CN111724331A

CN111724331A - Porous medium image reconstruction method based on generation network

Info

Publication number: CN111724331A
Application number: CN201910221978.3A
Authority: CN
Inventors: 滕奇志; 冯俊羲; 何小海; 卿粼波; 吴小强; 吴晓红
Original assignee: Sichuan University
Current assignee: Sichuan University
Priority date: 2019-03-22
Filing date: 2019-03-22
Publication date: 2020-09-29
Anticipated expiration: 2039-03-22
Also published as: CN111724331B

Abstract

The invention discloses a porous medium image reconstruction method based on a generation network. The invention provides a reconstruction method based on a generation network aiming at the problem of two-dimensional image missing or incomplete. The main innovations of the invention include: the method comprises the steps of providing a depth generation network to learn the mapping relation between a local image and a complete image; designing a loss function based on a mode and a loss function based on porosity; jointly combining the GAN loss and the L1loss, jointly constraining the reconstruction process by setting different weights; gaussian noise is introduced to achieve diversity in the reconstruction results. Corresponding data sets are made for different porous media, and the effectiveness of the method is verified by adopting a visual effect and statistical function mode. The method is rapid, accurate and strong in expansibility, can reconstruct a multi-phase medium, 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 method for reconstructing a porous medium image based on a generation network, in particular to a method for reconstructing a complete porous medium image by using extremely limited information, belonging to the technical field of image processing.

Background

Porous media such as rocks, soils, composite materials, etc. exist in large quantities in nature and in human life, and have wide application in practical engineering applications. The microstructure of porous media directly determines the macroscopic properties of the exterior, and thus, the understanding of their internal structure is of particular importance.

Taking rock as an example, there are two main ways to obtain an image of its internal microstructure. Firstly, a three-dimensional imaging technology, such as Computed Tomography (CT), Scanning Electron Microscope (SEM) and other technologies, is used for imaging, and a three-dimensional image of the core is directly obtained; and the second is to obtain a two-dimensional image (section) by using imaging equipment such as an optical microscope and the like and to reconstruct the two-dimensional image through a three-dimensional modeling algorithm so as to indirectly obtain a three-dimensional image. In recent years, the two methods are combined together and have been rapidly developed. However, in contrast, the acquisition of two-dimensional images has advantages of low cost, simple operation, and the like, and thus has received attention from researchers.

The method for performing three-dimensional reconstruction by using a single two-dimensional image mainly comprises the following steps: simulated annealing algorithm (SA), multi-point geostatistical computing (MPS), etc. These algorithms mostly have an 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 are generally not user-selectable, and they may be partially missing and incomplete. The incompleteness of the training images undoubtedly brings difficulties to the subsequent three-dimensional reconstruction and analysis based thereon. Therefore, it is a key issue to study how to reconstruct a two-dimensional image using the existing information. In addition, the reconstruction speed and accuracy are problems to be solved, and if the characteristics of the two-dimensional image of the porous medium need to be targeted, a corresponding constraint function (also called a loss function) is proposed to ensure the consistency of the reconstructed image and the real image.

Disclosure of Invention

The present invention aims to solve the above problems and provide an accurate and fast method for reconstructing a two-dimensional image of a porous medium based on a generation network.

The invention realizes the 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) making a two-dimensional image data set for training and testing a network;

(2) designing a constraint function based on mode distribution, and aiming at constraining the statistical characteristics of the reconstructed result;

(3) designing a constraint function based on the porosity, wherein the aim is to constrain the porosity of the reconstructed 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 generated samples;

(6) training and testing the neural network, and adjusting parameters until the reconstruction result accords with the real expectation.

The basic principle of the method is as follows:

restoring a complete picture with limited local information is an inverse problem in itself. One key element to solve this inverse problem is to make full use of the a priori information. For the reconstruction of porous media, we expect the reconstruction results to retain the original hard data on the one hand and 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, similarly to other reconstruction algorithms such as MPS, SA, etc., the porosity of the reconstruction result is the most important evaluation index. Therefore, a constraint function based on porosity needs to be designed to constrain the reconstruction process. Second, porosity essentially reflects single point statistics, and two or more points in the image are not constrained. Therefore, in order to ensure the statistical consistency of the reconstruction results, a cost function for constraining the statistical characteristics needs to be designed. Meanwhile, the diversity of the reconstruction results is a challenge to be faced, and since the nature of the inverse problem generally allows multiple solutions to be accepted, for the reconstruction problem, a variable needs to be introduced to ensure the diversity of the results. Furthermore, reconstruction time remains a considerable issue.

Specifically, in the step (1), because no existing data set exists, according to different tasks, a total of 600 and 800 image pairs are made, and each sample pair is composed of a pore partial image and a corresponding complete image. With 70% of the data randomly selected as training and the remaining 30% as testing. Adopting conditional GAN (conditional generic adaptive networks, CGAN) network as basic network structure

In the step (2), in order to constrain the statistical characteristics of the reconstructed result, a corresponding constraint function needs to be designed. The designed constraint function calculation process based on the mode distribution is as follows: scanning an image point by using an NxN fixed template to obtain all modes; leveling each mode into binary number for convenient subsequent calculation, and converting into corresponding decimal number; and thirdly, calculating the occurrence frequency of each mode and normalizing to 0-1 to obtain the mode distribution of the image. This mode distribution is used as a constraint in reconstruction. In 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. And setting a threshold value to divide the image, and then acquiring the mode.

In the step (3), in order to constrain the porosity of the reconstruction result, a constraint function based on the porosity is designed. Porosity is the most direct measure of the reconstruction and is the parameter that needs to be restored most during reconstruction. The segmentation is performed by a set threshold value, and the difference between the porosity of the segmented graph and the target value is calculated.

In the step (4), in addition to the two loss functions, another two loss functions are used. First, L1loss, which is used to ensure that the output image has the same hard data as the input image; and the second is GAN loss which is used for measuring the quality of the image generated by G by using a discriminator D. The smaller this value, the more realistic the image generated by the representative G. From the above, in the reconstruction, there are 4 loss functions in total, which will together constrain the reconstruction process.

In the step (5), in order to ensure the diversity of the reconstruction results, gaussian noise is introduced to ensure the variability of the generated samples. The input of the network G is gaussian noise in addition to the image to be reconstructed, and gaussian noise is added in each intermediate layer of the G network to ensure that the predicted value of G has sufficient variability.

In the step (6), the neural network is trained and tested, and parameters are adjusted until the reconstruction result accords with the real expectation. The parameters of the main adjustment include learning rate (learning rate), weight of each constraint function (weight), dimension of noise, etc.

The invention has the beneficial effects that:

the invention utilizes a deep learning method and recovers the complete image by using only a small amount of information. Similar problems can be applied to conventional approaches such as variations of DS and CCSIM. However, such methods are characterized by a strong dependence on how much data is known in a given image. The more data given, the more accurate the reconstruction result may be. However, the effect of the invention is general, and there is a large error; and the reconstruction time is longer. The method of the invention can quickly and accurately carry out reconstruction, and has other advantages: 1) processing the multi-phase reconstruction; 2) processing the anisotropic reconstruction; 3) hard data which can be defined by a user can be combined; 4) other reconstruction algorithms such as MPS, DS and CCSIM may be coupled for algorithm acceleration.

The invention is funded by the national science foundation 'three-dimensional image reconstruction of rock microscopic heterogeneous structure and resolution improvement technical research (61372174)'.

Drawings

FIG. 1 porous Medium reconstruction schematic

FIG. 2 two-point probability, linear path, two-point cluster function schematic

FIG. 3 data set schematic

FIG. 4 is a schematic diagram of a mode-based constraint function calculation

FIG. 5 visual comparison of rubber/silica Material image reconstruction results

FIG. 6 comparison of statistical parameters of rubber/silica Material image reconstruction results

FIG. 7 visual comparison of cell material image reconstruction results

FIG. 8 comparison of statistical parameters of battery material image reconstruction results

FIG. 9 visual comparison of sandstone image reconstruction results

FIG. 10 sandstone image reconstruction result statistical parameter comparison

Detailed Description

The invention will be further illustrated with reference to the following specific examples and the accompanying drawings:

example (b):

in order to make the reconstruction method of the present invention more easily understood and approximate to the real application, the following overall detailed description is made from each step of the reconstruction method based on deep learning, and the specific operation steps are as follows:

(1) and aiming at different reconstructed images, making a data set for deep neural network training. Figure 3 shows several samples of a rubber/silica material data set (where white is silica and black is rubber). The data set has a total of 800 image pairs, each image pair consisting of two 128 x 128 images to be reconstructed and the target image.

(2) The calculation of the constraint function based on the pattern is shown in fig. 4. in the experiment, in order to take account of the accuracy and speed of reconstruction, a template size of 3 × 3 is adopted, that is, the type of the pattern is at most 2^3×3512 modes. Counting the frequency of the appearance of these modes and calculating the difference from the target value as one of the loss L_pattern. Threshold segmentation is required before traversing the image to calculate the difference of the mode distribution. The threshold value adopted in the experiment is T ═ 10, that is, the value of the pixel point P (x, y) is:

(3) the calculation of the porosity-based constraint function is straightforward: threshold segmentation is performed first, and then the difference of porosity is calculated asA loss L_porosity。

(4) In addition to the two loss functions, two other loss functions are used. First, L1loss, which is used to ensure that the output image has the same hard data as the input image; the second is GAN loss, which is used to show how good the discriminator D determines the image generated by G. In the reconstruction, these 4 loss functions, which will jointly constrain the reconstruction process. Total loss function L_totallossComprises the following steps:

wherein the content of the first and second substances,

λ_patternand λ_porosityAre respectively set as 10, 1.0 × 10⁵And 1.0 × 10⁵. The scan template size N is set to 3.

(5) And the diversity of the reconstruction result is ensured by introducing Gaussian noise. The G network adopts a classical U-Net with skipconnection, and Gaussian noise is spliced with the input of the current layer at each layer of the U-Net and then used as the total network input. The basic dimension of Gaussian noise is 8X 1, and the Gaussian noise is expanded to 8X H W according to the situation (H, W are the height and width of the feature map of the current layer)

(6) Several important network parameters are that Adam optimizer is adopted, and learning rate is set to be 2 × 10^-4(ii) a The number of epochs of training is 400, and the learning rate of the last 200 times is linearly attenuated.

(7) And after the training is finished, evaluating the performance of the network by testing the quality of image reconstruction. To statistically measure the quality of the reconstruction, we reconstruct 20 times for each two-dimensional image, with a single run time on the CPU of only 0.08 seconds. We analyzed and compared 3 sets of images and the distribution of porosity and statistical parameters for 20 reconstructed images of each set. The experimental results are as follows:

① rubber/silica Material image reconstruction FIG. 5 shows the results of 3 reconstructions, all of which appear to remain unchangedThe input hard data (the part marked by the rectangular box) is also very diverse, and the aim of reconstruction is fulfilled. Fig. 6 shows a comparison of the statistical parameters of the reconstructed results, the middle dashed line being the average of the 20 results, very close to the target value. In addition, the porosity distribution of the 20 sets of reconstructed images is φ_CGAN0.099 ± 0.003, target porosity phi_targetThe difference between the two is seen to be very small at 0.0962. In conclusion, the reconstructed result is close to the target value regardless of the comparison of the visual effect and the quantitative parameter.

Rebuilding 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 results are very close to the true values.

And reconstructing a rock 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 of the present invention is significantly better than the DS algorithm in terms of visual effect and quantitative index. In addition, in time, the invention only needs 0.08 seconds, whereas the DS algorithm needs 1.6 seconds, and the invention realizes about 20 times of speed increase.

The above embodiments are merely preferred embodiments of the present invention, and are not intended to limit the technical solutions of the present invention, and any technical solutions that can be implemented on the basis of the above embodiments without creative efforts should be considered to fall within the protection scope of the present invention.

Claims

1. A porous medium image reconstruction method based on a generation network is characterized in that: the method comprises the following steps:

(1) making a two-dimensional image data set for training and testing a network;

(4) the two proposed constraint functions jointly constrain the whole reconstruction process by combining GAN loss and L1 loss;

2. The porous medium image reconstruction method based on the generation network according to claim 1, characterized in that:

in the step (1), because no existing data set exists, according to different tasks, 800 samples are prepared in total, and each sample pair consists of a pore local image and a corresponding complete image; wherein 70% of the data was randomly selected as training and the remaining 30% as testing;

in the step (2), designing a corresponding constraint function to constrain the statistical characteristics of the reconstructed result; the designed constraint function calculation process based on the mode distribution is as follows: scanning an image point by using a fixed template to obtain all modes; leveling each mode into binary number for convenient subsequent calculation, and converting into corresponding decimal number; calculating the occurrence frequency of each mode and normalizing to 0-1 to obtain the mode distribution of the image; this mode distribution is used as a constraint in 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 needs to be binarized. Dividing by setting a threshold value, and then obtaining a mode and calculating mode distribution of the obtained binary image;

in the step (3), a constraint function based on porosity is designed to constrain the porosity of the reconstructed result; segmenting the image through 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 settings of the two are 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, and the diversity of reconstruction results is ensured.