Method for identifying and positioning GPR overlapping signals of multi-domain double-row reinforcing steel bars

Abstract

The invention is applied to the technical field of detection, and particularly discloses a method for identifying and positioning GPR overlapping signals of multi-domain double-row steel bars. The method comprises the following steps: S1, establishing a physical characteristic modeling inversion module based on double-row steel bar signals; s2, collecting signal data; s3, preprocessing the signal data; s4, performing feature analysis; s5, recording and correcting the signal; s6, carrying out B-scan image analysis processing; s7, steel bar positioning and distance calculation; s8, repeating the steps S3-S7 for each piece of scanned data; and S9, reconstructing missing data. According to the multi-domain double-row reinforcing steel bar GPR overlapping signal identification and positioning method, in the double-row reinforcing steel bar identification process in a complex environment, especially when signal attenuation is serious, interference clutter is strong or echo characteristics are not obvious, the double-row reinforcing steel bars of a tunnel lining can still be identified in a time-frequency analysis and cross-correlation reconstruction mode, and the identification and positioning accuracy of the GPR overlapping signals is improved. And the identification precision and the positioning reliability are improved.

Description

Technical Field

[0001] The present invention relates to the field of detection technology, and in particular to a method for identifying and locating overlapping signals of multi-domain double-row steel bars GPR. Background Art

[0002] Highly reflective materials such as rebar and metal pipes have strong reflection and blocking properties for electromagnetic waves, far greater than their transmission capabilities. Therefore, they have important application value in building structure safety assessment and underground facility detection. In two-dimensional ground-penetrating radar images, when there are double rows of rebar structures, the strong reflection signal generated by the front row of rebar often obscures or interferes with the hyperbolic features corresponding to the rear row of rebar, especially under low-frequency conditions. This superposition effect of the front and rear signals makes it difficult to effectively identify the second row of rebar.

[0003] Although the visualization of hyperbolic features can be improved to a certain extent by adjusting radar system parameters or optimizing data processing procedures, most current research still focuses on the identification of simple single-layer rebar structures. The identification of more complex double-layer reinforced linings still faces challenges such as severe signal aliasing and frequent multipath interference. These problems reduce the sensitivity of radar echo signals, thereby limiting the in-depth understanding and accurate judgment of the spatial characteristics of double-row rebar. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for identifying and locating overlapping signals of multi-domain double-row steel bars GPR, so as to solve the problems of severe signal aliasing and frequent interference faced by radar signals when facing double-row steel bars identification proposed in the above background technology.

[0005] To achieve the above objectives, the present invention provides the following technical solutions: a method for identifying and locating overlapping signals of double-row steel bars in multiple domains, S1. establishing a physical feature modeling and inversion module based on the double-row steel bar signals to assist in determining the fluctuation position and overlapping characteristics of the steel bar reflection waveform;

[0006] S2. Signal data acquisition: A survey line is laid out longitudinally along the tunnel lining surface, and several measuring points are set at regular intervals. The GPR equipment collects reflected signals and extracts A-scan signals at the corresponding locations.

[0007] S3. Signal data preprocessing; preprocessing the collected signal to improve the background stability of the reflected signal, the preprocessing includes removing DC offset, median filtering noise reduction and bandpass filtering to enhance the characteristic frequency band;

[0008] S4. Feature analysis: In the processed A-scan curve, the presence of double-layered reinforcement is identified, and the structural effect of the double-layer signal superposition is preliminarily recognized;

[0009] S5. Signal recording and correction: After identifying the characteristic waveform of the steel bar, the steel bar characteristic data is represented as two triplets and recorded and stored. For signals that do not detect obvious local negative peaks or abnormal spectral characteristics, initial identification and correction are performed;

[0010] S6. B-scan image analysis and processing: Analyze the A-scan data to generate a complete B-scan image, and then form a multi-domain characteristic map of the steel bar distribution along the entire measurement line;

[0011] S7. Rebar Positioning and Spacing Calculation: Based on the corrected data, the second row of rebar is accurately located using signal correlation analysis, and the spacing between the two rows is calculated using a distance formula.

[0012] S8. Repeat S3-S7 for each scanned data to obtain a set of corrected A-scan images with steel bar characteristic waveforms;

[0013] S9. Reconstruct missing data: Based on the data from the corrected A-scan image where the double-row rebar was not identified, reanalyze each point to determine the potential echo response location of the double-row rebar in the A-scan signal.

[0014] Preferably, the physical feature modeling and inversion module in S1 is used to identify the phase offset, amplitude change and spectral characteristics in the signal. The physical feature modeling and inversion module uses short-time Fourier transform (STFT) to extract the time-frequency characteristics of the aliased signal to distinguish the frequency energy distribution characteristics of reflectors at different depths. The physical feature modeling and inversion module uses a cross-correlation analysis method to evaluate the consistency and matching degree of signals between different passes, thereby assisting in judging the fluctuation position and overlapping characteristics of the steel bar reflection waveform.

[0015] By adopting the above technical solution, the physical feature modeling inversion module can assist in judging the steel bar reflection waveform.

[0016] Preferably, the characteristic analysis of the A-scan curve in S4 is identified along the travel time axis direction, and the process is as follows: locate the first negative peak, which corresponds to the reflection signal of the first row of steel bars; find the next significant negative peak and analyze its corresponding positive amplitude to determine whether it meets the characteristic mode of the reflection signal of the second row of steel bars; use the three types of parameter characteristics of amplitude enhancement, phase reversal and frequency energy change as the basis for judging the existence of double-layer steel bars, and preliminarily identify the structural effect of the superposition of double-layer signals.

[0017] By adopting the above technical solution, the presence of double-layer steel bars can be judged by analyzing the characteristics of the A-scan curve.

[0018] Preferably, in said S5, the steel bar characteristic waveform identified in S4 is used to record and store the steel bar characteristic data of the identified steel bar characteristic waveform, and the steel bar characteristic data is the single and double row steel bar characteristic waveforms finally identified.

[0019] By adopting the above technical solution, steel bar characteristic data can be generated using the identified steel bar characteristic waveform.

[0020] Preferably, in S6, the generation process of the complete B-scan image is as follows: comparing the reflection points of the two rows of steel bars, marking the hyperbola vertices of the first row and the second row of steel bars in the B-scan image, comparing the positions and shapes of different reflection points, distinguishing the two rows of steel bars, and using the interp1 function and cubic spline interpolation option in MATLAB to smoothly fill in the missing data caused by signal aliasing, thereby generating a complete B-scan image.

[0021] By adopting the above technical solution and using MATLAB to interpolate and fill the B-scan image, a complete B-scan image can be generated.

[0022] Preferably, in said S8, the corrected A-scan image generation process is as follows: for the A-scan image in which the characteristic waveform of the steel bar cannot be identified, the second reflection point of the steel bar-concrete interface marked in each figure is plotted to obtain a black discontinuous curve, and the area where each peak in the black curve is located can be considered to have a second row of steel bars, and the possible abnormal steel bar characteristic waveform is identified and corrected to obtain a corrected A-scan image.

[0023] By adopting the above technical solution, the abnormal steel bar characteristic waveform is identified and corrected on the A-scan image, and a corrected A-scan image can be obtained.

[0024] Compared with the prior art, the present invention has the following beneficial effects: the identification and positioning method of the multi-domain double-row steel bar GPR overlapping signal:

[0025] 1. During the double-row steel bar identification process in complex environments, especially when signal attenuation is severe, interference clutter is strong, or echo characteristics are unclear, the present invention can still identify double-row steel bars in tunnel linings through time-frequency analysis and cross-correlation reconstruction, thereby improving recognition accuracy and positioning reliability.

[0026] 2. Through the joint analysis of time domain, frequency domain and cross-correlation features, the present invention can effectively separate the superimposed signals of the first and second rows of steel bars and accurately locate the true position of the second row of steel bars in the B-scan image. Even if the scanning signal in some areas is blocked or the waveform is missing, it can still be accurately completed through waveform reconstruction and feature fitting, ensuring the complete identification of the distribution of the two rows of steel bars and that the spacing meets the structural design requirements, providing stable and reliable technical support for the quality assessment of tunnel linings. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a schematic diagram of the GPR process structure for identifying double-row steel bars in the present invention;

[0028] Figure 2 This is a schematic diagram of the structure of the ground penetrating radar detecting steel bars of the present invention;

[0029] Figure 3 This is the B-scan scanning diagram and A-scan waveform attenuation diagram of the double-row steel bars of the present invention;

[0030] Figure 4 B-scan images of the double-row steel bars before and after correction of the present invention;

[0031] Figure 5 This is the relative error diagram of the double-row steel bar identification sampling in the tunnel of the present invention. DETAILED DESCRIPTION

[0032] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0033] See also Figure 1-Figure 5 The present invention provides a technical solution: a method for identifying and locating overlapping signals of multi-domain double-row steel bars GPR.

[0034] S1. Establish a physical feature modeling and inversion module based on double-row steel bar signals to assist in determining the fluctuation position and overlapping characteristics of the steel bar reflection waveform; S2. Signal data acquisition: Layout the survey line longitudinally on the tunnel lining surface, set up several measuring points at fixed intervals, collect the reflection signal through the GPR device, and extract the A-scan signal at the corresponding position; S3. Signal data preprocessing: Preprocess the collected signal to improve the background stability of the reflection signal. The preprocessing includes removing DC offset, median filtering noise reduction, and bandpass filtering to enhance the characteristic frequency band; The physical feature modeling and inversion module in S1 is used to identify the phase offset, amplitude change and spectral characteristics in the signal. The physical feature modeling and inversion module uses short-time Fourier transform (STFT) to extract the time-frequency characteristics of the aliased signal and distinguish the frequency energy distribution characteristics of reflectors at different depths. The physical feature modeling and inversion module uses the cross-correlation analysis method to evaluate the consistency and matching degree of the signals between different passes, thereby assisting in determining the fluctuation position and overlapping characteristics of the steel bar reflection waveform;

[0035] like Figure 1 As shown in the figure, a measuring line is laid out along the predetermined interval on the tunnel lining surface, with a total of m measuring points. At the position of each measuring point, i.e. the i-th measuring point (i = 1, 2, ..., m), its specific horizontal position coordinate is x i , using ground penetrating radar (GPR) to detect at each measuring point, the collected .dzt file contains multiple reflection data, each data is an A-scan, extracting the A-scan signal at the corresponding position, and generating a scanning image reflecting the change of amplitude with two-way travel time. The i-th reflection wave records the amplitude and phase information of the reflection signal at that point. Among them, in ground penetrating radar detection, the amplitude, phase and frequency of the signal will change significantly due to the difference in electromagnetic properties of the medium. When the electromagnetic wave propagates from concrete to steel bars, due to the large difference in dielectric constants between the two, the Fresnel reflection coefficient is negative, resulting in The reflected wave undergoes phase reversal. At the same time, the first row of steel bars in the double-layer steel bar structure causes signal attenuation and aliasing, which weakens the amplitude of the reflected signal of the second row of steel bars. In terms of frequency, different frequency bands have different energy losses during the propagation process, which manifests as spectral distortion. Therefore, the amplitude attenuation, phase reversal and frequency change characteristics provide important signal criteria for double-layer steel bar identification. The median filter and DC offset removal operations are applied to each reflected wave data to improve the background stability of the reflected signal, ensure that the true amplitude and phase information of the reflected signal can be more accurately reflected, and provide a reliable foundation for subsequent feature extraction.

[0036] In S4, the characteristic analysis of the A-scan curve is identified along the travel time axis. The process is as follows: locate the first negative peak, which corresponds to the reflection signal of the first row of steel bars; find the next significant negative peak and analyze its corresponding positive amplitude to determine whether it meets the characteristic mode of the reflection signal of the second row of steel bars; use the three types of parameter characteristics of amplitude enhancement, phase reversal and frequency energy change as the basis for judging the existence of double-layer steel bars, and preliminarily identify the structural effect of the superposition of double-layer signals. In S5, the steel bar characteristic waveform identified in S4 is used to record and store the steel bar characteristic data. The steel bar characteristic data is the final identified single and double row steel bar characteristic waveform.

[0037] like Figure 2 、 Figure 3 and Figure 4 As shown in the figure, in the processed A-scan curve, key points are identified along the travel axis direction. First, the first negative peak is located, which corresponds to the reflection signal of the first row of steel bars. Then, the next significant negative peak is searched and its corresponding positive amplitude is analyzed to determine whether it meets the characteristic mode of the reflection signal of the second row of steel bars. When the electromagnetic wave enters the steel bar with a very high dielectric constant from the concrete with a low dielectric constant, the reflection coefficient is negative, which will cause the phase of the reflected wave to be reversed by 180°. In addition, since the high conductivity of the steel bar is much higher than that of the concrete, its absorption and reflection of the electromagnetic wave are more significant, further enhancing the echo amplitude. In terms of reflection amplitude, multiple reflections and structural interference effects lead to the superposition of signal energy, which makes the echo amplitude corresponding to the second row of steel bars in the double-layer structure significantly higher than the cross signal or background clutter. At the same time, time-frequency analysis shows that the signal in the double-layer structure is significantly higher than the cross signal or background clutter in the STF. The T-time spectrum shows the characteristics of obvious frequency expansion and wider energy distribution, which is more different from the stable frequency response of a single-layer structure. Therefore, the three types of parameter characteristics, amplitude enhancement, phase reversal and frequency energy change, together constitute the key criteria for judging the existence of double-layer steel bars. These physical characteristics can be used to preliminarily identify the structural effect of double-layer signal superposition. Once the steel bar characteristic waveform is identified, the relevant steel bar characteristic data needs to be recorded and stored. This data is represented as two triplets, which contain the following information: The single and double row steel bar characteristic waveforms finally identified can be judged by extracting their multi-domain features in the time domain and frequency domain. Among them, the two-way travel time t1, t2 represents the time delay of the radar wave in propagating to the target and reflecting back, reflecting the target's burial depth; the amplitude A represents the energy intensity of the signal, which is used to judge the difference in the electromagnetic characteristics of the reflecting target; the horizontal position coordinate x i ,y iCorresponding to the spatial distribution positions of the first and second rows of steel bars in the tunnel lining structure, respectively, combined with time-frequency domain analysis, STFT and other methods are used to observe the frequency changes of the signal within a local time window, supplementing the deficiencies of traditional time-domain recognition, thereby improving the accuracy of distinguishing the position and layer of steel bars. If no obvious local negative peak or spectral abnormality is detected in the i-th reflected wave, the signal can be regarded as lacking identifiable steel bar information. Such signals will be initially distinguished and corrected through a comprehensive comparison of their neighboring signals in the time domain, frequency domain and envelope information.

[0038] In S6, the complete B-scan image generation process is as follows: the reflection points of the two rows of steel bars are compared, and the hyperbola vertices of the first and second rows of steel bars are marked in the B-scan image. The positions and shapes of the different reflection points are compared to distinguish the two rows of steel bars. The interp1 function and the cubic spline interpolation option in MATLAB are used to smoothly fill in the missing data caused by signal aliasing, thereby generating a complete B-scan image;

[0039] When analyzing A-scan data, the reflection points of the double rows of steel bars are first compared, and the vertices of the hyperbola of the first and second rows of steel bars are marked in the B-scan image. By comparing the position and shape of different reflection points, the two rows of steel bars can be effectively distinguished. During the analysis process, within the time range of the reflection signal of the second row of steel bars, the hyperbola may be partially or completely missing due to signal aliasing. The spline interpolation method is used to process and fit the data in the radar signal. By using the interp1 function and the cubic spline interpolation option in MATLAB, the missing data caused by signal aliasing can be smoothly filled, thereby generating a complete B-scan image. Ultimately, this method can form a multi-domain feature map of the steel bar distribution along the entire measuring line, realizing stable identification and precise positioning of the double-row steel bar signals.

[0040] In S8, the corrected A-scan image generation process is as follows: for A-scan images in which the characteristic waveform of the steel bar cannot be identified, the second reflection point of the steel bar-concrete interface marked in each image is plotted to obtain a black discontinuous curve. The area where each peak of the black curve is located can be considered to have a second row of steel bars. The possible abnormal steel bar characteristic waveform is identified and corrected to obtain a corrected A-scan image. S9. Reconstruct the missing data; based on the partial data of the corrected A-scan image in which the double row of steel bars is not identified, re-analyze each point to determine the potential echo response position of the double-layer steel bar in the A-scan signal;

[0041] On the basis of the corrected data, the correlation analysis of the signal is further used to accurately determine the position of the second row of steel bars, and the effective value of the reflection signal of the second row of steel bars is screened. The abnormal data points that deviate from the main group are set to 30% within the tolerance range, that is, the average value of 10.5ns is used as the basis for calculation. The spacing between the double rows of steel bars is calculated by the distance formula, providing accurate data support for structural health detection, so as to better understand and analyze the steel bar layout and possible defects in the structure, and improve the overall structural safety and reliability. The above operation is repeated for each scanned data. In the m A-scan images, it is assumed that the Y A-scan images successfully identify the steel bar characteristic waveform, while the remaining mY A-scan images fail to identify the steel bar characteristic waveform. By drawing the steel bar-concrete intersection marked in each figure, the above operation is repeated. The second reflection point of the interface is obtained, and a black discontinuous curve is obtained. This curve can be considered as the steel bar-concrete interface. The area where each wave peak in the black curve is located can be considered to have a second row of steel bars. Due to the horizontal gap problem of the steel bars, the positive and negative amplitude change points are not found in one dimension, resulting in a hyperbola shape with missing vertices in the B-scan, which makes the curve discontinuous. Through this process, possible abnormal steel bar characteristic waveforms are identified and corrected, and the engineering report is used to roughly calculate the two-way travel time range of the two rows of steel bars to ensure the accuracy of the data. After the correction is completed, a set of corrected Y-channel A-scan images with steel bar characteristic waveforms are obtained. The identified and corrected data are used to infer and reconstruct the missing steel bar characteristic waveforms, so as to finally obtain a complete steel bar identification curve. Sampling is carried out at different sampling points in the Husa Tunnel in Yunnan Province. The results are as follows Figure 5 As shown in the figure, the relative error between the measured vertical spacing and the actual designed vertical spacing in the actual sampled data basically does not exceed 5%. This error range can ensure engineering accuracy while taking into account the feasibility and cost-effectiveness of actual operations.

[0042] Working Principle: S1. Establish a physical feature modeling and inversion module based on double-row steel bar signals to assist in determining the fluctuation position and overlapping characteristics of the steel bar reflection waveform;

[0043] S2. Signal data acquisition: A survey line is laid out longitudinally along the tunnel lining surface, and several measuring points are set at regular intervals. The GPR equipment collects reflected signals and extracts A-scan signals at the corresponding locations.

[0044] S3. Signal data preprocessing: Preprocess the collected signals to improve the background stability of the reflected signals. Preprocessing includes removing DC offset, performing median filtering for noise reduction, and performing bandpass filtering to enhance the characteristic frequency band.

[0045] S4. Feature analysis: In the processed A-scan curve, the presence of double-layered reinforcement is identified, and the structural effect of the double-layer signal superposition is preliminarily recognized;

[0046] S5. Signal recording and correction: After identifying the characteristic waveform of the steel bar, the steel bar characteristic data is represented as two triplets and recorded and stored. For signals that do not detect obvious local negative peaks or abnormal spectral characteristics, initial identification and correction are performed;

[0047] S6. B-scan image analysis and processing: Analyze the A-scan data to generate a complete B-scan image, and then form a multi-domain characteristic map of the steel bar distribution along the entire measurement line;

[0048] S7. Rebar Positioning and Spacing Calculation: Based on the corrected data, the second row of rebar is accurately located using signal correlation analysis, and the spacing between the two rows is calculated using a distance formula.

[0049] S8. Repeat S3-S7 for each scanned data to obtain a set of corrected A-scan images with steel bar characteristic waveforms;

[0050] S9. Reconstruct missing data: Based on the data from the corrected A-scan image where the double-row rebar was not identified, reanalyze each point to determine the potential echo response location of the double-row rebar in the A-scan signal.

[0051] While the embodiments of the present invention have been shown and described, it will be apparent to those skilled in the art that various changes, modifications, substitutions, and alterations can be made to the embodiments without departing from the principles and spirit of the invention.

Claims

1. A method for identifying and locating overlapping signals of multi-domain double-row steel bars GPR, characterized by: The following steps are included: S1. Establish a physical feature modeling and inversion module based on double-row rebar signals to assist in determining the fluctuation position and overlapping characteristics of the rebar reflection waveform; S2. Signal data acquisition: A survey line is laid out longitudinally along the tunnel lining surface, and several measuring points are set at regular intervals. The GPR equipment collects reflected signals and extracts A-scan signals at the corresponding locations. S3 signal data preprocessing; preprocessing the collected signal, the preprocessing includes removing DC offset, median filtering noise reduction and bandpass filtering to enhance the characteristic frequency band; S4. Feature analysis; In the processed A-scan curve, the presence of double-layer reinforcement is identified, and the structural effect of the superposition of double-layer signals is preliminarily recognized; S5. Signal recording and correction: After identifying the characteristic waveform of the steel bar, the steel bar characteristic data is represented as two triplets and recorded and stored. For signals that do not detect obvious local negative peaks or abnormal spectral characteristics, initial identification and correction are performed; S6. B-scan image analysis and processing: Analyze the A-scan data to generate a complete B-scan image, and then form a multi-domain characteristic map of the steel bar distribution along the entire measurement line; S7. Rebar Positioning and Spacing Calculation: Based on the corrected data, the second row of rebar is accurately located using signal correlation analysis, and the spacing between the two rows is calculated using a distance formula. S8. Repeat S3-S7 for each scanned data to obtain a set of corrected A-scan images with steel bar characteristic waveforms; S9. Reconstruct missing data: Based on the data of the corrected A-scan image where the double-row rebar is not identified, reanalyze each point to determine the potential echo response location of the double-layer rebar in the A-scan signal.

2. The method for identifying and locating overlapping signals of multi-domain double-row steel bars GPR according to claim 1, characterized in that: The physical feature modeling and inversion module in S1 is used to identify the phase offset, amplitude change and spectral characteristics in the signal. The physical feature modeling and inversion module uses short-time Fourier transform (STFT) to extract the time-frequency characteristics of the aliased signal and distinguish the frequency energy distribution characteristics of reflectors at different depths. The physical feature modeling and inversion module uses the cross-correlation analysis method to evaluate the consistency and matching degree of the signals between different passes, thereby assisting in determining the fluctuation position and overlapping characteristics of the steel bar reflection waveform.

3. The method for identifying and locating overlapping signals of multi-domain double-row steel bars GPR according to claim 1, characterized in that: The characteristic analysis of the A-scan curve in S4 is identified along the travel-time axis. The process is as follows: locating the first negative peak, which corresponds to the reflection signal of the first row of steel bars; finding the next significant negative peak and analyzing its corresponding positive amplitude to determine whether it meets the characteristic pattern of the reflection signal of the second row of steel bars; using three types of parameter characteristics, namely amplitude enhancement, phase reversal, and frequency energy change, as the basis for judging the presence of double-layer steel bars, the structural effect of the superposition of double-layer signals is preliminarily identified.

4. The method for identifying and locating overlapping signals of multi-domain double-row steel bars GPR according to claim 1, characterized in that: In said S5, the steel bar characteristic waveform identified in S4 is used to record and store the steel bar characteristic data of the identified steel bar characteristic waveform, and the steel bar characteristic data is the single and double row steel bar characteristic waveform finally identified.

5. The method for identifying and locating overlapping signals of multi-domain double-row steel bars GPR according to claim 1, characterized in that: In S6, the complete B-scan image is generated as follows: the reflection points of the two rows of steel bars are compared, and the hyperbola vertices of the first and second rows of steel bars are marked in the B-scan image, the positions and shapes of different reflection points are compared to distinguish the two rows of steel bars, and the interp1 function and cubic spline interpolation option in MATLAB are used to smoothly fill in the missing data caused by signal aliasing, thereby generating a complete B-scan image.

6. The method for identifying and locating overlapping signals of multi-domain double-row steel bars GPR according to claim 1, characterized in that: In S8, the corrected A-scan image generation process is as follows: for the A-scan images in which the characteristic waveform of the steel bar cannot be identified, the second reflection point of the steel bar-concrete interface marked in each figure is plotted to obtain a black discontinuous curve. The area where each peak of the black curve is located can be considered to have a second row of steel bars. The possible abnormal steel bar characteristic waveform is identified and corrected to obtain a corrected A-scan image.

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