‘To verify the effectiveness of the proposed method, the results were compared with those of two traditional signal-processing methods.’ In this section, the authors must mention the specific names of the signal-processing methods for the reader to understand them better.

Response 3: Thank you for pointing this out. We have included the names of the signal-processing methods and references in lines 79-81 of the original manuscript. In line 77-80 of new manuscript, “To verify the effectiveness of the proposed method, the TOF was estimated using the traditional signal-processing methods, namely the “threshold method” and the “squared amplitude integral method”, and the results were compared [6, 8].”

Comment 4: In lines 90-92 of the manuscript, ‘Each grid point was categorized as background, normal, or anomaly, and each category was assigned specific acoustic properties.’ In the manuscript, a description is needed for background, normal, or anomaly in this section, or the authors needs to cite Fig. 1.a here for better understanding.

Response 4: Thank you for pointing this out. We have changed the sentence in lines 90-92 of our original manuscript to refer to Figure 1. We have also indicated the colors in Figure 1 in the text so that the reader can understand which section is represented. In line 108-110 of new manuscript, ”Figure 1(a) shows that each grid point was categorized as background (gray), normal (yellow), or anomaly (white), and each category was assigned specific acoustic properties.”

Comment 5: In lines 94-96 of the manuscript, ‘One of the receivers was placed at the same location as the transmitter, designated as CH0, and the receivers were numbered clockwise. The elements were arranged as uniformly as possible.’ In a scientific journal, the authors need to be specific during simulation. The arrangement of the receiving transducers needs to be specific. The authors mention that the elements are arranged as uniformly as possible, which decreases the reader's confidence in the article's acceptability.

Response 5: We agree with this comment. We have removed the ambiguous sentence in lines 94-96 of the original manuscript. We have added the physical installation requirements in the manuscript. In line 121-123 of new manuscript, “For the arrangement of the elements, we calculated the coordinates of the grid points so that the angle formed between two adjacent elements and the center of the normal section is 5.625 °, ensuring that all elements are evenly spaced.”

 

Comment 6: In lines 109-111 of the manuscript, ‘In this study, 768 simulations were conducted (6 radius positions from the center point × 64 movements of the anomaly × 2 types of anomaly radii).’ In this section, the design space of the training dataset is not specified. The six radius positions from the center point are not specified, and the two types of anomaly radii are also not specified in the manuscript.

Response 6: Thank you for pointing this out. We added in the manuscript anomaly radius and 6 radii from the center point of the normal section. We have moved the sentences in lines 98-102 of the original manuscript to lines 111-115 of the new manuscript. Additionally, Figure 1(b) has been changed. The sentence in lines 106-107 of the original manuscript has been changed to reflect the changes in Figure 1(b). In line 115-116 of new manuscript, “The size of the anomaly was set to a radius of 10 mm or 20 mm.” In line 125-127 of new manuscript, “As shown in Figure 1(b), the anomaly was placed at a distance of 20 mm, 30 mm, 40 mm, 50 mm, 60 mm, 70 mm from the center point of the normal section, with only one anomaly being installed.” In line 132-133 of new manuscript, “The initial position of the anomaly was near receiver CH48, and this position was set to zero.”

Comment 7: In Section 2.1 (Ultrasonic propagation simulation), the authors did not mention the boundary conditions of the simulation. The description of the boundary conditions of the simulation is required in the manuscript.

Response 7: Thank you for pointing this out. We have added our boundary conditions in the new manuscript. In line 137-140 of new manuscript, “The k-wave toolbox provides a perfectly matched layer (PML) as a setting item for boundary conditions. In this simulation, PML was used to set the boundary conditions [24-26]. The PML thickness was set to 20 grid points and the absorption coefficient was set to 2, effectively preventing wave reflections at the computational domain boundaries.”

 

Comment 8: Also, in Section 2.1, the authors did not provide the wave equation to understand the readers. I encourage the authors to introduce a section named “Mathematical Modeling” and mention the equations used for the wave simulation.

Response 8: Thank you for pointing this out. We have added a new section to the manuscript called Mathematical Modeling. In this section, we describe the equations used in ultrasonic propagation simulations. Please review lines 88-105 of the new manuscript.

 

Comment 9: In lines 156-157 of the manuscript, ‘A total of 64 profile datasets were collected for testing.’ According to the authors’s description, for the test objective, only one anomaly with a diameter of 30 mm at the center of the circle is created. Then, what is the importance of creating 64 profiles for a single anomaly?

Response 9: We apologize for the lack of explanation. When creating the test data, the anomaly is fixed, and the transmitter is moved 64 times to each position of the receivers CH0 to CH63. A simulation is conducted each time the transmitter is moved, resulting in the creation of 64 profile data sets. We created 64 profile data because we need 4096 passes (64 waveforms  64 profile data) to reconstruct a CT image. We have changed Figure 4 and its caption in the new manuscript. Additionally, the following sentence has been added to the new manuscript. In line 192-194 of new manuscript, “The ultrasonic propagation simulation was performed each time the transmitter was moved, with the anomaly fixed and the transmitter moved 64 times to each position of the receivers CH0 to CH63.”

Comment 10: In Section 2.3, the authors discuss the Network design. The authors did not mention the reason behind selecting this specific model. Also, for the CNN architecture, the hyperparameter tuning is missing, which is essential for improving the prediction accuracy of the CNN framework.

Response 10: Thank you for pointing this out. In this study, we selected the model with the highest image evaluation value for the CT images reconstructed using TOF estimated by a 2D CNNs. The accuracy of TOF estimation is proportional to the accuracy of the reconstructed CT images. Therefore, a high image evaluation value for the CT images indicates high TOF estimation accuracy. Additionally, we included the convergence curves of the loss function during the training of the proposed method in Section 3 (Figure 6). Figures 6(a) and 6(b) show that the training loss of the proposed method is convergent, suggesting that there is no problem in adjusting the hyperparameters. The following sentence was added with the addition of Figure 6. In addition, the sentence in lines 232-235 of the original manuscript was moved to lines 262-266 in the new manuscript. In line 262-266 of new manuscript, “Figure 6 shows the convergence curve of the loss function during CNNs training. The results of the proposed method are presented for two models trained with different types of training data: Proposed (Noise) and Proposed (Lowpass). Proposed (Noise) is a model trained using noise data, whereas Proposed (Lowpass) is a model trained using low-pass data.”

 

Comment 11: In line 210 of the manuscript, ‘The threshold method was the same as the one used to create the label data in Section 2.2.’ This statement implies that the training dataset for the CNN framework was generated using the threshold method. However, in the results section, it is mentioned that the performance of this model is lower than that of the CNN framework. Theoretically, the performance of the method used to generate the training data should not be lower than the CNN prediction accuracy, as the CNN is being trained to replicate the threshold method’s results. Can you please clarify how the CNN framework outperforms the method used to create its training labels?

Response 11: Thank you for pointing this out. Obtaining accurate TOF from ideal waveforms without noise is easily achievable using conventional threshold methods. Therefore, the label data is obtained using the threshold method from ideal waveforms without noise. After determining the correct TOF as label data, white noise is added to the waveforms, and supervised learning is performed using pairs of waveforms containing white noise and the previously created label data. Label data is not created from waveforms containing white noise using the threshold method.

 

Minor Issue:

Comment 1: The details of ultrasonic propagation simulation are insufficient. Additional details and visual aids are needed to help readers better understand the simulation setup and data generation process.

Response 1: Thank you for pointing this out. We have added a snapshot of the ultrasonic propagation simulation (Figure 2) in Section 2.2 of our new manuscript. We have also added our program for this simulation to the supplemental data. We have added a description of Figure 2 to lines 142-147 of our new manuscript. In line 142-147 of new manuscript, “Add a program for this simulation to the supplemental data. A snapshot of the visualization produced by this program is shown in Figure 2. Figure 2(a) shows the time variation of normal stress and Figure 2(b) shows the time variation of shear stress. Several small black dots arranged in a circular pattern represent receivers. One point with an x position of 0 and a y position near -100 is the transmitter. The colors in Figure 2 represent yellow for positive, white for zero, and blue for negative.”

 

Comment 2: In lines 90-91 of the manuscript, “Each grid point was categorized as background, normal, or anomaly, and each category was assigned specific acoustic properties.” It should define what background, normal, or anomaly is here.

Response 2: Thank you for pointing this out. The normal section assumes a wooden column and the anomaly section assumes a circular cavity. The background is also the section that is set up to prevent propagation outside of the sonic wooden column. We have added the following sentence to lines 116-118 of the new manuscript. In line 116-118 of new manuscript, “The background section was 100 times denser than air and served to prevent ultrasonic waves from propagating outside the normal section.”

 

Comment 3: In lines 135-136 of the manuscript, “The first peak that exceeded the set threshold was designated as the TOF. As shown in Figure 2(b), label data is created by assigning the value “1” at the position of the TOF and “0” elsewhere.” The label creation procedure is unclear in lines 136-137. Additional clarification is needed on what is done here.

Response 3: Thank you for pointing this out. We have made changes to Figure 2 in the original manuscript. Figure 3 in the new manuscript shows the changes. We have changed the sentence in lines 135-136 of the original manuscript to the following: In line 172-173 of new manuscript, “The sampling point when the absolute value of the waveform first becomes larger than the threshold value is TOF.”

 

Comment 4: The presented article worked on simulated data. The simulated ultrasonic waveforms are not discussed in terms of how realistic they are compared to real-world data. Have any steps been taken to validate the simulation against experimental data?

Response 4: Thank you for pointing this out. In this study, the parameters such as density and elasticity are set to values equivalent to those of wood, and a cavity is assumed for the anomaly. While actual wood is a heterogeneous material, this simulation measures it as a homogeneous material. The main objective of this paper is to estimate TOF using 2D CNNs with fan-beam profile data and evaluate the TOF estimation accuracy. Therefore, the realism of the simulation is not a primary concern. However, the noise levels used in this paper are equal to or larger than those found in real measurement data.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

See attached file with remarks and recommendations

Comments for author File: Comments.pdf

Author Response

Comment 1: UT-CT, applied for residual stress estimation were introduced by Hildebrand (Batelle PNL in the US) in literature in "1977". Hildebrands PhD. thesis was to this approach.

Response 1: Thank you for pointing this out. We would like to include this paper in our references. However, we regret to inform you that we were unable to find it. Could you please provide us with the title of the paper?

 

Comment 2: which was documented as the most accurate when combined with the analytical signal (envelope) technique

Response 2: Thank you for pointing this out. The cross-correlation method is a classical method and has recently been reported to be used in combination with other methods in some cases to improve the accuracy of TOF estimation. We have added the following sentence to the new manuscript. In line 52-53 of new manuscript, “Cross-correlation and envelope methods have been reported to be used in combination for more accurate TOF estimation [10].”

 

Comment 3: please justify this by real values obtained, may be in a table.

Response 3: Thank you for pointing this out. We have changed lines 82-85 of the new manuscript to the following sentence. “As a result, the maximum error value of TOF was  s for the signal processing method, while it was  s for the proposed method. In addition, the CT images reconstructed using the TOF estimated by the proposed method showed high evaluation values.”

 

Comment 4: Why these broken numbers with 3 positions after the comma? How accurate your positioning system must be?

Response 4: We apologize for the inconvenience. We have corrected our typos. The reason for the 5.625-degree angle is that it is the result of dividing 360 degrees by 64, in order to create 64 locations for anomalies. Based on this angle, we calculate the coordinates on the grid points. If there is no grid point at the calculated coordinates, the anomaly is placed on the nearest grid point to the calculated coordinates. In line 127-130 of new manuscript, “This angle was used to calculate the placement coordinates of the anomaly on the grid points. If there was no grid point at the calculated coordinates, the anomaly was placed on the nearest grid point to the calculated coordinates.”

 

Comment 5: please correct in fig. 1.(b) the mm indications by setting a blank between measurand and mm-unit.

Response 5: We apologize for the inconvenience. We have corrected our typos. Additionally, Figure 1(b) has been changed. The sentence in lines 106-107 of the original manuscript has been changed to reflect the changes in Figure 1(b). In line 132-123 of new manuscript, “The initial position of the anomaly was near receiver CH48, and this position was set to zero.”

 

Comment 6: please set a blank between 10 and %.

Response 6: We apologize for the inconvenience. We have corrected our typos.

 

Comment 7: do you think white noise is a proper model to simulate acoustic noise in a strong scattering medium like wood?

Response 7: Thank you for pointing this out. In ultrasonic speed-of-sound CT, it is necessary to measure the accurate TOF of longitudinal waves. However, in actual measurements, besides electrical noise, other types of acoustic waves and environmental noise can also mix in, burying the longitudinal waves in noise. It would be beneficial to simulate the formation of noise itself, but this paper stops short of introducing white noise.

 

Comment 8: please citations to give help to the non-experts.

Response 8: Thank you for pointing this out. We have added two new references related to deep learning. References are given in lines 213-216 of the new manuscript.
Additional References:

LeCun, Y.; Bengio, Y.; Hinton, G. Deep learning. Nature 2015, 521, 436-444, doi: 10.1038/nature14539.

Dumoulin, V.; Visin, F. A guide to convolution arithmetic for deep learning. arXiv 2018, doi: 10.48550/arXiv.1603.07285.

 

Comment 9: correct the dB-indications by inserting a blank.

Response 9: We apologize for the inconvenience. We have corrected our typos. Figure 7 in the new manuscript is the revised version.

Author Response File: Author Response.docx