A multi-grid-BPT-improved SIRT coal seam radio wave perspective geological interpretation image reconstruction method

Abstract

The present invention provides a coal seam radio wave perspective geological interpretation image reconstruction method of multi-grid BPT-improved SIRT. Firstly, coal rock radio wave detection injection and reception data are preprocessed, and the probability value of each pixel obtained by the maximum entropy method is used to replace the distance weighted average method in the BPT as the initial value of iteration; secondly, the magnetic field intensity is solved based on the Maxwell equations; on the basis of the SIRT algorithm, a multi-grid model is introduced, and the SIRT algorithm is improved and iterated by using the strategy of "fine mesh smoothing and coarse mesh correction"; then, the coal rock is reconstructed by using the improved SIRT algorithm to obtain a reconstructed image; finally, the signal-to-noise ratio SNR is used as a quantitative evaluation index to evaluate the image quality. If the predetermined effect value a is not reached, the multi-grid is returned to perform grid division iteration until the predetermined effect value is reached, so as to obtain the final mine radio wave perspective interpretation reconstruction image.

Description

Technical Field

[0001] The present invention relates to a coal seam radio wave perspective geological interpretation image reconstruction method of a multi-grid-BPT-improved SIRT, and in particular to the characteristics of excessive image noise and slow iteration speed obtained by the SIRT method. It is necessary to use a maximum entropy method and a multi-grid method in combination with SIRT for reconstruction, and belongs to the field of mine engineering geophysical exploration technology. Background Art

[0002] Traditional electromagnetic wave technology for detecting fault structures of coal and rock mainly uses mine DC exploration, mine transient electromagnetic exploration, radio wave perspective, bottom radar and seismic exploration methods. With the development of science and technology and years of efforts, mine DC exploration and radio wave perspective have made significant progress in theory, technology and exploration equipment.

[0003] In the present invention, the faults of coal rock are mainly studied by radio wave perspective method. When electromagnetic waves propagate in underground rock formations, due to the different electrical properties of various rocks and minerals, they have certain differences in the absorption of electromagnetic wave energy, and different electromagnetic waves will have different detection angles on rock formations. This takes into account the error problem in the reconstruction of electromagnetic wave wireless perspective images. Through the detection of hundreds of working faces, it can be fully demonstrated that the tunnel radio wave perspective method can delineate the normal area and abnormal area in the working face. In addition, in the process of radio wave perspective image reconstruction, when the electromagnetic waves are refracted and reflected by the occurrence of fracture structures or cavities, the energy loss of electromagnetic waves will be caused, which is the so-called attenuation. However, when electromagnetic waves propagate in underground rock formations, if there are water-bearing areas, collapse columns, faults, cavities or other uneven geological structures, the energy of electromagnetic waves will be absorbed or completely shielded by them, and at this time, the signal significance abnormality and perspective abnormality will occur.

[0004] For previous image reconstruction algorithms, most scholars use the image obtained by BPT as the initial value of SIRT iteration for improvement. However, the resolution of the BPT algorithm is poor, and the SIRT algorithm is an iterative method with strong globality, which has the characteristic of "over-update" and has certain computational redundancy, resulting in a slow calculation speed. Therefore, the present invention starts with improving the formula of BPT to improve the resolution of BPT. In addition, in the SIRT iteration process, the concept of multiple grids is added. In view of the inconsistent convergence of high-frequency and low-frequency information, the iteration is mainly focused on the reconstruction of low-resolution images. This not only saves the amount of calculation, but also accelerates the attenuation of low-frequency errors, and the overall convergence speed is significantly accelerated. Summary of the invention

[0005] The present invention provides a coal seam radio wave perspective geological interpretation image reconstruction method of multi-grid-BPT-improved SIRT, which greatly improves the calculation efficiency and accuracy, thereby solving the problems of poor resolution and slow iteration speed in the iterative process, achieving a clearer understanding of the mine structure, and providing support for effectively strengthening the safety of mines.

[0006] The technical solution of the present invention is: first, the coal rock radio wave detection transmission and reception data are preprocessed, and then the maximum entropy method is used to replace the distance weighted average method of BPT as the initial value of the iteration; then the magnetic field strength is solved based on the Maxwell equations; then, on the basis of the SIRT algorithm, a multi-grid model is introduced, and the SIRT algorithm is improved and iterated using the strategy of "fine mesh smoothing and coarse mesh correction"; finally, the improved SIRT algorithm is used to reconstruct the coal rock to obtain a reconstructed image.

[0007] The specific steps of this method are as follows:

[0008] Step 1: Pre-process the emission and reception data of coal rock electromagnetic wave detection to determine the coal rock conditions in the mine area. According to the difference between the electromagnetic waves before and after the radio waves penetrate the ore layer in the mine, the data required for the reconstruction algorithm is obtained and the actual situation of the mine is given.

[0009] Assuming that there are few geological interference factors in coal rock and the structure is simple, and there are circular isomers, for the safety of coal rock mining, certain measures need to be taken to determine the location of the isomers. At this time, the radio wave perspective method is used to perform grid detection of coal rock, and a matrix can be obtained. This matrix can be used as a coefficient matrix to perform linear iteration on the linear equation group. Figure 1 As shown, all operations of the present invention are based on the scene image below, that is, the cross-sectional display of the air inlet and return air channels. Here, the transmitting point is a transmitting point 8, and the value is H0 at this time. The corresponding receiving point is a group of 15 points 1-15, and the values ​​are H i On the contrary, the return air channel here can also be used as the launch area, which is also a point launch and 15 points receive. The variable of the isomer here is expressed as F (x，y) , polar coordinates are represented by r i，j .

[0010] In the radio wave perspective of mines, many technical studies on image reconstruction mainly include analytical algorithm image reconstruction and iterative algorithm image reconstruction. In iterative algorithms, when projection data is insufficient and projection angles are unevenly distributed, iterative algorithms can still solve the problem. The existing technical idea of ​​SIRT is to use all rays passing through the pixel. The update amount for each pixel of the image during the iteration process is to correct all projection lines by taking the weighted average according to the contribution factor, and then back-project to correct the image until the iteration requirements are met, and then the iteration can be ended. And the SIRT algorithm is to solve the direct problem, that is, predict the projection value according to the previous gray value and projection equation, so as to obtain the calculated projection value, and correct the estimated value, thereby solving the inverse problem.

[0011] Back projection method (BPT) is the most commonly used reconstruction method in tomography. It is basically a weighted average process, that is, the contribution of each ray is evenly distributed to each small reconstruction area through which the ray passes, and then a weighted method is used to calculate the average of the contribution of all rays passing through each small reconstruction area. Its advantage is that it takes less time, which is only equivalent to the time used for one iteration of algorithms such as ART and SART. Its basic idea is to distribute the travel time along the ray to each pixel, and the distribution is based on the length of the jth ray in the pixel and the total length of the ray. The ratio of is the weight, and then the weighted travel time of all rays passing through the i-th pixel is added, and divided by the total ray length in the unit to obtain the medium slowness of the unit. The constraints here have a realistic context for coal and rock, and the boundary conditions of the algorithm can be appropriately set.

[0012] Step 2. In the back-projection method, the formula of the BPT algorithm is given. The idea of ​​the maximum entropy method is used to replace the distance weighted average method in the BPT. The probability value of each pixel obtained by this method is used as the initial value of the iteration. Finally, the electromagnetic wave field intensity is solved according to the Maxwell equations. The specific steps are as follows:

[0013] Step 2.1. According to the BPT formula, the maximum entropy method is used to obtain the probability value of each grid, thereby replacing the original distance weighted average method to obtain the initial value of the iteration.

[0014] (1) Based on the BPT algorithm in mine radio wave fluoroscopic CT image reconstruction, the following algorithm formula is given:

[0015]

[0016] where f j is the slowness of each unit (pixel); a ij is the length of the i-th ray in the j-th grid; τ iis the travel time of the ray; n is the total number of rays, and m is the total number of grids;

[0017] The travel time along the ray is assigned to each pixel, and the distribution is based on the length of the i-th ray in the pixel and the total length of the ray. The ratio of is taken as the weight, and then the weighted travel time of all rays passing through the j-th pixel is added and divided by the total ray length in the unit to obtain the medium slowness of the unit.

[0018] (2) Use the maximum entropy model to replace the distance weighted average method in the BPT algorithm. The specific steps are as follows:

[0019] Assume that the pixels of the image are N random variables Y, that is, {y1, y2…y N}, assuming that the conditional probability distribution of the random variable Y satisfies the following conditions:

[0020]

[0021]

[0022] (3) Find the probability distribution P(Y) corresponding to the maximum entropy model

[0023] The objective function of the maximum entropy model is:

[0024]

[0025] Introduce Lagrange multipliers w0, w1 and define the Lagrange function:

[0026]

[0027] make Get the probability distribution corresponding to the maximum entropy model:

[0028]

[0029]

[0030] The probability value of each pixel obtained by the maximum entropy method is used to replace the weighted value obtained by the distance weighted average method in BPT to further improve the resolution of BPT. N represents N pixels, and M represents the Mth pixel from 0 to N.

[0031] (4) The radio wave perspective method initially selects coal tunnels with simple geological conditions and few interference factors, arranges 1 to 3 transmitting points, observes the field strength values ​​of each observation point at the distance from the transmitter, and then detects the attenuation of electromagnetic waves. The amount of attenuation depends on the absorption of electromagnetic waves by the coal seam. When electromagnetic waves propagate in coal rocks, part of the electromagnetic energy is gradually absorbed and attenuated as the distance increases. At this time, β represents the attenuation coefficient, and its specific formula is:

[0032]

[0033] In the formula, β is the coal seam absorption coefficient H i is the field strength value of measuring point 1 (dB); H2 is the field strength value of measuring point 2 (dB); r1 is the distance from the transmitting point to measuring point 1; r2 is the distance from the transmitting point to measuring point 2.

[0034] In summary, the above-mentioned attenuation absorption coefficient is related to the field strength and distance, which well describes the attenuation of electromagnetic waves.

[0035] Step 3: According to the iterative idea of ​​SIRT algorithm, process the coefficient matrix, control the factors of SIRT convergence, correct the image, combine SIRT algorithm with multi-grid model, enhance noise resistance, and improve iteration speed. The details are as follows:

[0036] Step 3.1. According to the iterative idea of ​​SIRT algorithm, find the factors that control the convergence of SIRT algorithm, including the selection of SIRT initial value, the design of SIRT iteration formula, the design of coefficient matrix, and the design of operation and iteration convergence criteria;

[0037] (1) The image obtained by combining BPT with the maximum entropy method is used as the initial value of the SIRT algorithm, and the radon function is used to randomly select the coefficient matrix. For the convergence criterion, forced convergence is used here;

[0038] (2) Based on the SIRT algorithm in mine radio wave fluoroscopic CT image reconstruction, the following algorithm formula is given:

[0039] The existing technical idea of ​​SIRT is to use all the rays passing through the pixel. In the iterative process, the update amount of each pixel of the image is to take the weighted average of the correction of all projection lines according to the contribution factor, and then back-project it to correct the image until the iteration requirements are met. The iteration can be ended. Based on the SIRT algorithm in the reconstruction of mine radio wave fluoroscopic CT images, the following algorithm formula is given:

[0040] Starting from the image obtained by BPT as the initial value, using formula (13)

[0041]

[0042] in, Y is the inversion value of the jth grid in the qth iteration; i q is the estimated attenuation value of the i-th ray at the q-th iteration.

[0043] Calculate Y jq , and then calculate the correction value of the jth (j=1,2,…,m) grid

[0044]

[0045] Among them, a ij is the length of the i-th ray in the j-th grid; l i is the length of the ray; Y is the inversion value of the jth grid in the qth iteration; i q is the estimated attenuation value of the i-th ray in the q-th iteration; r is the damping factor 0 <r≤1;

[0046] (3) Finally, calculate the estimated value of the jth grid at the qth iteration:

[0047]

[0048] Step 3.2, using the multi-grid method to focus the iteration process on the reconstruction of low-resolution images, the amount of calculation is significantly reduced, and the iteration speed of the SIRT algorithm can be greatly improved;

[0049] Step 3.3: The specific steps of the multi-grid algorithm based on algebraic iteration are as follows:

[0050] The image obtained by BPT is divided into three grids, and according to the strategy of "fine mesh smoothing, coarse mesh correction", it is combined with SIRT and iterated in three grids respectively;

[0051] (1) Assume that the reconstructed image is f and the image size is N×N:

[0052] SIRT iteration is performed according to formula (15), and the input image is The number of iterations is q1, and the output image is

[0053] (2) Initialization size is Image

[0054]

[0055] in To restrict the operator, the operator will Map to superior. Depend on The corresponding 4 pixels are averaged. Then SIRT iteration is performed according to formula (15), and the input image is The number of iterations is q1, and the output image is

[0056] (3) Initialization size is Image

[0057]

[0058] in To restrict the operator, the operator will Map to Likewise, Depend on The corresponding 4 pixels are averaged. Then SIRT iteration is performed according to formula (15), and the input image is The number of iterations is q1, and the output image is

[0059] (4) Calibration:

[0060]

[0061]

[0062]

[0063] in: and They are and Iterative correction amount on scale size; and is an interpolation operator, which interpolates the correction value to a higher resolution image. This paper adopts the Bicubic interpolation operator; f is the output result of one round of iteration. Return to the first step for the next iteration.

[0064] For simplicity, the sizes of q1, q2, and q3 can be selected empirically. It should be noted that after a sufficient number of iterations, the back-interpolation correction on the coarse grid is close to 0, and the iteration on the coarse grid can be stopped at this time. According to the previous analysis, SIRT has "over-update", so when selecting the number of iterations, if q2 and q3 are much larger than q1, the amount of calculation can be significantly reduced, thereby accelerating the iterative solution;

[0065] (5) The calculation basis of SIRT iteration algorithm is to solve the linear equations. However, after having data, we need to consider whether the equations have solutions. The judgment conditions of the linear equations are given below, and the coefficient equations and coefficient matrices of linear iteration can be obtained. Finally, it becomes to calculate the following equation AX=P, where A is the coefficient matrix, to determine whether this linear equation has solutions. The objective function is established below, and the existence conditions of the solution are used:

[0066] J(X)=‖AX-P 2 ‖=(AX-P) T (AX-P) (21)

[0067] This equation is the objective function of least squares. Optimizing this function can be used for judgment, so the partial derivative is calculated:

[0068]

[0069] Let the above equation be zero, and we get

[0070] 2A T AX-2A T P=0 (23) According to the above formula, we can get the optimal solution of the least squares method:

[0071] X=(A T A) -1 A T P (24)

[0072] The above formula is mainly used to classify and discuss the solutions to the linear equations. In the SIRT algorithm, it mainly reconstructs the image by performing multiple iterations on a certain point.

[0073] During radio wave perspective, the coal rock is detected at different points. The data obtained in this way can form a matrix, which can be used as the coefficient matrix of a linear equation system. At this time, the coefficient matrix is ​​A. Linear iteration is performed on this matrix to obtain a reconstructed image.

[0074] Step 4: Evaluate the reconstructed image. The specific steps are as follows:

[0075] (1) The signal-to-noise ratio is the ratio of the signal mean to the background standard deviation, which is expressed as follows:

[0076]

[0077] Among them, μ sig represents the signal mean (image mean); σ bg represents the background standard deviation.

[0078] (2) For images, the "signal value" here is often the grayscale value. The denominator sometimes uses the variance of the background signal value, which represents the physical meaning of noise power. For high-contrast black background images, the result of the above formula is usually infinite. So we use the signal mean and signal standard deviation (image standard deviation) to measure:

[0079]

[0080] where σ sig Represents the signal standard deviation.

[0081] (3) The calculation formula of the image mean is:

[0082]

[0083] Among them, w and h are the width and height of the image respectively, p ij is the pixel value corresponding to the ij position.

[0084] (4) Calculation formula of image standard deviation:

[0085]

[0086] (5) In summary, the image signal-to-noise ratio formula can be written as:

[0087]

[0088] In the application of radio electromagnetic wave perspective, the qualified level of signal-to-noise ratio depends on many factors, including the specific electromagnetic wave detection system, geological conditions, depth and characteristics of coal and rock, etc. Generally speaking, the signal-to-noise ratio requirement for underground coal and rock detection is relatively high to ensure accurate detection of underground structures.

[0089] Some suggested signal-to-noise ratio levels may be above 20dB to 30dB, and the specific requirements may vary according to the specific needs of the project. Therefore, the present invention selects a = 25dB as the quantitative evaluation index. When the obtained reconstructed image signal-to-noise ratio is greater than or equal to a, the quality of the image is qualified. When the obtained reconstructed image signal-to-noise ratio is less than a, return to the multi-grid iteration until the requirements are met.

[0090] The beneficial effects of the present invention are as follows: through the image reconstruction algorithm, the abnormal attenuation value of the electromagnetic wave when detecting coal and rock is effectively detected, and the cause of the electromagnetic wave abnormality is judged according to the parameters of the reconstructed image, including the position, size and dielectric coefficient, that is, the abnormal conditions existing in the coal and rock, such as: water-containing areas, collapse columns, faults, cavities or other uneven geological structures, so as to reduce personal injuries in coal and rock mining. For example, there will be flooding of coal and rock in water-containing areas, faults will cause unsafe conditions for workers when working, and collapse columns will easily cause the collapse of coal and rock. Therefore, it is very necessary to judge the abnormal conditions in coal and rock by scientific means. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 It is the physical scene graph under the first layer of grid.

[0092] Figure 2 It is the physical scene graph under the second layer of grid.

[0093] Figure 3This is the physical scene graph under the third layer of grid

[0094] Figure 4 It is a flow chart of the present invention.

[0095] Specific implementation process:

[0096] To make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be described clearly and completely in conjunction with the drawings in the embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. It should be noted that the embodiments in this application and the features in the embodiments can be combined with each other arbitrarily without conflict.

[0097] In terms of coal and rock image detection, only a very small number of coal mining scholars and experts have studied the methods of pit penetration and traditional mine radio and electromagnetic wave perspective hybrid imaging for the research on coal and rock based image reconstruction methods; in terms of coal and rock stratification interface detection, image imaging speed and imaging quality are important indicators; usually, the higher the number of coal and rock detection iterations and the more precise it is, the more time is wasted.

[0098] Traditional mine radio electromagnetic wave exploration uses a single detection data and a common algebraic iterative algorithm to visualize coal rock faults.

[0099] In order to solve the above problems, an embodiment of the present invention provides a coal seam radio wave perspective geological interpretation image reconstruction method based on multi-grid-BPT-improved SIRT.

[0100] Examples of the present invention are described with reference to the accompanying drawings.

[0101] like Figure 1 As shown, the present invention implements a coal seam radio wave perspective geological interpretation image reconstruction method of multiple grids-BPT-improved SIRT. First, the coal rock radio wave detection transmission and reception data are preprocessed, and then the maximum entropy method is used to replace the BPT distance weighted average method as the initial value of the iteration; then the magnetic field intensity is solved based on the Maxwell equations; then on the basis of the SIRT algorithm, a multiple grid model is introduced, and the SIRT algorithm is improved and iterated using the strategy of "fine mesh smoothing and coarse mesh correction"; finally, the improved SIRT algorithm is used to reconstruct the coal rock to obtain a reconstructed image. The specific steps of the method are as follows:

[0102] In the present invention, the main technical problem to be solved is: the present invention provides a multi-scale back-projection filtering and visual interpretation image reconstruction algorithm for parallel electromagnetic beam geological detection of coal seams, which improves the existing back-projection filtering reconstruction algorithm and greatly improves the calculation efficiency and accuracy, thereby solving the problems of poor resolution and slow iteration speed in the iterative process, achieving a clearer understanding of the mine structure and effectively enhancing the safety of the mine.

[0103] The technical solution of the present invention is: based on a multi-scale back-projection filtering and visual interpretation image reconstruction algorithm for coal seam parallel electromagnetic beam geological detection, the specific steps of this method are as follows:

[0104] Step 1: Pre-process the emission and reception data of coal rock electromagnetic wave detection to determine the coal rock conditions in the mine area. According to the difference between the electromagnetic waves before and after the radio waves penetrate the ore layer, the data required for the reconstruction algorithm is obtained and the actual situation of the mine is given.

[0105] In view of the hidden geological structure in the coal mine, multi-scale detection is carried out from the spatial dimension. The specific implementation method is to carry out multi-scale detection of multiple angles, widths and attenuation coefficients of different areas of the coal mine during the detection using parallel electromagnetic beams, aiming to obtain more comprehensive coal and rock structure data information, including both global overall information and local detailed information.

[0106] Assuming that there are few geological interference factors in coal rock and a simple structure, and there are circular isomers, for the safety of coal rock mining, certain measures need to be taken to determine the location of the isomers. At this time, the radio wave perspective method is used to perform grid detection of coal rock, and a matrix can be obtained. This matrix can be used as a coefficient matrix to perform linear iteration of the linear equations.

[0107] In the radio wave perspective of mines, many technical studies on image reconstruction mainly include analytical algorithm image reconstruction and iterative algorithm image reconstruction. In iterative algorithms, when projection data is insufficient and projection angles are unevenly distributed, iterative algorithms can still solve the problem. The existing technical idea of ​​SIRT is to use all rays passing through the pixel. The update amount for each pixel of the image during the iteration process is to correct all projection lines by taking the weighted average according to the contribution factor, and then back-project to correct the image until the iteration requirements are met, and then the iteration can be ended. And the SIRT algorithm is to solve the direct problem, that is, predict the projection value according to the previous gray value and projection equation, so as to obtain the calculated projection value, and correct the estimated value, thereby solving the inverse problem.

[0108] Back projection method (BPT) is the most commonly used reconstruction method in tomography. It is basically a weighted average process, that is, the contribution of each ray is evenly distributed to each small reconstruction area through which the ray passes, and then a weighted method is used to calculate the average of the contribution of all rays passing through each small reconstruction area. Its advantage is that it takes less time, which is only equivalent to the time used for one iteration of algorithms such as ART and SART. Its basic idea is to distribute the travel time along the ray to each pixel, and the distribution is based on the length of the jth ray in the pixel and the total length of the ray. The ratio of is the weight, and then the weighted travel time of all rays passing through the i-th pixel is added, and divided by the total ray length in the unit to obtain the medium slowness of the unit. The constraints here have a realistic context for coal and rock, and the boundary conditions of the algorithm can be appropriately set.

[0109] Step 2. In the back-projection method, the formula of the BPT algorithm is given, and the idea of ​​the maximum entropy method is used to replace the distance weighted average method in the BPT. The probability value of each pixel obtained by this method is used as the initial value of the iteration, and finally the electromagnetic wave field intensity is solved according to the Maxwell equations; the specific steps are as follows:

[0110] Step 2.1. According to the BPT formula, the maximum entropy method is used to obtain the probability value of each grid, thereby replacing the original distance weighted average method to obtain the initial value of the iteration.

[0111] (1) Based on the BPT algorithm in mine radio wave fluoroscopic CT image reconstruction, the following algorithm formula is given:

[0112]

[0113] where f j is the slowness of each unit (pixel); a ij is the length of the i-th ray in the j-th grid; τ i is the travel time of the ray.

[0114] The travel time along the ray is assigned to each pixel, and the distribution is based on the length of the i-th ray in the pixel and the total length of the ray. The ratio of is taken as the weight, and then the weighted travel time of all rays passing through the j-th pixel is added and divided by the total ray length in the unit to obtain the medium slowness of the unit.

[0115] (2) Use the maximum entropy model to replace the distance weighted average method in the BPT algorithm. The specific steps are as follows:

[0116] Assume that the pixels of the image are N random variables Y, that is, {y1, y2…y N}, assuming that the conditional probability distribution of the random variable Y satisfies the following conditions:

[0117]

[0118]

[0119] (3) Find the probability distribution P(Y) corresponding to the maximum entropy model

[0120] The objective function of the maximum entropy model is:

[0121]

[0122] Introduce Lagrange multipliers w0, w1 and define the Lagrange function:

[0123]

[0124] make Get the probability distribution corresponding to the maximum entropy model:

[0125]

[0126]

[0127] The probability value of each pixel obtained by the maximum entropy method is used to replace the weighted value obtained by the distance weighted average method in BPT to further improve the resolution of BPT. N represents N pixels, and M represents the Mth pixel from 0 to N.

[0128] (4) The radio wave perspective method initially selects coal tunnels with simple geological conditions and few interference factors, arranges 1 to 3 transmitting points, observes the field strength values ​​of each observation point at the distance from the transmitter, and then detects the attenuation of electromagnetic waves. The amount of attenuation depends on the absorption of electromagnetic waves by the coal seam. When electromagnetic waves propagate in coal rocks, part of the electromagnetic energy is gradually absorbed and attenuated as the distance increases. At this time, β represents the attenuation coefficient, and its specific formula is:

[0129]

[0130] In the formula, β is the coal seam absorption coefficient H1 is the field strength value (dB) at measuring point 1; H2 is the field strength value (dB) at measuring point 2; r1 is the distance from the transmitting point to measuring point 1; r2 is the distance from the transmitting point to measuring point 2.

[0131] In summary, the above-mentioned attenuation absorption coefficient is related to the field strength and distance, which well describes the attenuation of electromagnetic waves.

[0132] Step 3: According to the iterative idea of ​​SIRT algorithm, process the coefficient matrix, control the factors of SIRT convergence, correct the image, combine SIRT algorithm with multi-grid model, enhance noise resistance, and improve iteration speed. The details are as follows:

[0133] Step 3.1. According to the iterative idea of ​​SIRT algorithm, find the factors that control the convergence of SIRT algorithm, including the selection of SIRT initial value, the design of SIRT iterative formula, the design of coefficient matrix, and the design of operation and iterative convergence criteria.

[0134] (1) The image obtained by combining BPT with the maximum entropy method is used as the initial value of the SIRT algorithm, and the radon function is used to randomly select the coefficient matrix. For the convergence criterion, forced convergence is used here;

[0135] (2) Based on the SIRT algorithm in mine radio wave fluoroscopic CT image reconstruction, the following algorithm formula is given:

[0136] Starting from the image obtained by BPT as the initial value, using formula (36)

[0137]

[0138] in, Y is the inversion value of the jth grid in the qth iteration; i q is the estimated attenuation value of the i-th ray at the q-th iteration.

[0139] Calculate Y i q , and then calculate the correction value of the jth (j=1,2,…,m) grid

[0140]

[0141] Among them, a ij is the length of the i-th ray in the j-th grid; l i is the length of the ray; Y is the inversion value of the jth grid in the qth iteration; i q is the estimated attenuation value of the i-th ray in the q-th iteration; r is the damping factor 0 <r≤1;

[0142] (3) Finally, calculate the estimated value of the jth grid at the qth iteration:

[0143]

[0144] Step 3.2, the multi-grid method is an iterative method that can be used to solve linear equations. In the process of using the multi-grid method, the iteration process is mainly focused on the reconstruction of low-resolution images, the amount of calculation is significantly reduced, and the iteration speed of the SIRT algorithm can be greatly improved;

[0145] Step 3.3: The specific steps of the multi-grid algorithm based on algebraic iteration are as follows:

[0146] The image obtained by BPT is divided into three grids, and according to the strategy of "fine mesh smoothing, coarse mesh correction", it is combined with SIRT and iterated in three grids respectively;

[0147] (1) Assume that the reconstructed image is f and the image size is N×N,

[0148] SIRT iteration is performed according to formula (32), and the input image is The number of iterations is q1, and the output image is

[0149] (2) Figure 2 As shown, the initialization size is Image

[0150]

[0151] in To restrict the operator, the operator will Map to superior. Depend on The corresponding 4 pixels are averaged. Then SIRT iteration is performed according to formula (32), and the input image is The number of iterations is q1, and the output image is

[0152] (3) Figure 3 As shown, the initialization size is Image

[0153]

[0154] in To restrict the operator, the operator will Map to Likewise, Depend on The corresponding 4 pixels are averaged. Then SIRT iteration is performed according to formula (32), and the input image is The number of iterations is q1, and the output image is

[0155] (4) Calibration:

[0156]

[0157]

[0158]

[0159] in: and They are and Iterative correction amount on scale size; and is an interpolation operator, which interpolates the correction value to a higher resolution image. This paper adopts the Bicubic interpolation operator; f is the output result of one round of iteration. Return to the first step for the next iteration.

[0160] For simplicity, the sizes of q1, q2, and q3 can be selected empirically. It should be noted that after a sufficient number of iterations, the back-interpolation correction on the coarse grid is close to 0, and the iteration on the coarse grid can be stopped at this time. According to the previous analysis, SIRT has "over-update", so when selecting the number of iterations, if q2 and q3 are much larger than q1, the amount of calculation can be significantly reduced, thereby accelerating the iterative solution;

[0161] (5) The calculation basis of SIRT iteration algorithm is to solve the linear equations. However, after having data, we need to consider whether the equations have solutions. The judgment conditions of the linear equations are given below, and the coefficient equations and coefficient matrices of linear iteration can be obtained. Finally, it becomes to calculate the following equation AX=P, where A is the coefficient matrix, to determine whether this linear equation has solutions. The objective function is established below, and the existence conditions of the solution are used:

[0162] J(X)=‖AX-P 2 ‖=(AX-P) T (AX-P) (44)

[0163] This equation is the objective function of least squares. Optimizing this function can be used for judgment, so the partial derivative is calculated:

[0164]

[0165] Let the above equation be zero, and we get

[0166] 2A T AX-2A T P=0 (46)

[0167] According to the above formula, we can get the optimal solution of the least squares method:

[0168] X=(A T A) -1 A T P (47)

[0169] The above formula is mainly used to classify and discuss the solutions to the linear equations. In the SIRT algorithm, it mainly reconstructs the image by performing multiple iterations on a certain point.

[0170] During radio wave perspective, the coal rock is detected at different points. The data obtained in this way can form a matrix, which can be used as the coefficient matrix of a linear equation system. At this time, the coefficient matrix is ​​A. Linear iteration is performed on this matrix to obtain a reconstructed image.

[0171] Step 4: Evaluate the reconstructed image. The specific steps are as follows:

[0172] (1) The signal-to-noise ratio is the ratio of the signal mean to the background standard deviation, which is expressed as follows:

[0173]

[0174] Among them, μ sig represents the signal mean (image mean); σ bg represents the background standard deviation.

[0175] (2) For images, the "signal value" here is often the grayscale value. The denominator sometimes uses the variance of the background signal value, which represents the physical meaning of noise power. For high-contrast black background images, the result of the above formula is usually infinite. So we use the signal mean and signal standard deviation (image standard deviation) to measure:

[0176]

[0177] where σ sig Represents the signal standard deviation.

[0178] (3) The calculation formula of the image mean is:

[0179]

[0180] Among them, w and h are the width and height of the image respectively, p ij is the pixel value corresponding to the ij position.

[0181] (4) Calculation formula of image standard deviation:

[0182]

[0183] (5) In summary, the image signal-to-noise ratio formula can be written as:

[0184]

[0185] In the application of radio electromagnetic wave perspective, the qualified level of signal-to-noise ratio depends on many factors, including the specific electromagnetic wave detection system, geological conditions, depth and characteristics of coal and rock, etc. Generally speaking, the signal-to-noise ratio requirement for underground coal and rock detection is relatively high to ensure accurate detection of underground structures.

[0186] Some suggested signal-to-noise ratio levels may be above 20dB to 30dB, and the specific requirements may vary depending on the specific needs of the project. Therefore, the present invention selects quantization a=25dB. When the obtained reconstructed image signal-to-noise ratio is greater than or equal to a, the image quality is qualified. When the obtained reconstructed image signal-to-noise ratio is less than a, return to multi-grid iteration until the requirements are met.

[0187] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A coal seam radio wave perspective geological interpretation image reconstruction method based on multi-grid-BPT-improved SIRT, characterized in that: The specific steps of the method are as follows: Step 1: Pre-process the emission and reception data of coal rock electromagnetic wave detection to determine the coal rock conditions in the mine area. According to the difference between the electromagnetic waves before and after the radio waves penetrate the ore layer, the data required for the reconstruction algorithm is obtained, and the geological conditions of the mine are inverted. Step 2, give the formula of BPT algorithm in the back-projection method, use the idea of ​​maximum entropy method to replace the distance weighted average method in BPT, use the probability value of each pixel obtained by this method as the initial value of iteration, and finally solve the electromagnetic wave field intensity according to Maxwell equations; Step 3: According to the iterative idea of ​​SIRT algorithm, the coefficient matrix is ​​processed to control the factors of SIRT convergence, the image is corrected, and the SIRT algorithm is combined with the multi-grid model to enhance the noise resistance and improve the iteration speed; Step 4: After obtaining the reconstructed image, the quality of the obtained image needs to be evaluated. The present invention uses the signal-to-noise ratio (SNR) of the image as an evaluation index. If the signal-to-noise ratio of the reconstructed image is greater than the given standard, the image quality is qualified. If the signal-to-noise ratio of the reconstructed image is less than the given standard, the multi-grid iteration step is returned to reconstruct until the image quality is qualified. The Step 2 includes the BPT algorithm formula and the maximum entropy method as follows: (1) Based on the BPT algorithm in mine radio wave fluoroscopic CT image reconstruction, the following algorithm formula is given: where f j is the slowness of each unit, i.e., pixel; a ij is the length of the i-th ray in the j-th grid; τ i is the travel time of the ray; n is the total number of rays, and m is the total number of grids; The travel time along the ray is assigned to each pixel, and the distribution is based on the length of the i-th ray in the pixel and the total length of the ray. The ratio of is the weight, then the weighted travel time of all rays passing through the j-th pixel is added up, and divided by the total ray length in the unit to obtain the medium slowness of the unit; (2) The maximum entropy method of the statistical model based on the maximum entropy principle gives the following algorithm: Assume that the pixels of the image are N random variables Y, that is, {y1, y2…y N }, assuming that the conditional probability distribution of the random variable Y satisfies the following conditions: (3) Find the probability distribution P(Y) corresponding to the maximum entropy model The objective function of the maximum entropy model is: Introduce Lagrange multipliers w0, w1 and define the Lagrange function: make Get the probability distribution corresponding to the maximum entropy model: The probability value of each pixel obtained by the maximum entropy method is used to replace the weighted value obtained by the distance weighted average method in BPT to further improve the resolution of BPT. N represents N pixels, and M represents the Mth pixel from 0 to N.

2. A coal seam radio wave perspective geological interpretation image reconstruction method based on multi-grid-BPT-improved SIRT according to claim 1, characterized in that: In Step 1: In view of the hidden geological structure in the coal mine, multi-scale detection is carried out from the spatial dimension. The specific implementation method is to carry out multi-scale detection of multiple angles, widths and attenuation coefficients of different areas of the coal mine during the detection using parallel electromagnetic beams, aiming to obtain more comprehensive coal and rock structure data information, including both global overall information and local detailed information.

3. A coal seam radio wave perspective geological interpretation image reconstruction method based on multi-grid-BPT-improved SIRT according to claim 1, characterized in that the Step 3 includes the following: Step 3.

1. According to the iterative idea of ​​SIRT algorithm, find the factors that control the convergence of SIRT algorithm, including the selection of SIRT initial value, the design of SIRT iteration formula, the design of coefficient matrix, and the design of operation and iteration convergence criteria; The image obtained by combining BPT with the maximum entropy method is used as the initial value of the SIRT algorithm, and the radon function is used to randomly select the coefficient matrix. For the convergence criterion, forced convergence is used here; Step 3.2, using the multi-grid method to focus the iteration process on the reconstruction of low-resolution images, the amount of calculation is significantly reduced, and the iteration speed of the SIRT algorithm can be greatly improved; Step 3.3, the image obtained by BPT is divided into three grids. According to the strategy of "fine mesh smoothing, coarse mesh correction", it is combined with SIRT and iterated in three grids respectively.

4. A coal seam radio wave perspective geological interpretation image reconstruction method based on multi-grid-BPT-improved SIRT according to claim 1, characterized in that said Step 3 includes the following: The existing technical idea of ​​SIRT is to use all the rays passing through the pixel. In the iterative process, the update amount of each pixel of the image is to take the weighted average of the correction of all projection lines according to the contribution factor, and then back-project it to correct the image until the iteration requirements are met. The iteration can be ended. Based on the SIRT algorithm in the reconstruction of mine radio wave fluoroscopic CT images, the following algorithm formula is given: in, a ij is the length of the i-th ray in the j-th grid; l i is the length of the ray; Y is the inversion value of the jth grid in the qth iteration; i q is the estimated attenuation value of the i-th ray in the q-th iteration; r is the damping factor 0 <r≤1; The multi-grid method is an iterative method used to solve linear equations. In the process of using the multi-grid method, the iteration process is concentrated on the reconstruction of low-resolution images, the amount of calculation is significantly reduced, and the iteration speed of the SIRT algorithm can be greatly improved. On the basis of SIRT, the idea of ​​multi-grid is combined with SIRT, and the reconstructed image is obtained after iteration.

Images