Full-Wave Modeling and Inversion of UWB Radar Data for Wave Propagation in Cylindrical Objects

Round 1

Reviewer 1 Report

The authors present a full-wave model and an inverse scattering approach for reconstructing the properties of cylindrical objects from UWB radar data. The full-wave model combines the radar equation of Lambot et al. with cylindrical Green’s functions in far-field conditions, as previously done for planar layered media. In the proposed paper, this model is validated for cylindrical objects. The inversion strategy exploits a look up table (LUT) approach followed by local optimization and its performances are verified against experimental data collected in laboratory controlled conditions and regarding both metallic and plastic pipes. A numerical analysis is also performed to investigate the well-posedness of the inverse problem and the robustness of the inversion strategy.

Although the paper is technically steady, well organized and written clearly, there are some critical aspects that, if properly faced up, could greatly improve the understanding of the paper and its value. Due to that, I suggest a major revision.

Major comments

• Line 186: “In the full-wave inversion procedure, a LUT is built for looking up for a coarse solution to be set as the initial guess parameter vector ?0”. At this regard, the authors must explain:
  1) how the LUT is built and how it is used to define the initial guess;
  2) why the LUT provides a suitable initial guess or, in other words, how the reconstruction capabilities depend on the adopted initial guess;
  3) how ?0 has been chosen in the presented experimental validation.
• Table1, model 6. Is it correct? It is not clear if the conductivity value does not change or it varies in a range, e.g. from 1 to 100, with a certain step.
• The authors claim that models 5 and 6 are used to build the LUT but no more details are given and these models are not considered in the Results section, nor in paragraph “ 3.1 The effects of conductivity, radius, and relative permittivity on time domain GPR signals” nor in paragraph “3.2. Full-Wave Inversion Analysis”. The authors must clarify why these models are introduced and how they are used.
• Table 2 and Table 3: it is crucial to provide also the real/measured values of the relative permittivity and the error concerning the reconstruction of the permittivity value.
• In my opinion, the behavior of the cost function shown in Fig.7 can be presented better by adopting a different saturation for the color-scale. Specifically, I suggest to use the same maximum and minimum values of the color scale and to explain how these values are chosen.
• The analysis provided in Section 3.2.1 is interesting but I strongly recommend to improve its presentation by relating the behavior of the objective function with the degree of non-linearity of the problem.

Minor comments
Line 108: it should be ?1instead of ?0
Line 247: a reference went lost
Line 252: a reference went lost
Line 259: a reference went lost
Line 274: a reference went lost
Line 302: a reference went lost
Line 328: two references went lost

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

Manuscript ID remotesensing-1185462

 

Title:

Full-wave modeling and inversion of UWB radar data for wave propagation in cylindrical objects

 

Authors

Lan Gao , Chiara Dachena , Kaijun Wu , Alessandro Fedeli , Matteo Pastorino , Andrea Randazzo , Xiaoping Wu , Sébastien Lambot *

 

Comments

 

In this study, the radar equation is combined with cylindrical Green’s functions to fully model and invert ground-penetrating radar (GPR) data and using full-wave model modelling to invert the properties of cylindrical homogeneous objects.The authors implement laboratory measurements to demonstrated the accuracy of the forward modeling and reconstructions for far-field conditions. Full-waveform inversion(FWI) is a challengingdata fitting task and to overcome these difficulties the authors approach the problem applied the method to a homogeneous and geometrically simple body

 

The theoretical and numerical approach to the problem is done in a very complete, clear and clarifying way.

I have only a few comments and suggestions to the authors

 

Although conductivity has been introduced in modeling and laboratory experiment, this parameter is not explored in inversion. It must be made very clear in the introduction that this parameter is not explored in the inversion process. To do this, enter a sentense that will clarify it.

 

The numerical and experimental methodology is well explained and developed, however the topic related to the description of the inversion process is not made in a clear way. It should be explained more clearly how the space for posterior solutions is explored for models ?= [?, ?, ?],

 

The influence of data uncertainties on the final solution is not estimated. Please, introduce this estimate.

 

 

186 -187 - Please explain better the sentence “… Inversion is performed in the time domain in order to remove the reflections from other objects in the laboratory by defining a maximum time range”

 

352 – 353 – “Nevertheless, the inverse problem becomes more complicated when 352 electrical conductivity is also considered, due to correlations with the other parameters.” This corelation not explained / demonstrated in the text. Please clarify better this statement.

 

357 – 358 - “For small radius cylinders, we did not detect any local minimum in the objective function, but the global minimum is quite flat” and why “For the cylinders with an intermediate or larger radius, the global minimum is very well defined”. No explanation is given for this finding. Please try an explanation, or state that you cannot find it.

 

362 – 363 - “For the conductive cylindrical media, both the radius and the conductivity are highly correlated” This statement is not demonstrated.

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

It is a very interesting article and uses a simple and efficient laboratory set-up that can be easily implemented by the reader.

 

The mathematical background is clearly presented and shows the potential of this measurement strategy. It is also impressive how the measured and computed data match in far-field conditions, proving the mathematical background.

 

There are the following remarks:

 

• Figure 1. It’s missing a dot after “Figure 1”.
• equation (4): I could not follow the deduction of the reflection matrix. Is it possible to explain better how you came to equation (4)?
• Link error message on text: see lines 247, 252, 259, 274, 302 and 328;
• Conclusion: it is missing a comment about the possibility of a tree trunk inspection or concrete column testing with this approach and how far are your set-up and results from these applications.

 

I wonder if the mathematical background could also be applied or easily extended to a measurement set-up, where the radar:

• cannot transmit in the frequency band from  1 to 4 GHz but at L, S and C bands, where radars are allowed to operate;
• can suffer a specific translation, for example, a circular or other pattern, to compensate lack of the UWB operation.

Author Response

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Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

My concerns are resolved in the modified manuscript and it can be published to Remote Sensing.