CN111724331B - Porous medium image reconstruction method based on generation network - Google Patents

Porous medium image reconstruction method based on generation network Download PDF

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CN111724331B
CN111724331B CN201910221978.3A CN201910221978A CN111724331B CN 111724331 B CN111724331 B CN 111724331B CN 201910221978 A CN201910221978 A CN 201910221978A CN 111724331 B CN111724331 B CN 111724331B
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滕奇志
冯俊羲
何小海
卿粼波
吴小强
吴晓红
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Sichuan University
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Abstract

The invention discloses a porous medium image reconstruction method based on a generation network. Aiming at the problem of two-dimensional image missing or incomplete, the invention provides a reconstruction method based on a generated network. The main innovation of the invention comprises: a depth generation network is proposed to learn the mapping relation between the local image and the complete image; a mode-based loss function and a porosity-based loss function are designed; combining GAN loss and L1loss, and jointly restricting the reconstruction process by setting different weights; gaussian noise is introduced to achieve diversity in the reconstruction results. For different porous media, corresponding data sets are prepared, and the effectiveness of the invention is verified by adopting a visual effect and statistical function mode. The method is quick, accurate and strong in expansibility, can reconstruct multiphase media, process anisotropic image reconstruction, combine user-defined data, accelerate other reconstruction algorithms and the like, and has good application value.

Description

Porous medium image reconstruction method based on generation network
Technical Field
The invention relates to a reconstruction method of a porous medium image based on a generation network, in particular to a method for reconstructing a complete image of a porous medium by using extremely limited information, and belongs to the technical field of image processing.
Background
Porous media such as rock, soil, composite materials, etc. are present in large numbers in nature and people's life, and have wide application in practical engineering applications. The microstructure of porous media directly determines the macroscopic nature of the exterior and therefore an understanding of their internal structure is particularly important.
Taking rock as an example, there are two main ways to obtain an image of its internal microstructure. Firstly, imaging is carried out by utilizing a three-dimensional imaging technology, such as a computed tomography Computed Tomography (CT), a scanning electron microscope (scanning electron microscope, SEM) and the like, and a three-dimensional image of the rock core is directly obtained; and secondly, acquiring a two-dimensional image (section) by using imaging equipment such as an optical microscope and the like, and reconstructing by using a three-dimensional modeling algorithm to indirectly acquire a three-dimensional image. In recent years, these two methods complement each other and have been rapidly developed. However, in contrast, two-dimensional image acquisition has advantages such as low cost and simpler operation, and thus is getting more attention from researchers.
The method for three-dimensional reconstruction by using a single two-dimensional image mainly comprises the following steps: simulated annealing algorithm (SA), multipoint geostatistical algorithm (MPS), etc. Most of these algorithms have the assumption that the two-dimensional Training Image (TI) is required to be stationary. For non-stationary images, it is often difficult to reconstruct a relatively realistic result. In practice, moreover, two-dimensional images often do not allow the user to choose from, which may be partially missing and incomplete. The incompleteness of the training image is undoubtedly a difficulty in subsequent three-dimensional reconstruction and analysis based thereon. Therefore, it is a critical issue to study how to reconstruct two-dimensional images using existing information. In addition, the reconstruction speed and accuracy are also issues to be solved, such as the need to propose corresponding constraint functions (also called loss functions) for the characteristics of the two-dimensional image of the porous medium, so as to ensure the consistency of the reconstructed image and the real image.
Disclosure of Invention
The invention aims to solve the problems and provide an accurate and rapid porous medium two-dimensional image reconstruction method based on a generation network.
The invention realizes the above purpose through the following technical scheme:
an accurate and rapid porous medium two-dimensional reconstruction method based on deep learning comprises the following steps:
(1) Manufacturing a two-dimensional image data set for training and testing of a network;
(2) Designing a constraint function based on mode distribution, wherein the purpose is to constrain the statistical characteristics of the reconstruction result;
(3) Designing a constraint function based on porosity, wherein the purpose is to constrain the porosity of the reconstruction result;
(4) The two proposed constraint functions are combined with GAN loss and L1loss to jointly constrain the whole reconstruction process;
(5) In reconstruction, gaussian noise is introduced to ensure the diversity of the generated samples;
(6) Training and testing the neural network, and adjusting parameters until the reconstruction result meets the actual expectation.
The basic principle of the method is as follows:
restoration of a complete image with limited local information is itself an inverse problem. A major key element to solve this inverse problem is to make full use of the a priori information. For reconstruction of porous media, it is desirable that the reconstruction result retains the original hard data on the one hand and is able to recover statistical properties close to the target values on the other hand. Preserving the original hard data can be directly constrained by L1loss, while maintaining the accuracy of the reconstructed structure requires more constraints. First, similar to other reconstruction algorithms such as MPS, SA, etc., the porosity of the reconstructed result is the most important evaluation index. Therefore, it is necessary to design a porosity-based constraint function to constrain the reconstruction process. Second, in essence, the porosity reflects only a single point statistic, and two or more points in the image are not constrained. Therefore, to ensure statistical consistency of the reconstruction results, a cost function that constrains the statistical properties needs to be designed. At the same time, the diversity of the reconstructed results is also a challenge to be faced, since the nature of the inverse problem generally allows accepting multiple solutions, for which variables need to be introduced to guarantee the diversity of the results. In addition, reconstruction time remains a considerable problem.
Specifically, in the step (1), since there is no ready-made data set, 600-800 image pairs are fabricated according to different tasks, and each sample pair is composed of one local image of the aperture and one corresponding complete image. Wherein 70% of the data were randomly selected for training and the remaining 30% were tested. Using conditional GAN (conditional generative adversarialnetworks, CGAN) networks as the basic network structure
In the step (2), in order to constrain the statistical characteristics of the reconstruction result, a corresponding constraint function needs to be designed. The constraint function calculation process based on the mode distribution is designed as follows: (1) scanning the image point by using an NxN fixed template to obtain all modes; (2) in order to facilitate subsequent calculation, each mode is leveled into a binary number and converted into a corresponding decimal number; (3) and calculating the occurrence times of each mode and normalizing to 0-1 to obtain the mode distribution of the image. This mode distribution is the constraint at the time of reconstruction. During the whole training process, the output of the neural network may have values other than 0 and 255 gray values, and the middle needs to be subjected to binarization processing. The segmentation is performed by setting a threshold value, and then the mode is acquired.
In the step (3), in order to restrict the porosity of the reconstruction result, a restriction function based on the porosity is designed. Porosity is the most direct indicator of the measurement of the reconstruction result and is also the parameter that most needs to be restored in the reconstruction. The graph after segmentation is segmented by a set threshold value, and the difference between the porosity and the target value is calculated.
In the step (4), two other loss functions are used in addition to the two loss functions. L1loss, which is used for ensuring that the output image and the input image have the same hard data; and secondly, GAN loss, which is used for measuring whether the image generated by G is good or bad by using the discriminator D. The smaller this value, the more realistic the image generated by the representative G. From the above, it is known that in reconstruction there are a total of 4 loss functions, which will together constrain the reconstruction process.
In the step (5), to ensure the diversity of the reconstruction result, gaussian noise is introduced to ensure the variability of the generated samples. The input to the network G has gaussian noise in addition to the image to be reconstructed and gaussian noise is added at each intermediate layer of the G network to ensure that the predicted value of G has sufficient variability.
In the step (6), training and testing the neural network, and adjusting parameters until the reconstruction result meets the actual expectation. The parameters mainly adjusted include learning rate (learning rate), weight (weight) of each constraint function, dimension of noise, and the like.
The invention has the beneficial effects that:
the invention uses the deep learning method and uses only a small amount of information to recover the complete image. Variations of conventional methods such as DS and CCSIM can also be used with similar problems. However, the nature of such methods is very dependent on how much data is known in a given image. The more data is given, the more accurate the reconstruction result may be. However, the effect is relatively general and there is a large error in the problem solved by the present invention; and the reconstruction time is longer. The method of the invention can quickly and accurately reconstruct and has other advantages: 1) Processing the multi-phase reconstruction; 2) Processing the anisotropic reconstruction; 3) Hard data that can be customized by a user can be combined; 4) Other reconstruction algorithms such as MPS, DS and CCSIM may be coupled for algorithm acceleration.
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FIG. 1 schematic diagram of porous media reconstruction
FIG. 2 schematic diagram of two-point probability, linear path, two-point cluster function
FIG. 3 dataset schematic
FIG. 4 is a schematic diagram of a mode-based constraint function calculation scheme
FIG. 5 visual contrast of image reconstruction results for rubber/silica materials
FIG. 6 statistical parameter contrast for rubber/silica Material image reconstruction results
Fig. 7 visual contrast of battery material image reconstruction results
FIG. 8 statistical parameter contrast for battery material image reconstruction results
Visual contrast of sandstone image reconstruction results of FIG. 9
Figure 10 comparison of statistical parameters for sandstone image reconstruction results
Detailed Description
The invention is further described below with reference to specific examples and figures:
examples:
in order to make the reconstruction method of the present invention easier to understand and closer to the actual application, the following detailed overall description will be made from the respective steps of the reconstruction method based on deep learning, and the specific operation steps are as follows:
(1) For different reconstructed images, a dataset for deep neural network training is made. FIG. 1 shows a schematic representation of porous media reconstruction. Fig. 3 gives several samples in the dataset of rubber/silica materials (where white is silica and black is rubber). The dataset has a total of 800 image pairs, each image pair consisting of two 128 x 128 images to be reconstructed and a target image.
(2) The calculation of the mode-based constraint function is shown in fig. 4. In the experiment, in order to achieve both accuracy and speed of reconstruction, a 3×3 template size was used. That is, the types of modes are at most 2 3×3 =512 modes. Counting the frequency of occurrence of these patterns and calculating the difference from the target value as one of the loss L pattern . It is necessary to first thresholding and then traverse the differences in the image computation mode distribution. The threshold value adopted in the experiment is t=10, that is, the value of the pixel point P (x, y) is:
Figure GDA0002042825680000041
(3) The calculation of the porosity-based constraint function is straightforward: threshold segmentation is performed, and the difference of porosity is calculated as one of loss L porosity
(4) In addition to the two loss functions described above, two other loss functions are used. L1loss, which is used for ensuring that the output image and the input image have the same hard data; and secondly, GAN loss, which is used for judging whether the image generated by G is good or bad by using the discriminator D. In the reconstruction, these 4 loss functions, which will together constrain the reconstruction process. Total loss function L total loss The method comprises the following steps:
Figure GDA0002042825680000042
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure GDA0002042825680000043
and lambda is porosity The method comprises the following steps of: 10,1.0 ×10 5 And 1.0X10 5 . The scan template size N is set to 3.
(5) The diversity of the reconstruction result is ensured by introducing gaussian noise. The G network adopts a classical U-Net with skip connection, and Gaussian noise is spliced with the input of the current layer at each layer of the U-Net and then is used as the total network input. The basic dimension of Gaussian noise is 8 x 1, and the basic dimension is 8 x H x W (H, W is the height and width of the current layer characteristic spectrum) according to the situation
(6) Several important network parameters are: adopting an Adam optimizer; the learning rate is set to 2×10 -4 The method comprises the steps of carrying out a first treatment on the surface of the The number of epochs trained was 400, and the learning rate of the last 200 decays linearly.
(7) After training is completed, the performance of the network is evaluated by testing the quality of the image reconstruction. To statistically measure the quality of the reconstructed results, we reconstructed 20 times for each two-dimensional image, with a single run time on the CPU of only 0.08 seconds. We quantitatively analyzed and compared 3 sets of images and for each set the porosity of the 20 reconstructed images and the distribution of statistical parameters (defined as shown in fig. 2). The experimental results are as follows:
(1) image reconstruction of rubber/silica material. The reconstruction results of 3 times are shown in fig. 5, and all of them show that the input hard data (the part marked by the rectangular box) is maintained, and the reconstruction is very diverse, so that the aim of reconstruction is fulfilled. Fig. 6 shows a comparison of the statistical parameters of the reconstruction results, the middle dashed line being the average of 20 results, very close to the target value. In addition, the porosity distribution of the 20 reconstructed images was phi CGAN =0.099+ -0.003, the target porosity is phi target = 0.0962, it can be seen that the difference between the two is very small. From the above, it can be seen that the reconstructed result is very close to the target value, regardless of visual effect or quantitative parameter comparison.
(2) Reconstruction of the battery material. Fig. 7 and 8 show the reconstruction and quantitative analysis of an input image (a battery material) containing 4 sub-regions. Likewise, the reconstruction result is very close to the true value.
(3) And reconstructing a core image. In this reconstruction we also compare the performance of the classical algorithm DS. As can be seen from fig. 9 and 10, the algorithm in the present invention is significantly superior to the DS algorithm in terms of visual effect, quantitative index. In addition, the present invention only requires 0.08 seconds in time, whereas the DS algorithm requires 1.6 seconds, the present invention achieves a speed increase of about 20 times.
The above embodiments are only preferred embodiments of the present invention, and are not limited to the technical solutions described in the present invention, and any technical solution that can be implemented on the basis of the above embodiments without inventive effort should be considered as falling within the scope of the present invention.

Claims (2)

1. A porous medium image reconstruction method based on a generation network is characterized by comprising the following steps of: the method comprises the following steps:
(1) Manufacturing a two-dimensional image data set for training and testing of a network;
(2) Designing a constraint function based on mode distribution, wherein the purpose is to constrain the mode distribution of a reconstruction result; the constraint function calculation process based on the mode distribution is designed as follows: (1) scanning the image point by using a fixed template to obtain all modes; (2) in order to facilitate subsequent calculation, each mode is leveled into a binary number and converted into a corresponding decimal number; (3) calculating the occurrence times of each mode and normalizing to 0-1 to obtain the mode distribution of the image; this mode distribution is the constraint at the time of reconstruction; it should be noted that during the whole training process, the output of the neural network may have values other than 0 and 255 gray values, and the middle of the neural network needs to be subjected to binarization processing; dividing by setting a threshold value, and obtaining a mode and calculating mode distribution of the obtained binary image;
(3) Designing a constraint function based on porosity, wherein the purpose is to constrain the porosity of the reconstruction result;
(4) The two proposed constraint functions are combined with GANloss and L1loss to jointly constrain the whole reconstruction process;
(5) In reconstruction, gaussian noise is introduced to ensure the diversity of the generated samples;
(6) Training and testing the neural network, and adjusting parameters until the reconstruction result meets the actual expectation.
2. The porous media image reconstruction method based on the generation network according to claim 1, wherein:
in the step (1), as no existing data set exists, 600-800 samples are manufactured according to different tasks, and each sample pair consists of a pore local image and a corresponding complete image; wherein 70% of the data are randomly selected for training and the remaining 30% are tested;
in the step (3), a constraint function based on the porosity is designed to constrain the porosity of the reconstruction result; dividing the image by a set threshold value, and calculating the difference between the porosity and a target value;
in the step (4), the total cost function is composed of GAN loss, L1loss, mode-based loss and porosity-based loss, and the weight setting of the total cost function is obtained through multiple experiments;
in the step (5), gaussian noise is introduced to ensure the diversity of the generated samples; different samples can be generated by setting different noise values, so that the diversity of reconstruction results is ensured.
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