AWTV-MSART coal seam radio wave perspective geological interpretation image reconstruction method and system

Abstract

The invention relates to an AWTV-MSART coal seam radio wave perspective geological interpretation image reconstruction method and system, and belongs to the technical field of mine engineering geophysical prospecting. The method comprises the following steps: firstly, preprocessing coal rock electromagnetic wave detection data to obtain geological data required by reconstruction; secondly, pixel normalization weight is introduced on the basis of a traditional SART algorithm, an MSART algorithm is obtained, and the electromagnetic wave field intensity is obtained by solving a Maxwell equation; then, an adaptive weighted total variation (AWTV) method is adopted to optimize the image, noise and artifacts are suppressed, and edge details are enhanced at the same time; and through an FISTA acceleration algorithm, the convergence speed is improved, and the reconstruction efficiency is improved. And finally, evaluating the image quality by using a signal-to-noise ratio (SNR), and ensuring that the image quality is qualified when the signal-to-noise ratio is greater than 25dB. The method can effectively improve the image reconstruction quality, and is suitable for complex geological conditions with large noise or sparse data.

Description

Technical Field

[0001] The present invention relates to a method and system for reconstructing a geological interpretation image of coal seam radio wave penetration of AWTV-MSART, belonging to the technical field of mine engineering geophysical prospecting. Background Art

[0002] Traditional electromagnetic wave techniques for detecting fault structures in coal and rock mainly use mine direct current electrical prospecting, mine transient electromagnetic prospecting, radio wave penetration, ground penetrating radar, and seismic prospecting methods. With the development of technology and years of efforts, significant progress has been made in the theory, technology, and exploration equipment of mine direct current electrical prospecting and radio wave penetration methods.

[0003] In the present invention, the study of faults in coal and rock mainly relies on the method of radio wave penetration. When electromagnetic waves propagate in underground rock formations, due to the differences in the electrical properties of various rocks and minerals, there are certain differences in their absorption of electromagnetic wave energy, and different electromagnetic waves also have different detection angles for rock formations. Considering the error problem in the reconstruction of electromagnetic wave radio penetration images, through the detection of hundreds of working faces, it can be fully demonstrated that the tunnel radio wave penetration method can delineate the normal area and abnormal area within the working face. In addition, during the reconstruction process of radio wave penetration images, when fractures or cavities occur, which cause refraction and reflection of electromagnetic waves, energy loss of electromagnetic waves will occur, which is the so-called attenuation amount. However, when electromagnetic waves propagate in underground rock formations, if there are water-bearing sections, 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, signal significance anomalies and penetration anomalies will occur.

[0004] Although the traditional SART algorithm has made great improvements in convergence speed and consistency compared to ART, it still has some disadvantages. It is easily interfered by noise when processing sparse projection data, resulting in artifacts and loss of details in the reconstructed image; due to the lack of special optimization for edges and noise, edge details may be over-smoothed; in addition, although the pixel-by-pixel iterative update of SART simplifies the calculation, there is still a problem of insufficient computational efficiency under large-scale data. Therefore, the traditional SART has limited performance in reconstructing high-quality images with high noise and sparse sampling data and cannot meet the requirements of complex applications. The present invention provides a method for reconstructing a geological interpretation image of coal seam radio wave penetration of AWTV-MSART. Summary of the Invention

[0005] The technical problem solved by the present invention is that the present invention provides a method and system for reconstructing the geological interpretation image of coal seam radio wave penetration of AWTV-MSART, which greatly improves the calculation efficiency and accuracy, thereby solving the problems of poor resolution and slow iteration speed in the iterative process. The present invention effectively improves the image reconstruction quality and adapts to the image reconstruction tasks under complex geological conditions with high noise or sparse data.

[0006] The technical solution of the present invention is: a method for reconstructing the geological interpretation image of coal seam radio wave penetration of AWTV-MSART, the method comprising:

[0007] Step1. Preprocess the data of coal and rock electromagnetic wave detection and reception, determine the coal and rock conditions in the area where the mine is located, obtain the projection data required for the reconstruction algorithm according to the difference value before and after the electromagnetic wave penetrating the ore layer in the mine, and invert the geological conditions of the mine;

[0008] Step2. Use the initialized reconstruction image obtained by the SART algorithm based on pixel normalization weights as the initial value of the iteration, and then solve the electromagnetic field strength according to Maxwell's equations;

[0009] Step3. Optimize the reconstruction image by using the adaptive weighted total variation method AWTV;

[0010] Step4. Accelerate the convergence of the reconstruction image through the fast iterative shrinkage threshold algorithm FISTA;

[0011] Step5. Evaluate the reconstruction image by using the signal-to-noise ratio of the image. When the signal-to-noise ratio is greater than the quantization evaluation index, the image quality is qualified. When the signal-to-noise ratio is less than the quantization evaluation index, iteratively execute Step2-Step4 until the requirements of the quantization evaluation index are met.

[0012] Further, the Step1 includes:

[0013] For the concealed geological structures in the coal mine, multi-scale detection is carried out from the spatial dimension; the specific method is: in the process of detecting with parallel electromagnetic wave beams, multi-scale detection is carried out on the attenuation coefficients at multiple angles, widths, and different regions of the coal mine to obtain more comprehensive coal and rock structure data information, including both global overall information and local detailed information.

[0014] Further, the Step2 includes:

[0015] (1) Initialize the projection data to generate an initialized reconstruction image; the process of generating the initialized reconstruction image is expressed as:

[0016] n = 1 and F MSART-DATA (n,0) = 0 (1)

[0017] where n is the total number of iterations, and F MSART-DATA is the reconstructed image by the MSART algorithm, and F MSART-DATA (n, 0) represents the projection value of the initial image;

[0018] (2) The SART algorithm based on pixel-normalized weights is the MSART algorithm that introduces pixel-normalized weights on the basis of the traditional SART algorithm; the MSART algorithm normalizes the updated value using pixel weights according to the formula of SART; the iterative update formula of the SART algorithm based on pixel-normalized weights, that is, the MSART algorithm, is:

[0019]

[0020] where k represents the number of iterations, 0 ≤ d < N, N = W × H is the number of projection directions, r ∈ [0, …, N r-1 , N C is the number of projections along one direction, W is the M × N weight matrix, M = N × N r is the total number of projections, θ d is the projection angle, is the line segment (d, r) passing through the image, F represents the reconstructed image, R represents the sinogram, λ is the relaxation factor that can accelerate convergence, and R k represents the relaxation factor parameter; F k,d represents the inversion value of the d-th grid at the k-th iteration; F k,d-1 represents the inversion value of the (d - 1)-th grid at the k-th iteration; H is the number of projection directions (the total number of projection angles), indicating how many projections at different angles are made; C represents the number of single-direction projections (the number of projection lines / rays in each projection direction); N r represents the r-th projection number in one direction; W(θ d , r) is the row corresponding to the d-th projection direction and the r-th ray of the coefficient matrix W, indicating which pixels the ray passes through in the image and the path length; F k,d-1 (θ d , r) is the projection of the reconstructed image in this direction; D is the norm of the line segment (d, r) passing through the image;

[0021] (3) Select coal roadways with simple geological conditions and few interference factors, arrange 1 - 3 emission points, and observe the field strength values of each observation point from the transmitter; then detect the attenuation amount of the electromagnetic wave, and the amount of attenuation depends on the absorption amount of the coal seam for the electromagnetic wave; when the electromagnetic wave propagates in coal and rock, part of the electromagnetic energy is gradually absorbed and attenuated as the distance increases, and at this time, β represents the coal seam attenuation coefficient; the calculation formula of the coal seam attenuation coefficient β is:

[0022]

[0023] In the formula, β is the attenuation coefficient of the coal seam (dB / m); H1 is the field strength value at the first measurement point (dB); H2 is the field strength value at the second measurement point (dB); r1(dB) and r2(dB) represent the path loss correction terms, which are the signal losses caused by the propagation path from the emission point to the first and second measurement points, with the unit of dB. They represent the intensity attenuation that should occur when the electromagnetic wave propagates a distance of r1(m) and r2(m) under the ideal condition of no coal seam absorption; r1(m) and r2(m) represent the distances between the transmitting antenna and the first and second receiving measurement points, with the unit of meter. This is one of the path lengths of the electromagnetic wave propagating in the coal seam. The magnitudes of r1(dB) and r2(dB) determine the distance the signal propagates through and are also important input parameters for calculating the path loss correction terms.

[0024] The calculation basis of the MSART iterative algorithm is to solve a system of linear equations. However, after obtaining the data, it is necessary to consider whether the equation has a solution. First, the judgment conditions for the system of linear equations are given below. The coefficient equation and coefficient matrix for linear iteration can be obtained, and finally, it becomes calculating the following equation AX = P. The objective function equation of the least squares method is used to optimize and determine whether the system of linear equations AX = P has a solution. A is the coefficient matrix, X represents the reconstructed image to be solved, and P represents the projection data vector.

[0025] The objective function is established below using the existence condition of the solution:

[0026] J(X) = ||AX - P 2 || = (AX - P) T (AX - P)(4)

[0027] This equation is the objective function of the least squares method. Optimizing this function can be used for judgment. Take the partial derivative of the objective function equation of the least squares method:

[0028]

[0029] Let the partial derivative equation of the objective function of the least squares method be zero, and we get:

[0030] 2A T AX - 2A T P = 0 (6)

[0031] Based on the above formula, the optimal solution of the least squares method is obtained:

[0032] X = (A T A) -1 A T P (7)

[0033] The above formula is used to classify and discuss the solution situation of the system of linear equations. In the MSART algorithm, multiple iterations are performed on a certain point to reconstruct the image.

[0034] During radio wave perspective exploration, point-by-point detection operations were performed on coal and rock, and the obtained data formed a matrix. This matrix served as the coefficient matrix A of a system of linear equations, and a reconstructed image was obtained through linear iteration of this coefficient matrix A.

[0035] Furthermore, in Step 3, after restricting all pixel values of the reconstructed image to non-negative values, the weighted total variation (WTV) was used to suppress artifacts and noise in the reconstructed image and enhance edge details by weighting the image gradients. The adaptive weights were dynamically adjusted according to the gradient intensity of the local image, enabling appropriate processing of the smooth regions and edge regions respectively, with the overall aim of optimizing the image quality.

[0036] Furthermore, Step 3 includes:

[0037] (1) Performing pixel positive constraint processing on the reconstructed image: By checking the pixel values of the reconstructed image pixel by pixel, all negative values were set to zero, and only non-negative values were retained, generating an image result F pos (n) that conforms to physical meaning; the process of positive constraint is expressed as:

[0038]

[0039] (2) Performing adaptive weighted total variation processing on the reconstructed image after pixel positive constraint processing: Using the weighted total variation to suppress artifacts and noise in the reconstructed image and enhance edge details by weighting the gradients of the reconstructed image; the adaptive weights were dynamically adjusted according to the gradient intensity of the local image to enable appropriate processing of the smooth regions and edge regions respectively, with the overall aim of optimizing the image quality;

[0040] The weight calculation formula for the weighted total variation is as follows:

[0041]

[0042] where ω 11 , ω 12 , ω 21 , ω 22 are weighting coefficients, and G x , G y , G xy , G yx are the horizontal, vertical, and two diagonal partial gradient operators respectively, and h1, h2 are scale factors that control the diffusion intensity during each iteration;

[0043] The calculation process of the adaptive weighted total variation is expressed as: Applying the TV gradient descent method, for m1 = 1,..., N grad ;

[0044]

[0045] d = ||f TV-GRAD (n,1)-f MSART-GRAD (n)||(11)

[0046] f MSART-DATA (n)=f TV-GRAD (n,1)(12)

[0047]

[0048] Among them, N grad is the number of iterations of the TV term, v(n,m1) represents the gradient direction vector of the image in the m1-th TV gradient descent in the n-th iteration, m1 represents the number of times of TV gradient descent, represents the partial derivative of the horizontal and vertical gradient parts of the weighted total variation with respect to the pixel f s,t of, represents the partial derivative of the two diagonal direction gradient parts of the weighted total variation with respect to the pixel f s,t of, γ represents the proportionality factor that controls the weight of the diagonal direction gradient in the total variation, f TV-GRAD (n,m1) represents the image in the m1-th TV gradient descent iteration in the n-th iteration, f MSART-DATA (n) represents the image calculated by the MSART algorithm in the n-th iteration, b represents the learning rate / step size factor, which is used to control the update speed, ||v|| represents the L2 norm of the vector v, which is used to normalize the gradient direction.

[0049] Furthermore, in the said Step4, the process of accelerating the convergence of the reconstructed image by the Fast Iterative Shrinkage Threshold Algorithm FISTA is expressed as:

[0050]

[0051]

[0052] Among them, t n represents the FISTA dynamic acceleration parameter of the n-th iteration, which is used to update the momentum, t n+1 represents the acceleration parameter of the (n + 1)-th iteration, f MSART-DATA (n + 1,0) represents the image after FISTA acceleration, which is used as the initial value for the next round of MSART projection consistency iteration, f TV-GRAD (n) represents the image result after TV gradient descent in the n-th iteration, f TV-GRAD (n + 1) represents the image result after TV gradient descent in the (n + 1)-th iteration.

[0053] Furthermore, in the said Step5, the signal-to-noise ratio formula of the image is expressed as:

[0054]

[0055] where w and h are the width and height of the image respectively, and p ij is the pixel value corresponding to the ij position.

[0056] The present invention also provides a coal seam radio wave penetration geological interpretation image reconstruction system based on the AWTV-MSART model. The system includes a module for executing the coal seam radio wave penetration geological interpretation image reconstruction method of the above-mentioned AWTV-MSART.

[0057] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. The processor executes the coal seam radio wave penetration geological interpretation image reconstruction method of the above-mentioned AWTV-MSART.

[0058] The beneficial effects of the present invention are as follows:

[0059] 1. First, the present invention preprocesses the coal and rock electromagnetic wave detection data to obtain the geological data required for reconstruction. Secondly, pixel normalization weights are introduced on the basis of the traditional SART algorithm to obtain the MSART algorithm, and the electromagnetic field strength is obtained by solving the Maxwell equation. Then, the adaptive weighted total variation (AWTV) method is used to optimize the image, suppress noise and artifacts, and enhance edge details at the same time. The FISTA acceleration algorithm is used to improve the convergence speed and enhance the reconstruction efficiency. Finally, the signal-to-noise ratio (SNR) is used to evaluate the image quality, and it is ensured that the image quality is qualified when the SNR is greater than 25 dB. The method of the present invention effectively improves the image reconstruction quality and adapts to complex geological conditions with high noise or sparse data.

[0060] 2. Through the image reconstruction algorithm, the abnormal attenuation values of electromagnetic waves during coal and rock detection can be effectively assisted in detection. According to the parameters included in the reconstructed image, such as position, size, and dielectric constant, the reasons for the abnormal electromagnetic waves can be judged, 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 the personal injuries occurring in coal and rock mines. For example, there will be situations of coal and rock flooding in water-containing areas, unsafe situations for workers during operation in faults, and easy collapse of coal and rock in collapse columns. The abnormal conditions in coal and rock can be assisted in judgment by scientific means.

[0061] 3. By introducing an adaptive weight to dynamically adjust the local gradient of the image, the present invention can effectively preserve edge details while suppressing noise and artifacts; the optimization model based on weighted total variation enhances the reconstruction quality of sparse sampling data and reduces the reconstruction error caused by noise amplification in the traditional SART algorithm; in addition, this method significantly improves the convergence speed of the algorithm through Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), and has both robustness and efficiency, being applicable to image reconstruction tasks under high-noise and complex geological conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 is a physical scene diagram of the present invention;

[0063] Figure 2 is a flowchart of the present invention;

[0064] Figure 3 is a graph showing the changing trend of the signal-to-noise ratio (SNR) of various image reconstruction methods in different numbers of iterations in the embodiments of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0065] The following is to make the objectives, technical solutions and advantages of the embodiments of the present invention clearer. The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention. It should be noted that, without conflict, the embodiments and features in the embodiments in this application can be combined with each other arbitrarily.

[0066] In the aspect of coal and rock image detection, for the research on image reconstruction methods based on coal and rock, only a very small number of coal mine scholars and experts study the way of combined detection of mine penetration and traditional mine wireless electromagnetic wave penetration for hybrid imaging; in the aspect of coal and rock stratification interface detection, the image imaging speed and imaging quality are important indicators; usually, the higher the number of iterations in coal and rock detection, the finer it is, but the longer the time is wasted.

[0067] Traditional mine wireless electromagnetic wave exploration visualizes coal and rock faults by using a single detection data and applying a common algebraic iterative algorithm.

[0068] To solve the above problems, an embodiment of the present invention provides a method for reconstructing a geological interpretation image of coal seam radio wave penetration based on AWTV-MSART.

[0069] First, the embodiments of the present invention will be described with reference to the accompanying drawings.

[0070] Embodiment 1: As Figures 1 - 3As shown, a method for reconstructing the geological interpretation image of coal seam radio wave penetration in AWTV-MSART improves the existing back-projection filtering reconstruction algorithm. First, preprocess the coal and rock electromagnetic wave detection data to obtain the geological data required for reconstruction. Second, introduce pixel normalization weights based on the traditional SART algorithm to obtain the MSART algorithm and obtain the electromagnetic field strength by solving Maxwell's equations. Then, use the adaptive weighted total variation (AWTV) method to optimize the image, suppress noise and artifacts, and enhance edge details at the same time. Improve the convergence speed through the FISTA acceleration algorithm and enhance the reconstruction efficiency. Finally, use the signal-to-noise ratio (SNR) to evaluate the image quality, and ensure that the image quality is qualified when the signal-to-noise ratio is greater than 25 dB. This method can effectively improve the image reconstruction quality and adapt to complex geological conditions with high noise or sparse data. The specific steps of the method include:

[0071] Step1. Preprocess the emission and reception data of coal and rock electromagnetic wave detection, determine the coal and rock conditions in the mining area, obtain the projection data required for the reconstruction algorithm according to the difference value before and after the electromagnetic wave penetrating the ore layer in the mine, and invert the geological conditions of the mine;

[0072] Assume that the interference factors of coal and rock geology are few and the structure is simple, and there are circular isomers. For the safety of coal and rock industrial and mining operations, certain measures need to be taken to determine the position of the isomers. At this time, the radio wave penetration method is used to conduct grid detection on coal and rock, and a matrix can be obtained. Using this matrix as the coefficient matrix, linear iteration can be performed on the linear equations. As Figure 1 shown, all operations of the present invention are based on the following scene image, that is, the cross-section display diagram of the intake airway and the return airway. Here, the emission point is a single emission point 7, and the value is H0 at this time. Its corresponding receiving points are a group of 10 points 2-11. At this time, the values are H i respectively; on the contrary, the return airway here can also be used as the emission area, and it is also a single-point emission and 10-point reception. The variable of the isomer here is represented by F (x，y) and the polar coordinate is represented by r i，j .

[0073] Regarding the image reconstruction problem in mine radio wave penetration, many technical studies mainly focus on analytical algorithm image reconstruction and iterative algorithm image reconstruction. In the iterative algorithms, even when the projection data is insufficient and the projection angle distribution is uneven, the iterative algorithms can still solve the problem. The principle of SART is based on the idea of gradual approximation. By using the error between the projection data and the current image estimate, the image is updated synchronously ray by ray to meet the consistency of the projection data. Different from ART, SART considers the average contribution of a group of projections in each iteration, thus reducing the local oscillation of each update and making the convergence faster and smoother. Its update formula adjusts the pixel values through a weighted error correction term, improving the stability of the reconstruction while ensuring global consistency.

[0074] Further, the Step1 includes:

[0075] For the concealed geological structures in coal mines, multi-scale detection is carried out from the spatial dimension; the specific method is: during the detection using parallel electromagnetic beams, multi-scale detection is carried out on the attenuation coefficients at multiple angles, widths, and different regions of the coal mine to obtain more comprehensive coal and rock structure data information, including both global overall information and local detailed information.

[0076] Step2: Use the initial reconstructed image obtained by the SART algorithm based on pixel normalization weights (MSART algorithm) as the initial value of the iteration, and then solve the electromagnetic field strength according to Maxwell's equations;

[0077] Further, the Step2 includes:

[0078] (1) Initialize the projection data to generate an initial reconstructed image; the process of generating the initial reconstructed image is expressed as:

[0079] n = 1 and F MSART-DATA (n,0) = 0 (1)

[0080] where n is the total number of iterations, F MSART-DATA is the reconstructed image of the MSART algorithm, and F MSART-DATA (n,0) represents the projection value of the initial image;

[0081] (2) The SART algorithm based on pixel normalization weights is the MSART algorithm that introduces pixel normalization weights on the basis of the traditional SART algorithm; the MSART algorithm normalizes the updated value using pixel weights according to the formula of SART to improve the accuracy and consistency of the reconstructed image; the iterative update formula of the SART algorithm based on pixel normalization weights, that is, the MSART algorithm, is:

[0082]

[0083] Among them, k represents the number of iterations, 0 ≤ d < N, N = W × H is the number of projection directions, r ∈ [0, …, N r-1 , N C is the number of projections along one direction, W is the M × N weight matrix, M = N × N r is the total number of projections, θ d is the projection angle, is the line segment (d, r) passing through the image, F represents the reconstructed image, R represents the sinogram, λ is a relaxation factor that can accelerate convergence, R k represents the relaxation factor parameter; F k,d represents the inversion value of the d-th grid at the k-th iteration; F k,d-1 represents the inversion value of the (d - 1)-th grid at the k-th iteration; H is the number of projection directions (total number of projection angles), indicating how many different-angle projections are made; C represents the number of single-direction projections (number of projection lines / rays per projection direction); N r represents the r-th projection number in one direction; W(θ d , r) is the row corresponding to the d-th projection direction and the r-th ray of the coefficient matrix W, indicating which pixels the ray passes through in the image and the path length; F k,d-1 (θ d , r) is the projection of the reconstructed image in this direction; D is the norm of the line segment (d, r) passing through the image;

[0084] (3) Select coal roadways with simple geological conditions and few interference factors, arrange 1 - 3 emission points, and observe the field strength values at each observation point from the transmitter; then detect the attenuation amount of the electromagnetic wave, and the amount of attenuation depends on the absorption amount of the coal seam for the electromagnetic wave; when the electromagnetic wave propagates in coal and rock, a part of the electromagnetic energy is gradually absorbed and attenuated as the distance increases, and at this time β represents the coal seam attenuation coefficient; the calculation formula for the coal seam attenuation coefficient β is:

[0085]

[0086] In the formula, β is the attenuation coefficient of the coal seam (dB / m); H1 is the field strength value at the first measurement point (dB); H2 is the field strength value at the second measurement point (dB); r1(dB) and r2(dB) represent the path loss correction terms, which are the signal losses caused by the propagation path from the emission point to the first and second measurement points, with the unit of dB. They represent the intensity attenuation that should occur when the electromagnetic wave propagates over distances r1(m) and r2(m) under the ideal condition of no coal seam absorption; r1(m) and r2(m) represent the distances between the transmitting antenna and the first and second receiving measurement points, with the unit of meter, which is one of the path lengths of the electromagnetic wave propagating in the coal seam. The magnitudes of r1(dB) and r2(dB) determine the distance traveled by the signal and are also important input parameters for calculating the path loss correction terms. The above attenuation absorption coefficient, field strength, and distance are related, which well describes the attenuation of the electromagnetic wave.

[0087] The calculation basis of the MSART iterative algorithm is to solve a system of linear equations. However, after obtaining the data, it is necessary to consider whether the equation has a solution. First, the judgment conditions for the system of linear equations are given below. The coefficient equation and coefficient matrix of the linear iteration can be obtained, and finally, it becomes the calculation of the following equation AX = P. The objective function equation of the least squares method is used for optimization to determine whether the system of linear equations AX = P has a solution. A is the coefficient matrix, X represents the reconstructed image to be solved, and P represents the projection data vector.

[0088] The following is to establish the objective function and use the existence condition of the solution:

[0089] J(X) = ||AX - P 2 || = (AX - P) T (AX - P)(4)

[0090] This equation is the objective function of the least squares method. Optimizing this function can be used for judgment. Take the partial derivative of the objective function equation of the least squares method:

[0091]

[0092] Let the partial derivative equation of the objective function of the least squares method be zero, and we get:

[0093] 2A T AX - 2A T P = 0 (6)

[0094] According to the above formula, the optimal solution of the least squares method is obtained:

[0095] X = (A T A) -1 A T P (7)

[0096] The above formula is used to classify and discuss the solutions of linear equations. In the MSART algorithm, a certain point is iterated multiple times to reconstruct the image.

[0097] During radio wave penetration, point-by-point detection operations are performed on coal and rock, and the obtained data form a matrix. This matrix serves as the coefficient matrix A of the linear equation system, and linear iteration is performed on this coefficient matrix A to obtain the reconstructed image.

[0098] Step3. Optimize the reconstructed image using the adaptive weighted total variation method AWTV;

[0099] Furthermore, in the said Step3, after restricting all pixel values of the reconstructed image to be non-negative, the weighted total variation WTV (Weighted Total Variation) is used to suppress artifacts and noise in the reconstructed image and enhance edge details by weighting the image gradient. The adaptive weight dynamically adjusts the weight according to the gradient intensity of the local image, so that the smooth area and the edge area are respectively properly processed. The overall purpose is to optimize the image quality, retain important details, and reduce noise interference.

[0100] Furthermore, the said Step3 includes:

[0101] (1) Perform pixel positive constraint processing on the reconstructed image: By checking the pixel values of the reconstructed image pixel by pixel, set all negative values to zero and only retain non-negative values to generate an image result F pos (n); This step can effectively avoid the interference of negative values on subsequent optimization and physical interpretation, and at the same time improve the stability and robustness of the algorithm, providing a reliable initial image basis for subsequent iteration and quality optimization; The process of positive constraint is expressed as:

[0102]

[0103] (2) Perform adaptive weighted total variation processing on the reconstructed image after pixel positive constraint processing: Use the weighted total variation to suppress artifacts and noise in the reconstructed image and enhance edge details by weighting the gradient of the reconstructed image; The adaptive weight dynamically adjusts the weight according to the gradient intensity of the local image to properly process the smooth area and the edge area respectively. The overall purpose is to optimize the image quality;

[0104] The weight calculation formula of the weighted total variation is as follows:

[0105]

[0106] where ω 11 、ω 12 、ω 21 、ω 22is the weighting coefficient, G x , G y , G xy , G yx are the horizontal, vertical, and two diagonal partial gradient operators respectively, and h1, h2 are the scale factors that control the diffusion intensity during each iteration;

[0107] The calculation process of adaptive weighted total variation is expressed as: applying the TV gradient descent method, for m1 = 1, …, N grad ;

[0108]

[0109] d = ||f TV-GRAD (n,1) - f MSART-GRAD (n)|| (11)

[0110] f MSART-DATA (n) = f TV-GRAD (n,1) (12)

[0111]

[0112] where N grad is the number of iterations of the TV term, v(n,m1) represents the gradient direction vector of the image in the m1-th TV gradient descent in the n-th iteration, m1 represents the number of times of TV gradient descent, represents the partial derivative of the horizontal and vertical gradient parts of the weighted total variation with respect to the pixel f s,t ; represents the partial derivative of the two diagonal direction gradient parts of the weighted total variation with respect to the pixel f s,t ; γ represents the scale factor that controls the weight of the diagonal direction gradient in the total variation, f TV-GRAD (n,m1) represents the image in the m1-th TV gradient descent iteration in the n-th iteration, f MSART-DATA (n) represents the image calculated by the MSART algorithm in the n-th iteration, b represents the learning rate / step size factor, which is used to control the update speed, ||v|| represents the L2 norm of the vector v, which is used to normalize the gradient direction.

[0113] Step4. Accelerate the convergence of the reconstructed image through the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA); FISTA is an accelerated gradient descent method, aiming to improve the convergence speed of the optimization process. By introducing an acceleration factor and historical iteration results, FISTA can quickly approximate the optimization goal while reducing the computational overhead, making the image reconstruction algorithm more efficient;

[0114] Furthermore, in the said Step4, the process of accelerating the convergence of the reconstructed image through the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) is expressed as:

[0115]

[0116]

[0117] where t n represents the FISTA dynamic acceleration parameter for the n-th iteration, which is used to update the momentum, and t n+1 represents the acceleration parameter for the (n + 1)-th iteration, and f MSART-DATA (n + 1, 0) represents the image after FISTA acceleration and is used as the initial value for the next round of MSART projection consistency iteration, and f TV-GRAD (n) represents the image result after TV gradient descent in the n-th iteration, and f TV-GRAD (n + 1) represents the image result after TV gradient descent in the (n + 1)-th iteration.

[0118] Step 5. Evaluate the reconstructed image using the signal-to-noise ratio (SNR) of the image. When the SNR is greater than the quantization evaluation index, the image quality is qualified; when the SNR is less than the quantization evaluation index, iteratively execute Step 2 - Step 4 until the requirements of the quantization evaluation index are met.

[0119] The signal-to-noise ratio is the ratio of the signal mean to the background standard deviation, and its formula is as follows:

[0120]

[0121] where μ sig represents the signal mean (image mean); σ bg represents the background standard deviation.

[0122] For an image, the "signal value" here is often the gray value. Sometimes the denominator uses the variance of the background signal value, and the physical meaning it represents is the noise power. For a high-contrast black background image, the result directly calculated by the above formula is usually infinite. Therefore, we use the signal mean and the signal standard deviation (image standard deviation) to measure:

[0123]

[0124] where σ sig represents the signal standard deviation.

[0125] The formula for calculating the image mean is:

[0126]

[0127] where w and h are the width and height of the image respectively, and p ij is the pixel value corresponding to the ij position.

[0128] The formula for calculating the image standard deviation:

[0129]

[0130] The signal-to-noise ratio formula of the said image is expressed as:

[0131]

[0132] where w and h are the width and height of the image respectively, and p ij is the pixel value corresponding to the ij position.

[0133] In the application of wireless electromagnetic wave perspective, the qualified level of the signal-to-noise ratio depends on multiple factors, including the specific electromagnetic wave detection system, geological conditions, depth and characteristics of coal and rock, etc. Generally speaking, the requirement for the signal-to-noise ratio in underground coal and rock detection is relatively high to ensure the accurate detection of underground structures.

[0134] Some proposed 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. The present invention selects the quantization evaluation index a = 25dB. The present invention selects 25dB as the quantization evaluation index. When the signal-to-noise ratio of the obtained reconstructed image is greater than or equal to 25dB, the quality of the image is qualified. When the signal-to-noise ratio of the obtained reconstructed image is less than 25dB, then Steps 2 - 4 are iteratively executed until the requirement is met.

[0135] The present invention also provides a coal seam radio wave perspective geological interpretation image reconstruction system based on the AWTV-MSART model, and the said system includes: a module for executing the coal seam radio wave perspective geological interpretation image reconstruction method of the said AWTV-MSART.

[0136] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the said memory and operable on the said processor, and the said processor executes the coal seam radio wave perspective geological interpretation image reconstruction method of the said AWTV-MSART.

[0137] To verify the effectiveness of the present invention, experimental verification has been carried out for the present invention. Image reconstructions have been carried out using the method of the present invention and traditional TV, AwTV, NTV, and NWTV methods respectively. The change trends of the signal-to-noise ratio (SNR) of the method of the present invention and various traditional image reconstruction methods at different iteration times are as Figure 3 shown.

[0138] Figure 3 It clearly shows the change trends of the signal-to-noise ratio (SNR) of various image reconstruction methods at different iteration times. Compared with traditional TV, AwTV, NTV, and NWTV methods, the AWTV-MSART algorithm proposed by the present invention shows significant performance advantages in the process of image reconstruction.

[0139] The specific embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the scope of knowledge possessed by those of ordinary skill in the art.

Claims

1. A method for reconstructing a geological interpretation image of coal seam radio wave penetration of AWTV-MSART, characterized in that: The method includes: Step 1: Preprocess the data of coal-rock electromagnetic wave detection and reception, determine the coal-rock situation in the area where the mine is located, obtain the projection data required for the reconstruction algorithm based on the difference value of the electromagnetic wave before and after penetrating the ore layer in the mine, and inversely deduce the geological situation of the mine; Step 2: Use the initialized reconstruction image obtained by the SART algorithm based on pixel normalization weight as the initial value of the iteration, and then solve the electromagnetic field strength according to Maxwell's equations; Step 3: Optimize the reconstruction image by using the adaptive weighted total variation method AWTV; Step 4: Accelerate the convergence of the reconstruction image through the fast iterative shrinkage threshold algorithm FISTA; Step 5: Evaluate the reconstruction image by using the signal-to-noise ratio of the image. When the signal-to-noise ratio is greater than the quantization evaluation index, the image quality is qualified. When the signal-to-noise ratio is less than the quantization evaluation index, iteratively execute Step 2 - Step 4 until the requirements of the quantization evaluation index are met.

2. A method for reconstructing a geological interpretation image of coal seam radio wave penetration of AWTV-MSART according to claim 1, characterized in that: The said Step 1 includes: For the concealed geological structure in the coal mine, multi-scale detection is carried out from the spatial dimension; the specific method is: during the detection using parallel electromagnetic wave beams, multi-scale detection is carried out on the attenuation coefficient at multiple angles, widths, and different areas of the coal mine to obtain more comprehensive coal-rock structure data information, including both global overall information and local detailed information.

3. A method for reconstructing a geological interpretation image of coal seam radio wave penetration in AWTV-MSART according to claim 1, characterized in that: The said Step 2 includes: (1) Initialize the projection data to generate an initialized reconstruction image; the process of generating the initialized reconstruction image is expressed as: n = 1 and F MSART-DATA (n, 0) = 0 (1) where n is the total number of iterations, and F MSART-DATA is the reconstructed image by the MSART algorithm, and F MSART-DATA (n, 0) represents the projection value of the initial image; (2) The SART algorithm based on pixel normalization weight is the MSART algorithm that introduces pixel normalization weight on the basis of the traditional SART algorithm; the MSART algorithm normalizes the updated value using pixel weights according to the formula of SART; the iterative update formula of the SART algorithm based on pixel normalization weight, that is, the MSART algorithm, is: where k represents the number of iterations, 0 ≤ d < N, N = W × H is the number of projection directions, r ∈ [0, …, N r-1 , N C is the number of projections along one direction, W is the M × N weight matrix, M = N × N r is the total number of projections, θ d is the projection angle, is the line segment (d, r) passing through the image, F represents the reconstructed image, R represents the sinogram, λ is a relaxation factor that can accelerate convergence, R k represents the relaxation factor parameter; F k,d represents the inversion value of the d-th grid at the k-th iteration; F k,d-1 represents the inversion value of the (d - 1)-th grid at the k-th iteration; H is the number of projection directions (total number of projection angles), indicating how many different angle projections are made; C represents the number of single-direction projections (number of projection lines / rays in each projection direction); N r represents the r-th projection number in one direction; W(θ d , r) is the row corresponding to the d-th projection direction and the r-th ray of the coefficient matrix W, indicating which pixels the ray passes through in the image and the path length; F k,d-1 (θ d , r) is the projection of the reconstructed image in this direction; D is the norm of the line segment (d, r) passing through the image; (3) Select a coal roadway with simple geological conditions and few interference factors, arrange 1 - 3 emission points, and observe the field strength values at each observation point from the transmitter; then detect the attenuation amount of the electromagnetic wave, and the amount of attenuation depends on the absorption amount of the coal seam for the electromagnetic wave; when the electromagnetic wave propagates in the coal rock, part of the electromagnetic energy is gradually absorbed and attenuated as the distance increases. At this time, β represents the coal seam attenuation coefficient; the calculation formula of the coal seam attenuation coefficient β is: In the formula, β is the coal seam attenuation coefficient (dB / m); H1 is the field strength value of the first measurement point (dB); H2 is the field strength value of the second measurement point (dB); r1(dB) and r2(dB) represent the path loss correction terms, the signal losses caused by the propagation path from the emission point to the first and second measurement points, with the unit of dB. They represent the intensity attenuation that should be generated by the electromagnetic wave propagation distances r1(m) and r2(m) under the ideal condition of no coal seam absorption. r1(m) and r2(m) represent the distances between the transmitting antenna and the first and second receiving measurement points, with the unit of meters. This is one of the path lengths of the electromagnetic wave propagation in the coal seam. The magnitudes of r1(dB) and r2(dB) determine the distance that the signal propagates through and are also important input parameters for calculating the path loss correction terms.

4. A method for reconstructing a geological interpretation image of coal seam radio wave penetration in AWTV-MSART according to claim 1, characterized in that: In Step 3, after restricting all pixel values of the reconstructed image to non - negative values, the weighted total variation (WTV) is used to suppress artifacts and noise in the reconstructed image and enhance edge details by weighting the image gradient. The adaptive weight dynamically adjusts the weight according to the gradient intensity of the local image, so that the smooth region and the edge region are appropriately processed respectively. The overall purpose is to optimize the image quality.

5. A method for reconstructing a geological interpretation image of coal seam radio wave perspective according to claim 1 of AWTV-MSART, characterized in that: Step 3 includes: (1) Perform pixel positive constraint processing on the reconstructed image: By checking the pixel values of the reconstructed image pixel by pixel, set all negative values to zero and only retain non-negative values to generate an image result F pos (n); The process of positive constraint is expressed as: (2) Perform adaptive weighted total variation processing on the reconstructed image after positive pixel constraint processing: Use weighted total variation to suppress artifacts and noise in the reconstructed image and enhance edge details by weighting the gradient of the reconstructed image; the adaptive weight dynamically adjusts the weight according to the gradient intensity of the local image to appropriately process the smooth region and the edge region respectively. The overall purpose is to optimize the image quality; The weight calculation formula of the weighted total variation is as follows: Among them, ω 11 , ω 12 , ω 21 , ω 22 are weighting coefficients, G x , G y , G xy , G yx are the horizontal, vertical, and two diagonal part gradient operators respectively, and h1, h2 are the scale factors that control the diffusion intensity during each iteration; The calculation process of adaptive weighted total variation is expressed as: applying the TV gradient descent method, for m1 = 1, …, N grad ; d = ||f TV-GRAD (n,1)-f MSART-GRAD (n)|| (7) f MSART-DATA f(n) = TV-GRAD f(n, 1) (8) Among them, N grad is the number of iterations of the TV term. v(n, m1) represents the gradient direction vector of the image in the m1-th TV gradient descent in the n-th iteration. m1 represents the number of TV gradient descents. represents the partial derivative of the horizontal and vertical gradient parts of the weighted total variation with respect to the pixel f s,t of, represents the partial derivative of the two diagonal direction gradient parts of the weighted total variation with respect to the pixel f s,t of. γ represents the proportionality factor that controls the weight of the diagonal direction gradient in the total variation. f TV-GRAD (n, m1) represents the image at the m1-th TV gradient descent iteration in the n-th iteration. f MSART-DATA (n) represents the image calculated by the MSART algorithm in the n-th iteration. b represents the learning rate / step size factor, which is used to control the update speed. ||v|| represents the L2 norm of the vector v, which is used to normalize the gradient direction.

6. A method for reconstructing a geological interpretation image of coal seam radio wave perspective in AWTV-MSART according to claim 1, characterized in that: In Step 4, the process of accelerating the convergence of the reconstructed image by the fast iterative shrinkage threshold algorithm (FISTA) is expressed as: where t n represents the FISTA dynamic acceleration parameter for the n-th iteration, which is used to update the momentum, and t n+1 represents the acceleration parameter for the (n + 1)-th iteration, and f MSART-DATA (n + 1, 0) represents the image after FISTA acceleration, which is used as the initial value for the next round of MSART projection consistency iteration, and f TV-GRAD (n) represents the image result after TV gradient descent in the n-th iteration, and f TV-GRAD (n + 1) represents the image result after TV gradient descent in the (n + 1)-th iteration.

7. A method for reconstructing a geological interpretation image of coal - seam radio - wave penetration, according to claim 1 of AWTV - MSART, characterized in that: in Step 5, the signal - to - noise ratio formula of the image is expressed as: Among them, Let \(w\) and \(h\) be the width and height of the image respectively, and \(p\) ij be the pixel value corresponding to the \(i,j\) position.

8. The coal seam radio wave perspective geological interpretation image reconstruction system based on the AWTV-MSART model is characterized in that, The system includes: a module for executing a method for reconstructing a geological interpretation image of coal - seam radio - wave penetration of AWTV - MSART according to any one of claims 1 to 7.

9. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein, When the processor executes the program, it implements a method for reconstructing a geological interpretation image of coal - seam radio - wave penetration of AWTV - MSART according to any one of claims 1 to 7.

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