# Superresolution Reconstruction Algorithm of Ultrasonic Logging Images Based on High-Frequency Enhancement

Authors: Ao Qiu; Yibing Shi; Xinyi Luo; Zhipeng Li; Wei Zhang
Journal: Journal of Sensors
 (2022)

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## Abstract

High-resolution logging images with glaring detail information are useful for analysing geological features in the field of ultrasonic logging. The resolution of logging images is, however, severely constrained by the complexity of the borehole and the frequency restriction of the ultrasonic transducer. In order to improve the image superresolution reconstruction algorithm, this paper proposes a type of ultrasonic logging based on high-frequency characteristics, with multiscale dilated convolution to feature as the basis of network-learning blocks, training in the fusion of different scale texture feature. The outcomes of other superresolution reconstruction algorithms are then compared to the outcomes of the two-, four-, and eightfold reconstruction. The proposed algorithm enhances subjective vision while also enhancing PSNR and SSIM evaluation indexes, according to a large number of experiments.


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## Body

## 1. Introduction

Diverse sensing technologies are being applied to environment sensing or source exploration with the advancement of material technology [1–3]. By providing a crucial insight logging map with fracture and hole information to reflect the well’s state, borehole imaging logging has grown to be a significant technology in the field of petroleum logging for oil exploration. The two primary logging techniques used in borehole imaging logging are circumference ultrasonic imaging and microresistivity scanning, with ultrasonic imaging being more widely used due to its high penetrability, high borehole coverage, and simple instrument structure. Figure 1 shows the principle of ultrasonic imaging logging. This instrument mainly uses ultrasonic transducer to send and receive ultrasonic signals in oil wells and adopts the principle of pulse reflection. Rotate the transducer while exciting the transducer to generate ultrasonic waves, so that it can rotate circumferentially downwards and emit scanning to the borehole wall; after the ultrasonic wave is transmitted, the reflected echo will be generated when it meets the borehole wall, and it will be returned to the transducer to be received. If the borehole diameter is different, the propagation time of ultrasonic wave in the borehole will be different, so the geometric image of the borehole wall can be inferred according to the propagation time of ultrasonic wave [4].Figure 1
The principle of ultrasonic image logging. It is clear that raw logging images have numerous elements of high frequency.However, because of the influence of the downhole environment and hardware constraints, it is possible that the actual logging images obtained have low contrast and the detail information of the images may not be obvious [5], which makes it challenging to interpret the existing logging images and calls for image enhancement. Superresolution reconstruction is one of the most widely used processes for image enhancement. This method’s objective is to generate a part with a certain degree of confidence while recovering a high-resolution image from a low-resolution part [6–8]. The research method is divided into interpolation-based reconstruction algorithms, such as the dual cubic interpolation method [9], which computes the weighted average of 16 known pixel points within the 4∗4 domain of the current pixel point. Many superresolution reconstruction techniques have been proposed in recent years [10, 11]. This interpolation method has a broad reconstruction effect but is simple to calculate. It also loses edge details. Li and Orchard proposed an edge-oriented natural image interpolation algorithm [12] to estimate the local covariance coefficients from low-resolution images and derive higher-resolution images based on the covariance coefficients. Zhang and Wu proposed an edge-guided nonlinear interpolation method based on directional filtering and data fusion to obtain the pixels to be interpolated by linear minimum mean square error estimation [13]. Edge blurring is effectively suppressed by G. Cheng and L. Cheng’s wavelet-based directional adaptive interpolation algorithm [14], which combines local directional adaptation with wavelet transform. Although the interpolation-based superresolution reconstruction method is simpler to compute, the image reconstruction effect is far from ideal because it lacks high-level image features [15]. More and more people are researching learning-based reconstruction algorithms because they can learn from a lot of image data and create a suitable network model to enhance the reconstruction effect. The SRCNN was proposed by Dong et al. [16] and uses dual triple interpolation to perform upsampling before using deep learning to reconstruct images using a three-layer neural network. When compared to the conventional interpolation method, the image reconstruction effect is significantly improved. The residual network [17] used as a reference in VDSR [18], which was developed by Kim et al., can prevent gradient disappearance and enhance network training stability in addition to deepening the network structure.Inverse convolution is used for upsampling, and a small convolution kernel is used in place of the large convolution kernel in FSRCNN [19], which enhances the SRCNN model. In order to preserve as much feature information as possible and enhance the reconstruction effect, Shi et al. proposed the ESPCN [20] method, which can perform feature extraction directly on low-resolution images and then upsample using subpixel convolution. Ledig et al.’s [21] proposed SRResNet and SRGAN, which introduced generative adversarial networks, to enhance the visual effect. The EBRN networks proposed by Qiu [22] suggest that the complexity of low-frequency and high-frequency information in images varies, and that low-frequency information is recovered with simple networks to avoid overfitting while high-frequency information is recovered with complex networks to avoid underfitting.The aforementioned algorithms also suffer from flaws like insufficient high-frequency feature reconstruction, ineffective feature correlation, and insufficient feature acquisition. However, unlike other optical images, raw logging images created by ultrasonic waves only have a single channel and contain a significant amount of high-frequency data, as shown in Figure1.In light of this, this paper suggests an ultrasonic logging image superresolution reconstruction algorithm based on high-frequency feature enhancement. The network is first fed with the low-resolution image, and after a predetermined number of layers, the multiscale dilated convolution block mapping high-level feature is applied. Upsampling and downsampling are then applied, and the low-resolution image and the resulting results are compared to derive the unlearned high-frequency information. The original results are kept while the high-frequency data is fed into a different multiscale dilated convolution block for strengthening training. The enhanced training of high-frequency information is then repeated several times after the results of the high-frequency information training are combined with the initial results. The proposed method can effectively improve the reconstruction effect in terms of both objective index and subjective vision when compared to the classical hypersegmentation models of SRCNN, VDSR, SRResNet, and SRGAN.The main innovations and contributions of this paper include the following: (1) proposing a multiscale dilated convolution block that uses dilated convolution to build convolution kernels of various sizes, fully acquiring the scale features of various perceptual fields of the image and fusing them to make the features more global.(2) In the high-level feature mapping, the high-frequency feature enhancement structure is designed to compare with the original image several times in order to find unlearned high-frequency features and improve learning. All math symbols existing in the paper are defined as in Table1.Table 1
Math symbols in the paper.
ILRLow-resolution imageIHROriginal high-resolution imageF0Feature extraction layer functionOUT0Output of the first layerFiFunction of multiscale dilated convolution block at stageiLRHF1Missing high-frequency information after the first stage trainingFTTransform of upsampling, downsampling, and converting to three-channel imagesFHFiFunction of multiscale dilated convolution residual block at stageiHFiHigh-level feature of high-frequency information at stageiOUTiHigh-level feature obtained at stageiKiConvolution kernel size after expansion,i∈1,3HFunction of upsampling and generating a three-channel imageouti−1Output of thei−1 layerFkiConvolutional layer function of the3∗3 convolution kernel with expansion rate i, i∈1,3F1∗1Convolutional layer function of the1∗1 convolution kerneloutoutOutput of feature fusionoutiOutput of thei multiscale dilated convolution residual blockBNBatch normalizationPReLUParametric rectified linear unit


## 2. Related Work

Deep learning (DL) has developed greatly with computers developing over the last decade, which has remarkably promoted the development of information technology in various fields [23–25]. Scientists reconstructed DL frameworks and proposed some revolutionary techniques such as convolutional neural network (CNN) [26], recurrent neural network (RNN) [23], or generative adversarial network (GAN) [27, 28]. During these techniques, dilated convolution and residual network are representatives that can improve performances of models in forward and backward phases when training.


### 2.1. Dilated Convolution

When the convolution kernel processes the data, the dilated convolution [29] layer adds a new “dilation” coefficient that establishes the value spacing. The same amount of computation will produce a 5∗5 receptive field with the same number of parameters as the 3∗3 convolution kernel if the normal convolution kernel is assumed to be 3∗3, 2 dilation rates, and the input. In the papers [30, 31] and others, dilated convolution was introduced to obtain a wider range of feature information and capture richer detailed features, all with predictable outcomes.


### 2.2. Residual Network

The problem of gradient disappearance and gradient explosion while training a deep network was addressed by He et al. in 2015 when they proposed a residual network that uses a skip connection to transfer information from the earlier convolutional layer directly to the later convolutional layer, allowing the original input to be transferred directly to the output. The residual network, which sped up network convergence and significantly reduced the issue of model overfitting for better deep-level network training, was introduced and improved in the papers [32–37].


## 2.1. Dilated Convolution

When the convolution kernel processes the data, the dilated convolution [29] layer adds a new “dilation” coefficient that establishes the value spacing. The same amount of computation will produce a 5∗5 receptive field with the same number of parameters as the 3∗3 convolution kernel if the normal convolution kernel is assumed to be 3∗3, 2 dilation rates, and the input. In the papers [30, 31] and others, dilated convolution was introduced to obtain a wider range of feature information and capture richer detailed features, all with predictable outcomes.


## 2.2. Residual Network

The problem of gradient disappearance and gradient explosion while training a deep network was addressed by He et al. in 2015 when they proposed a residual network that uses a skip connection to transfer information from the earlier convolutional layer directly to the later convolutional layer, allowing the original input to be transferred directly to the output. The residual network, which sped up network convergence and significantly reduced the issue of model overfitting for better deep-level network training, was introduced and improved in the papers [32–37].


## 3. Proposed Method

### 3.1. Network

In this paper, a multiscale dilated convolutional residual network with enhanced high-frequency features is proposed as shown in Figure2. Suppose the input image be the low-resolution image ILR after double-triple interpolation of the original high resolution IHR, and the low-level features are extracted by the shallow feature extraction layer of the low-resolution image reconstruction network, which is expressed by the following equation:
(1)OUT0=F0ILR,where F0 is the shallow feature extraction layer function and OUT0 represents the output of this layer. Then, input to four multiscale dilated convolution blocks for high-level feature extraction to get the result OUT1, upsampling and downsampling in turn. Then, compare the output low frequency information ILR and OUT1 to get high-frequency information LRHF1; input LRHF1 to four multiscale dilated convolution blocks separately for enhanced training to get HF1; continue to input OUT1 to four multiscale dilated convolution residual blocks to get high-level feature OUT2. These can be expressed by the following equation:
(2)OUT1=F1OUT0,LRHF1=ILR−FTOUT1,HF1=FHF1LRHF1,OUT2=F2OUT1+HF1,where Fi is the function of multiscale dilated convolution block at stage i, i∈1,4, LRHF1 is the missing high-frequency information after the first stage training, FT is the function that has been upsampled, downsampled, and converted to three-channel images, FHF1 is the function of multiscale dilated convolution residual block used for high-frequency information enhancement, HF1 is the high-level feature of high-frequency information, and OUTi is the high-level feature obtained at stage i. The specific structure of the multiscale dilated convolution block will be discussed in Section 3.2. The above process is repeated to obtain high-frequency information several times to enhance the reconstruction of logging images:
(3)HF2=FHF2ILR−FTF2OUT2,OUT3=F3OUT2+HF2,HF3=FHF3ILR−FTF3OUT3,OUT=OUT3+HF3=OUT2+HF2+HF3=OUT1+HF1+HF2+HF3.Figure 2
Our networks: the superresolution reconstruction algorithm based on high-frequency feature enhancement is based on multiscale dilated convolution blocks.OUT is upsampled by a subpixel convolutional layer to obtain a three-channel reconstructed image SRL, as shown in the following equation.
(4)SRL=HOUT,where H is a function of upsampling and generating a three-channel image.


### 3.2. Multiscale Dilated Convolution Blocks

Convolution kernels of various sizes can be used to obtain features of various scales, and the features obtained by combining these features are often superior to those obtained by a single scale [38–41]. The yellow arrow in Figure 2 shows the multiscale dilated convolution block (MRB) designed in this paper, which adopts a convolution kernel of size 3∗3 on which the dilated convolution with a dilation rate of 2 and a dilation rate of 3 is used to obtain receptive fields of 5∗5 and 7∗7 convolution kernel sizes, respectively, as shown in Figure 3, which is centered on the red number 3. And the grid occupied by 3 indicates the range of features extracted by the convolution kernel of size 3∗3 and the grid occupied by 5. The feature range extracted by 3∗3 convolutional kernel with expansion factor of 2 is represented by grid 3, and the feature range extracted by 3∗3 convolutional kernel with the expansion factor of 3 is represented by grid 7.Figure 3
Diagram of receptive field by multiscale dilated convolution block.The computation does not increase the computational effort because the expansion is done with 0 as shown in the following equation:(5)K1=k+k−1r−1=3,K2=k+k−1r−1=5,K3=k+k−1r−1=7,where k is the convolution kernel size, r is the expansion coefficient, and Ki is the convolution kernel size after expansion, i∈1,3.The output results of three different convolutional kernel sizes are summed and input again into these three convolutional kernels, and a1∗1 size convolutional kernel is used for feature fusion, and finally, the feature fusion and input results are summed to establish a residual structure that facilitates network convergence, as shown in the equation below:
(6)out11=Fk1outi−1,out12=Fk2outi−1,out13=Fk3outi−1,out=torch.catout11+out12+out13,out21=Fk1out,out22=Fk2out,out23=Fk3out,outout=PReluBNF1∗1out21,out22,out23,outi=outout+outi−1,where outi−1 is the output of the i−1 layer, Fki is the convolutional layer function of the 3∗3 convolution kernel with expansion rate i, i∈1,3, F1∗1 is the convolutional layer function of the 1∗1 convolution kernel, outout is the output of feature fusion, and outi is the output of the i multiscale dilated convolution residual block.


## 3.1. Network

In this paper, a multiscale dilated convolutional residual network with enhanced high-frequency features is proposed as shown in Figure2. Suppose the input image be the low-resolution image ILR after double-triple interpolation of the original high resolution IHR, and the low-level features are extracted by the shallow feature extraction layer of the low-resolution image reconstruction network, which is expressed by the following equation:
(1)OUT0=F0ILR,where F0 is the shallow feature extraction layer function and OUT0 represents the output of this layer. Then, input to four multiscale dilated convolution blocks for high-level feature extraction to get the result OUT1, upsampling and downsampling in turn. Then, compare the output low frequency information ILR and OUT1 to get high-frequency information LRHF1; input LRHF1 to four multiscale dilated convolution blocks separately for enhanced training to get HF1; continue to input OUT1 to four multiscale dilated convolution residual blocks to get high-level feature OUT2. These can be expressed by the following equation:
(2)OUT1=F1OUT0,LRHF1=ILR−FTOUT1,HF1=FHF1LRHF1,OUT2=F2OUT1+HF1,where Fi is the function of multiscale dilated convolution block at stage i, i∈1,4, LRHF1 is the missing high-frequency information after the first stage training, FT is the function that has been upsampled, downsampled, and converted to three-channel images, FHF1 is the function of multiscale dilated convolution residual block used for high-frequency information enhancement, HF1 is the high-level feature of high-frequency information, and OUTi is the high-level feature obtained at stage i. The specific structure of the multiscale dilated convolution block will be discussed in Section 3.2. The above process is repeated to obtain high-frequency information several times to enhance the reconstruction of logging images:
(3)HF2=FHF2ILR−FTF2OUT2,OUT3=F3OUT2+HF2,HF3=FHF3ILR−FTF3OUT3,OUT=OUT3+HF3=OUT2+HF2+HF3=OUT1+HF1+HF2+HF3.Figure 2
Our networks: the superresolution reconstruction algorithm based on high-frequency feature enhancement is based on multiscale dilated convolution blocks.OUT is upsampled by a subpixel convolutional layer to obtain a three-channel reconstructed image SRL, as shown in the following equation.
(4)SRL=HOUT,where H is a function of upsampling and generating a three-channel image.


## 3.2. Multiscale Dilated Convolution Blocks

Convolution kernels of various sizes can be used to obtain features of various scales, and the features obtained by combining these features are often superior to those obtained by a single scale [38–41]. The yellow arrow in Figure 2 shows the multiscale dilated convolution block (MRB) designed in this paper, which adopts a convolution kernel of size 3∗3 on which the dilated convolution with a dilation rate of 2 and a dilation rate of 3 is used to obtain receptive fields of 5∗5 and 7∗7 convolution kernel sizes, respectively, as shown in Figure 3, which is centered on the red number 3. And the grid occupied by 3 indicates the range of features extracted by the convolution kernel of size 3∗3 and the grid occupied by 5. The feature range extracted by 3∗3 convolutional kernel with expansion factor of 2 is represented by grid 3, and the feature range extracted by 3∗3 convolutional kernel with the expansion factor of 3 is represented by grid 7.Figure 3
Diagram of receptive field by multiscale dilated convolution block.The computation does not increase the computational effort because the expansion is done with 0 as shown in the following equation:(5)K1=k+k−1r−1=3,K2=k+k−1r−1=5,K3=k+k−1r−1=7,where k is the convolution kernel size, r is the expansion coefficient, and Ki is the convolution kernel size after expansion, i∈1,3.The output results of three different convolutional kernel sizes are summed and input again into these three convolutional kernels, and a1∗1 size convolutional kernel is used for feature fusion, and finally, the feature fusion and input results are summed to establish a residual structure that facilitates network convergence, as shown in the equation below:
(6)out11=Fk1outi−1,out12=Fk2outi−1,out13=Fk3outi−1,out=torch.catout11+out12+out13,out21=Fk1out,out22=Fk2out,out23=Fk3out,outout=PReluBNF1∗1out21,out22,out23,outi=outout+outi−1,where outi−1 is the output of the i−1 layer, Fki is the convolutional layer function of the 3∗3 convolution kernel with expansion rate i, i∈1,3, F1∗1 is the convolutional layer function of the 1∗1 convolution kernel, outout is the output of feature fusion, and outi is the output of the i multiscale dilated convolution residual block.


## 4. Experiments

### 4.1. Experiment Setups

As shown in Figure4, we created a unique imaging logging tool that consists of a downhole logging device and a ground control system. The computer and power supply that are part of the ground control system are intended to let ground engineers control the transmission and reception of ultrasonic signals as well as the creation of images of borehole walls. A downhole logging device is used to transmit bipolar pulses to drive the transducer while simultaneously gathering and processing ultrasonic signals reflected from strata at various depths. An armored cluster cable that connects the two pieces acts as a conduit for power and communication between the surface and the underground. The field-programmable gate array (FPGA) on the main control circuit board first receives the order during a signal processing cycle. It then sends a bipolar pulse to the drive circuit, which causes the piezoelectric ceramic to generate ultrasonic waves. The same piezoelectric ceramic will pick up the signals reflected off the borehole walls and transmit them to the main control circuit board using an analog-to-digital converter (ADC) with a 20 MHz sampling rate. All of the acquisition circuit’s hardware filters are present. The time of flight (ToF), amplitude, and other ancillary data of echo signals are then calculated using the preset algorithm using the same FPGA. These data are kept in a large-capacity NAND flash and sent to the ground control system by the downhole instrument bus of the enhancing logging image system (EDIB). Finally, using data from the main control circuit board, the ground system can visualize strata at various depths by creating borehole walls based on ToF and echo signal amplitudes that correspond to the various strata’s positions. The ground system’s host display software is in charge of combining logging images and interaction with instructions. In this paper, the training and test sets are sequentially derived from the circumference ultrasonic logging tool data acquired in the field in Zhanjiang. The echoes are gathered underground and transmitted to the surface control system via the EDIB bus. The surface computer receives the data via a USB port, extracts the echo’s amplitude and arrival time, and then synthesizes the final logging images, of which 1462 images are used as the training set and 589 images as the test set.Figure 4
Logging operation in Zhanjiang.The local hardware environment used for the experiments is a laptop with a 64-bit Windows 10-based operating system and an AMD Ryzen 5 3550H CPU. Computational acceleration was performed using Colaboratory, a cloud-based environment provided by Google, with 16G of video memory.The specific training process is as follows:(1)
Initialize the network parameters and set 64 images as a batch, and the learning rate is 0.0001(2)
InputIHR and four times downsampling using bitriple interpolation to obtain ILR(3)
InputILR to the network; after the first segment of the residual network composed of four multiscale dilated convolution blocks, get OUT1; the results of ILR and OUT1 are differenced by upsampling and downsampling in turn to get high-frequency information LRHF1; in order to strengthen the training of high-frequency information, LRHF1 is input to the residual network composed of four multiscale dilated convolution blocks. Obtain the high-level feature HF1 and sum up HF1 and OUT1 as the input of the second residual network(4)
Repeat step (3) to get the second stage resultOUT2 and enhanced high-frequency information HF2, respectively, and take them as the input of the third segment of the residual network; repeat step (3) again to get the third stage result OUT3 and enhanced high-frequency information HF3, then take them as the input of the fourth segment of the residual network to get the result OUT4.(5)
Upsample and reconstructOUT4 to get three-channel reconstructed image SRL.(6)
CalculateL1 loss function from SRL and the original high-resolution image IHR to obtain LLR and use the Adam optimization algorithm to update the parameters of the low-resolution image reconstruction network(7)
Based on the results ofLHR, the network is updated with parameters using the Adam optimization algorithm(8)
After 200 iterations, the trained network model is obtained, and the images of the test set are tested directly in the low-resolution image reconstruction networkIn this paper, we use peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), which are common evaluation metrics in the field of image hypersegmentation [42–44]; to compare the reconstruction effect, PSNR is used to describe the distortion caused by random noise on the reconstructed image as shown in the following equation.
(7)PSNR=10log102n−12MSE,where n is the number of bits per pixel, generally taken as 8, and MSE is the mean square error.SSIM is a comparison of two images in terms of contrast, structural features and brightness; the higher the PSNR the less distortion, and the higher the SSIM the closer the image is.(8)lX,Y=2μXμY+C1μX2+μY2+C1,cX,Y=2σXσY+C2σX2+σY2+C2,sX,Y=σXY+C3σXσY+C3,SSIMX,Y=lX,Y∙cX,Y∙sX,Y.Among them,μX and μY represent the mean values of image SR and image HR, respectively; σX and σY represent the standard deviation of image SR and HR, respectively; σX2 and σY2 represent the variance of image SR and HR, respectively. σXY represents the image SR and HR covariance and C1, C2, and C3 are constants.


### 4.2. Experiment Analysis

In order to verify the merits of the algorithm proposed in this paper, the structure of this paper is verified step by step.


#### 4.2.1. Ablation Study: Effect of Multiscale Dilated Convolution Blocks on the Results

The structures in Figure5 are compared in this subsection to show the efficacy of the proposed multiscale dilated convolution block for feature extraction in this paper, where the latter three structures are used for multiscale feature extraction. Figure 5(a) depicts the SRResNet base block, Figure 5(b) depicts the modified structure modeled after the inception V1 base block, Figure 5(c) depicts the dilated convolution base block, and Figure 5(d) depicts the multiscale dilated convolution block proposed in this paper. The results of doing 2 times, 4 times, and 8 times of reconstruction are shown in Table 2, with the number of all five base blocks in Figures 5(a)–5(d) being 16 and the rest of the modules and parameter settings being identical.Figure 5
Multiscale feature extraction structure: (a) is the single-scale SRResNet base block, (b) the modified structure of inception V1 base block for multiscale structure, (c) is the multiscale structure proposed in paper [18], and (d) is the multiscale structure proposed in this paper.
(a)(b)(c)(d)Table 2
The reconstruction effect of multiscale dilated convolution block.
MagnificationMetrics(a)(b)(c)(d)×2PSNR36.46235.98035.83036.496SSIM0.9630.9590.9560.961Parameters1401 k4672 k1981 k7505 k×4PSNR30.99030.89530.71631.126SSIM0.8580.8570.8570.860Parameters1542 k4812 k2131 k7653 k×8PSNR/dB27.32527.17226.76727.355SSIM0.7140.7160.7000.718Parameters1691 k7262 k2283 k9713 kFrom the above results, we can see that in the 2 times, 4 times, and 8 times magnification, the single-scale feature acquisition structure in Figure5(a) is significantly worse than the remaining three multiscale feature acquisition structures, whereas the proposed Figure 5(d) structure in this paper has the best metrics, with about 0.136 improvement in PSNR and 0.002 improvement in SSIM when compared to the single-scale under 4 times of reconstruction.The feature maps Figure6(a) of the residual block through SRResNet and the feature maps Figure 6(b) of the multiscale dilated convolution block are compared in Figure 6 to better understand the proposed multiscale dilated convolution block in this paper. Figures 6(d), 6(f), and 6(h) are feature maps of the multiscale dilated convolution block through the scale dilated convolution block of the 4th, 42nd, and 58th channels, respectively, and Figures 6(c), 6(e), and 6(g) are feature maps of the 4th, 42nd, and 58th channels through the residual block of SRResNet, respectively. The proposed structure in this paper obtains more comprehensive features and clearer textures, as can be seen.Figure 6
Feature map comparison: (a) is the 64-channel feature map extracted from the 16th residual block of SRResNet; (c), (e), and (g) are the amplification display of the feature map of the 4th, 42nd, and 58th channels, respectively; (b) is the 64-channel feature map extracted from the 16th block of the multiscale cavity convolution block proposed in this paper; and (d), (f), and (h) are the enlarged display of the feature map of the 4th, 42nd, and 58th channels, respectively.
(a)(b)(c)(d)(e)(f)(g)(h)


#### 4.2.2. Impact of High-Frequency Feature Enhancement

Table3 shows the comparative effects of objective metrics after reconstruction of SRResNet (a in the table), SRResNet-based primary high-frequency feature-enhanced structure (b in the table), and SRResNet-based four high-frequency feature-enhanced structure (c in the table) with the effect of ×2 and ×4 magnification. a, b, and c structures in Table 3 have the same residual block structure and number, and the remaining parameter settings are exactly the same.Table 3
The reconstruction effect of Parallel structure.
MagnificationSpecificationabc×2PSNR36.46236.69236.800SSIM0.9630.9620.962Parameters140174923288703188406×4PSNR30.99030.68231.247SSIM0.8580.8490.859Parameters154946228209044369082We can obtain the unlearned high-frequency detail information by comparing the reconstruction effect of the mapped high-level features with the original low-resolution image using the above experiments, and it is effective to do strengthening learning of this high-frequency detail information alone and repeat this process several times. Under fourfold reconstruction, the PSNR improves by 0.257 and the SSIM improves by about 0.001.The feature maps of low-resolution images with direct feature learning Figure7(a) and enhanced high-frequency feature training Figure 7(b) are compared in Figure 7, where Figures 7(c), 7(e), and 7(g) are the feature maps of the 4th, 42nd, and 55th channels through SRResNet residual blocks, respectively, and Figures 7(d), 7(f), and 7(h) are the feature maps of the 4th, 42nd, and 55th channels after high-frequency feature enhancement proposed in this paper.Figure 7
Feature map comparison: (a) is the 64-channel feature map extracted from the 16th residual block of SRResNet; (c), (e), and (g) are the amplification display of the feature map of the 4th, 42nd, and 55th channels, respectively; (b) is the 64-channel feature map extracted from the 16th block of the multiscale cavity convolution block proposed in this paper; and (d), (f), and (h) are the enlarged display of the feature map of the 4th, 42nd, and 55th channels, respectively.
(a)(b)(c)(d)(e)(f)(g)(h)


#### 4.2.3. Comparison of the Method in This Paper with Others

The multiple average PSNR and average SSIM values of this algorithm and other hypersegmentation algorithms in the test set for single image reconstruction tests are shown in Figure8 and Table 4.Figure 8
The reconstruction effect of single log image.Table 4
The reconstruction effect of our method and others.
MagnificationSpecificationSRCNNVDSRSRResNetOurs×2PSNR35.23336.39836.46237.981SSIM0.9350.9510.9630.973Parameters8129664707140174915188965×4PSNR29.83330.83130.99031.425SSIM0.8640.8300.8580.867Parameters8129664707154946215336678The PSNR and SSIM metrics, as well as the number of model parameters, are compared in Table4 between this method and other classical hypersegmentation methods. On a single log image, Figure 8 shows the reconstruction results as well as a comparison of PSNR and SSIM metrics between this method and other classical hypersegmentation methods. The method has significantly improved the metrics when compared to traditional methods and other classical deep learning methods, with PSNR of more than 0.435 and SSIM of more than 0.009, and the subjective visual effect has also been improved, with clearer and more accurate edges, as shown in the figure.


## 4.1. Experiment Setups

As shown in Figure4, we created a unique imaging logging tool that consists of a downhole logging device and a ground control system. The computer and power supply that are part of the ground control system are intended to let ground engineers control the transmission and reception of ultrasonic signals as well as the creation of images of borehole walls. A downhole logging device is used to transmit bipolar pulses to drive the transducer while simultaneously gathering and processing ultrasonic signals reflected from strata at various depths. An armored cluster cable that connects the two pieces acts as a conduit for power and communication between the surface and the underground. The field-programmable gate array (FPGA) on the main control circuit board first receives the order during a signal processing cycle. It then sends a bipolar pulse to the drive circuit, which causes the piezoelectric ceramic to generate ultrasonic waves. The same piezoelectric ceramic will pick up the signals reflected off the borehole walls and transmit them to the main control circuit board using an analog-to-digital converter (ADC) with a 20 MHz sampling rate. All of the acquisition circuit’s hardware filters are present. The time of flight (ToF), amplitude, and other ancillary data of echo signals are then calculated using the preset algorithm using the same FPGA. These data are kept in a large-capacity NAND flash and sent to the ground control system by the downhole instrument bus of the enhancing logging image system (EDIB). Finally, using data from the main control circuit board, the ground system can visualize strata at various depths by creating borehole walls based on ToF and echo signal amplitudes that correspond to the various strata’s positions. The ground system’s host display software is in charge of combining logging images and interaction with instructions. In this paper, the training and test sets are sequentially derived from the circumference ultrasonic logging tool data acquired in the field in Zhanjiang. The echoes are gathered underground and transmitted to the surface control system via the EDIB bus. The surface computer receives the data via a USB port, extracts the echo’s amplitude and arrival time, and then synthesizes the final logging images, of which 1462 images are used as the training set and 589 images as the test set.Figure 4
Logging operation in Zhanjiang.The local hardware environment used for the experiments is a laptop with a 64-bit Windows 10-based operating system and an AMD Ryzen 5 3550H CPU. Computational acceleration was performed using Colaboratory, a cloud-based environment provided by Google, with 16G of video memory.The specific training process is as follows:(1)
Initialize the network parameters and set 64 images as a batch, and the learning rate is 0.0001(2)
InputIHR and four times downsampling using bitriple interpolation to obtain ILR(3)
InputILR to the network; after the first segment of the residual network composed of four multiscale dilated convolution blocks, get OUT1; the results of ILR and OUT1 are differenced by upsampling and downsampling in turn to get high-frequency information LRHF1; in order to strengthen the training of high-frequency information, LRHF1 is input to the residual network composed of four multiscale dilated convolution blocks. Obtain the high-level feature HF1 and sum up HF1 and OUT1 as the input of the second residual network(4)
Repeat step (3) to get the second stage resultOUT2 and enhanced high-frequency information HF2, respectively, and take them as the input of the third segment of the residual network; repeat step (3) again to get the third stage result OUT3 and enhanced high-frequency information HF3, then take them as the input of the fourth segment of the residual network to get the result OUT4.(5)
Upsample and reconstructOUT4 to get three-channel reconstructed image SRL.(6)
CalculateL1 loss function from SRL and the original high-resolution image IHR to obtain LLR and use the Adam optimization algorithm to update the parameters of the low-resolution image reconstruction network(7)
Based on the results ofLHR, the network is updated with parameters using the Adam optimization algorithm(8)
After 200 iterations, the trained network model is obtained, and the images of the test set are tested directly in the low-resolution image reconstruction networkIn this paper, we use peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), which are common evaluation metrics in the field of image hypersegmentation [42–44]; to compare the reconstruction effect, PSNR is used to describe the distortion caused by random noise on the reconstructed image as shown in the following equation.
(7)PSNR=10log102n−12MSE,where n is the number of bits per pixel, generally taken as 8, and MSE is the mean square error.SSIM is a comparison of two images in terms of contrast, structural features and brightness; the higher the PSNR the less distortion, and the higher the SSIM the closer the image is.(8)lX,Y=2μXμY+C1μX2+μY2+C1,cX,Y=2σXσY+C2σX2+σY2+C2,sX,Y=σXY+C3σXσY+C3,SSIMX,Y=lX,Y∙cX,Y∙sX,Y.Among them,μX and μY represent the mean values of image SR and image HR, respectively; σX and σY represent the standard deviation of image SR and HR, respectively; σX2 and σY2 represent the variance of image SR and HR, respectively. σXY represents the image SR and HR covariance and C1, C2, and C3 are constants.


## 4.2. Experiment Analysis

In order to verify the merits of the algorithm proposed in this paper, the structure of this paper is verified step by step.


### 4.2.1. Ablation Study: Effect of Multiscale Dilated Convolution Blocks on the Results

The structures in Figure5 are compared in this subsection to show the efficacy of the proposed multiscale dilated convolution block for feature extraction in this paper, where the latter three structures are used for multiscale feature extraction. Figure 5(a) depicts the SRResNet base block, Figure 5(b) depicts the modified structure modeled after the inception V1 base block, Figure 5(c) depicts the dilated convolution base block, and Figure 5(d) depicts the multiscale dilated convolution block proposed in this paper. The results of doing 2 times, 4 times, and 8 times of reconstruction are shown in Table 2, with the number of all five base blocks in Figures 5(a)–5(d) being 16 and the rest of the modules and parameter settings being identical.Figure 5
Multiscale feature extraction structure: (a) is the single-scale SRResNet base block, (b) the modified structure of inception V1 base block for multiscale structure, (c) is the multiscale structure proposed in paper [18], and (d) is the multiscale structure proposed in this paper.
(a)(b)(c)(d)Table 2
The reconstruction effect of multiscale dilated convolution block.
MagnificationMetrics(a)(b)(c)(d)×2PSNR36.46235.98035.83036.496SSIM0.9630.9590.9560.961Parameters1401 k4672 k1981 k7505 k×4PSNR30.99030.89530.71631.126SSIM0.8580.8570.8570.860Parameters1542 k4812 k2131 k7653 k×8PSNR/dB27.32527.17226.76727.355SSIM0.7140.7160.7000.718Parameters1691 k7262 k2283 k9713 kFrom the above results, we can see that in the 2 times, 4 times, and 8 times magnification, the single-scale feature acquisition structure in Figure5(a) is significantly worse than the remaining three multiscale feature acquisition structures, whereas the proposed Figure 5(d) structure in this paper has the best metrics, with about 0.136 improvement in PSNR and 0.002 improvement in SSIM when compared to the single-scale under 4 times of reconstruction.The feature maps Figure6(a) of the residual block through SRResNet and the feature maps Figure 6(b) of the multiscale dilated convolution block are compared in Figure 6 to better understand the proposed multiscale dilated convolution block in this paper. Figures 6(d), 6(f), and 6(h) are feature maps of the multiscale dilated convolution block through the scale dilated convolution block of the 4th, 42nd, and 58th channels, respectively, and Figures 6(c), 6(e), and 6(g) are feature maps of the 4th, 42nd, and 58th channels through the residual block of SRResNet, respectively. The proposed structure in this paper obtains more comprehensive features and clearer textures, as can be seen.Figure 6
Feature map comparison: (a) is the 64-channel feature map extracted from the 16th residual block of SRResNet; (c), (e), and (g) are the amplification display of the feature map of the 4th, 42nd, and 58th channels, respectively; (b) is the 64-channel feature map extracted from the 16th block of the multiscale cavity convolution block proposed in this paper; and (d), (f), and (h) are the enlarged display of the feature map of the 4th, 42nd, and 58th channels, respectively.
(a)(b)(c)(d)(e)(f)(g)(h)


### 4.2.2. Impact of High-Frequency Feature Enhancement

Table3 shows the comparative effects of objective metrics after reconstruction of SRResNet (a in the table), SRResNet-based primary high-frequency feature-enhanced structure (b in the table), and SRResNet-based four high-frequency feature-enhanced structure (c in the table) with the effect of ×2 and ×4 magnification. a, b, and c structures in Table 3 have the same residual block structure and number, and the remaining parameter settings are exactly the same.Table 3
The reconstruction effect of Parallel structure.
MagnificationSpecificationabc×2PSNR36.46236.69236.800SSIM0.9630.9620.962Parameters140174923288703188406×4PSNR30.99030.68231.247SSIM0.8580.8490.859Parameters154946228209044369082We can obtain the unlearned high-frequency detail information by comparing the reconstruction effect of the mapped high-level features with the original low-resolution image using the above experiments, and it is effective to do strengthening learning of this high-frequency detail information alone and repeat this process several times. Under fourfold reconstruction, the PSNR improves by 0.257 and the SSIM improves by about 0.001.The feature maps of low-resolution images with direct feature learning Figure7(a) and enhanced high-frequency feature training Figure 7(b) are compared in Figure 7, where Figures 7(c), 7(e), and 7(g) are the feature maps of the 4th, 42nd, and 55th channels through SRResNet residual blocks, respectively, and Figures 7(d), 7(f), and 7(h) are the feature maps of the 4th, 42nd, and 55th channels after high-frequency feature enhancement proposed in this paper.Figure 7
Feature map comparison: (a) is the 64-channel feature map extracted from the 16th residual block of SRResNet; (c), (e), and (g) are the amplification display of the feature map of the 4th, 42nd, and 55th channels, respectively; (b) is the 64-channel feature map extracted from the 16th block of the multiscale cavity convolution block proposed in this paper; and (d), (f), and (h) are the enlarged display of the feature map of the 4th, 42nd, and 55th channels, respectively.
(a)(b)(c)(d)(e)(f)(g)(h)


### 4.2.3. Comparison of the Method in This Paper with Others

The multiple average PSNR and average SSIM values of this algorithm and other hypersegmentation algorithms in the test set for single image reconstruction tests are shown in Figure8 and Table 4.Figure 8
The reconstruction effect of single log image.Table 4
The reconstruction effect of our method and others.
MagnificationSpecificationSRCNNVDSRSRResNetOurs×2PSNR35.23336.39836.46237.981SSIM0.9350.9510.9630.973Parameters8129664707140174915188965×4PSNR29.83330.83130.99031.425SSIM0.8640.8300.8580.867Parameters8129664707154946215336678The PSNR and SSIM metrics, as well as the number of model parameters, are compared in Table4 between this method and other classical hypersegmentation methods. On a single log image, Figure 8 shows the reconstruction results as well as a comparison of PSNR and SSIM metrics between this method and other classical hypersegmentation methods. The method has significantly improved the metrics when compared to traditional methods and other classical deep learning methods, with PSNR of more than 0.435 and SSIM of more than 0.009, and the subjective visual effect has also been improved, with clearer and more accurate edges, as shown in the figure.


## 4.2.1. Ablation Study: Effect of Multiscale Dilated Convolution Blocks on the Results

The structures in Figure5 are compared in this subsection to show the efficacy of the proposed multiscale dilated convolution block for feature extraction in this paper, where the latter three structures are used for multiscale feature extraction. Figure 5(a) depicts the SRResNet base block, Figure 5(b) depicts the modified structure modeled after the inception V1 base block, Figure 5(c) depicts the dilated convolution base block, and Figure 5(d) depicts the multiscale dilated convolution block proposed in this paper. The results of doing 2 times, 4 times, and 8 times of reconstruction are shown in Table 2, with the number of all five base blocks in Figures 5(a)–5(d) being 16 and the rest of the modules and parameter settings being identical.Figure 5
Multiscale feature extraction structure: (a) is the single-scale SRResNet base block, (b) the modified structure of inception V1 base block for multiscale structure, (c) is the multiscale structure proposed in paper [18], and (d) is the multiscale structure proposed in this paper.
(a)(b)(c)(d)Table 2
The reconstruction effect of multiscale dilated convolution block.
MagnificationMetrics(a)(b)(c)(d)×2PSNR36.46235.98035.83036.496SSIM0.9630.9590.9560.961Parameters1401 k4672 k1981 k7505 k×4PSNR30.99030.89530.71631.126SSIM0.8580.8570.8570.860Parameters1542 k4812 k2131 k7653 k×8PSNR/dB27.32527.17226.76727.355SSIM0.7140.7160.7000.718Parameters1691 k7262 k2283 k9713 kFrom the above results, we can see that in the 2 times, 4 times, and 8 times magnification, the single-scale feature acquisition structure in Figure5(a) is significantly worse than the remaining three multiscale feature acquisition structures, whereas the proposed Figure 5(d) structure in this paper has the best metrics, with about 0.136 improvement in PSNR and 0.002 improvement in SSIM when compared to the single-scale under 4 times of reconstruction.The feature maps Figure6(a) of the residual block through SRResNet and the feature maps Figure 6(b) of the multiscale dilated convolution block are compared in Figure 6 to better understand the proposed multiscale dilated convolution block in this paper. Figures 6(d), 6(f), and 6(h) are feature maps of the multiscale dilated convolution block through the scale dilated convolution block of the 4th, 42nd, and 58th channels, respectively, and Figures 6(c), 6(e), and 6(g) are feature maps of the 4th, 42nd, and 58th channels through the residual block of SRResNet, respectively. The proposed structure in this paper obtains more comprehensive features and clearer textures, as can be seen.Figure 6
Feature map comparison: (a) is the 64-channel feature map extracted from the 16th residual block of SRResNet; (c), (e), and (g) are the amplification display of the feature map of the 4th, 42nd, and 58th channels, respectively; (b) is the 64-channel feature map extracted from the 16th block of the multiscale cavity convolution block proposed in this paper; and (d), (f), and (h) are the enlarged display of the feature map of the 4th, 42nd, and 58th channels, respectively.
(a)(b)(c)(d)(e)(f)(g)(h)


## 4.2.2. Impact of High-Frequency Feature Enhancement

Table3 shows the comparative effects of objective metrics after reconstruction of SRResNet (a in the table), SRResNet-based primary high-frequency feature-enhanced structure (b in the table), and SRResNet-based four high-frequency feature-enhanced structure (c in the table) with the effect of ×2 and ×4 magnification. a, b, and c structures in Table 3 have the same residual block structure and number, and the remaining parameter settings are exactly the same.Table 3
The reconstruction effect of Parallel structure.
MagnificationSpecificationabc×2PSNR36.46236.69236.800SSIM0.9630.9620.962Parameters140174923288703188406×4PSNR30.99030.68231.247SSIM0.8580.8490.859Parameters154946228209044369082We can obtain the unlearned high-frequency detail information by comparing the reconstruction effect of the mapped high-level features with the original low-resolution image using the above experiments, and it is effective to do strengthening learning of this high-frequency detail information alone and repeat this process several times. Under fourfold reconstruction, the PSNR improves by 0.257 and the SSIM improves by about 0.001.The feature maps of low-resolution images with direct feature learning Figure7(a) and enhanced high-frequency feature training Figure 7(b) are compared in Figure 7, where Figures 7(c), 7(e), and 7(g) are the feature maps of the 4th, 42nd, and 55th channels through SRResNet residual blocks, respectively, and Figures 7(d), 7(f), and 7(h) are the feature maps of the 4th, 42nd, and 55th channels after high-frequency feature enhancement proposed in this paper.Figure 7
Feature map comparison: (a) is the 64-channel feature map extracted from the 16th residual block of SRResNet; (c), (e), and (g) are the amplification display of the feature map of the 4th, 42nd, and 55th channels, respectively; (b) is the 64-channel feature map extracted from the 16th block of the multiscale cavity convolution block proposed in this paper; and (d), (f), and (h) are the enlarged display of the feature map of the 4th, 42nd, and 55th channels, respectively.
(a)(b)(c)(d)(e)(f)(g)(h)


## 4.2.3. Comparison of the Method in This Paper with Others

The multiple average PSNR and average SSIM values of this algorithm and other hypersegmentation algorithms in the test set for single image reconstruction tests are shown in Figure8 and Table 4.Figure 8
The reconstruction effect of single log image.Table 4
The reconstruction effect of our method and others.
MagnificationSpecificationSRCNNVDSRSRResNetOurs×2PSNR35.23336.39836.46237.981SSIM0.9350.9510.9630.973Parameters8129664707140174915188965×4PSNR29.83330.83130.99031.425SSIM0.8640.8300.8580.867Parameters8129664707154946215336678The PSNR and SSIM metrics, as well as the number of model parameters, are compared in Table4 between this method and other classical hypersegmentation methods. On a single log image, Figure 8 shows the reconstruction results as well as a comparison of PSNR and SSIM metrics between this method and other classical hypersegmentation methods. The method has significantly improved the metrics when compared to traditional methods and other classical deep learning methods, with PSNR of more than 0.435 and SSIM of more than 0.009, and the subjective visual effect has also been improved, with clearer and more accurate edges, as shown in the figure.


## 5. Conclusion

In this paper, a high-frequency feature-enhanced superresolution reconstruction method for logging images is proposed as a solution to the problem of feature extraction being insufficiently thorough and detail information not being learned in depth. The algorithm uses multiscale dilated convolution blocks to extract various feature information, and the dilated convolution expands the receptive field without adding more parameters. As a result of the method’s repeated extraction of high-frequency features, detail information that was not learned during reconstruction can be learned and improved. The circumference ultrasonic logging tool’s real logging images are used as the training set to assess the method’s efficacy. The reconstructed images are evaluated using the PSNR and SSIM image quality evaluation criteria. The experimental results show that the method described in this paper can recover better high-resolution images and extract more feature information. Lightweight networks will be the primary area of research for future optimization.



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*Source: 9928993-2022-11-21.xml*