Sound wave remote detection data reconstruction technology and device based on high-fidelity data mapping

Abstract

The invention provides a sound wave remote exploration data reconstruction technology and device based on high-fidelity data mapping, and the technology comprises the steps: converting sound wave remote exploration data with missing channels or bad channels into a mapping domain through employing a high-resolution Radon operator, and carrying out the separation and removal of the data in the mapping domain if the data have noise; the mapping domain data are converted back to a time domain through a high-resolution inverse radon mapping operator, and reconstruction data corresponding to a missing track or a bad track are obtained; and performing energy balance processing on the reconstructed single-channel data and the original data, and outputting reconstructed sound wave remote detection data. Compared with the prior art, the fidelity data reconstruction technology based on logging sound wave remote exploration data mapping is good in stability, high in adaptability and good in fidelity. According to the method, based on the seismic wave propagation theory, the high-fidelity data mapping operator is utilized to reconstruct the sound wave remote exploration data, the reconstruction result complies with the geophysical law, and the reasonability is high.

Description

Technical Field

[0001] This solution belongs to the field of acoustic wave remote exploration data processing in oil and gas well logging exploration technology, and specifically involves a fidelity data reconstruction technology for well logging acoustic wave remote exploration data mapping. Background Art

[0002] During the logging data acquisition process, some recording channels may be missing or bad due to equipment or operation reasons. In order to ensure the quality of subsequent imaging, data reconstruction is required for the missing channels or bad channels. Based on different principles and different mathematical algorithms, exploration geophysicists have proposed many data reconstruction methods, such as triangulation interpolation, inverse distance interpolation, radial basis function interpolation, Kriging interpolation, etc. Data mapping is a data transformation method that transforms data under one parameter configuration to data under another parameter configuration. It can be used for data reconstruction. The core of different methods producing different effects is the difference in the data mapping operators used. Different operators have different construction forms and fidelity.

[0003] Commonly used data reconstruction methods are mostly interpolation and reconstruction through different interpolation operators, such as the triangulation interpolation method mentioned above. This method is a local interpolation algorithm with simple calculation and high interpolation efficiency, but the quality of the triangulation result directly affects the interpolation result and has poor stability; inverse distance interpolation, radial basis function interpolation and Kriging interpolation are global interpolation algorithms. These types of interpolation methods do not require triangulation, have lower requirements on data distribution than local interpolation, and have relatively high interpolation accuracy. However, their application involves the optimization of key parameters such as basis functions, which has high complexity, poor adaptability and fidelity. Summary of the invention

[0004] The embodiment of the present application provides a technology for reconstructing acoustic wave remote exploration data based on high-fidelity data mapping. Starting from the theory of seismic wave propagation, a high-fidelity data mapping operator is used to reconstruct acoustic wave remote exploration data. The reconstruction result complies with geophysical laws and is highly reasonable.

[0005] In a first aspect, an embodiment of the present application provides a technology for reconstructing acoustic wave remote sensing data based on high-fidelity data mapping, including:

[0006] S101, for acoustic remote exploration data with missing or bad tracks, a high-resolution Radon operator is used to transform the data into a mapping domain. If the data has noise, it can be separated and removed in the mapping domain;

[0007] S103, transforming the mapping domain data back to the time domain through a high-resolution inverse Radon mapping operator to obtain reconstructed data corresponding to the missing track or bad track;

[0008] S105, performing energy equalization processing on the reconstructed single-channel data and the original data, and outputting the reconstructed acoustic wave remote sensing data.

[0009] In step S101, for the hyperbolic Radon transform, a sparse constraint condition is introduced, and its objective function is expressed by the following equation:

[0010]

[0011] The first term on the right side of the equation is the target expression of conventional inversion, R(m) represents the sparse constraint term, and λ represents the regularization parameter, which is used to adjust the weight between the constraint term and the observed data error.

[0012] The sparse constraint term R(m) is expressed as follows:

[0013]

[0014] Where σ is the scale factor. 1 / 2 The norm promotes the sparsity of the inversion problem, L 2 The norm ensures the stability of the solution and can alleviate the L 1 / 2 The numerical oscillation problem of the norm.

[0015] The objective function of Radon transform based on elastic semi-norm constraint is:

[0016]

[0017] It can ensure the stability and uniqueness of the solution. When σ=0, the elastic semi-norm regularization degenerates into the standard L 1 / 2 Regularization. Formula (3) contains L 1 / 2 norm, so the optimization problem is a non-convex problem. In order to solve the optimization problem, it is necessary to introduce an auxiliary variable T = m, then formula (3) is expressed as:

[0018]

[0019] Its augmented Lagrangian form is:

[0020]

[0021] In the formula, ξ is a non-negative balance term used to control the convergence speed, and c represents the Lagrange multiplier. The optimization problem of formula (5) can be solved by the ADMM algorithm. In the solution process, an intermediate variable z needs to be introduced. By fixing one variable among m, T, z and updating the other two variables, formula (5) is iteratively solved. The iterative update formula of each variable is:

[0022]

[0023] z k+1 =zk +m k+1 -T k+1 (8)

[0025] Where z = c / ξ represents the scaling Lagrange multiplier, and k represents the number of iterations.

[0026]

[0027] Where η = λ / ξ. Using (9), we can iteratively solve formula (5) and finally obtain the Radon model m' with high sparsity.

[0028] In the whole calculation process, only the inverse of a matrix [L T L+(2σ+ε)I] -1 , this matrix has nothing to do with the input data, it is only related to the dimension of the input data and can be reused.

[0029] In step S103, the mapping domain data is transformed back to the time domain through a high-resolution inverse Radon mapping operator to obtain reconstructed data corresponding to the missing track or bad track.

[0030] In step S105, the reconstructed single-channel data and the original data are subjected to energy equalization processing, and the reconstructed acoustic wave remote sensing data is output.

[0031] In a second aspect, the present application also provides an acoustic wave remote exploration data reconstruction device based on high-fidelity data mapping, comprising:

[0032] Transformation unit: For acoustic remote sounding data with missing or bad channels, a high-resolution Radon operator is used to transform the data into a mapping domain. If the data has noise, it can be separated and removed in the mapping domain.

[0033] Regression unit: transforms the mapping domain data back to the time domain through the high-resolution reverse Radon mapping operator to obtain the reconstructed data corresponding to the missing track or bad track;

[0034] Reconstruction unit: performs energy balance processing on the reconstructed single-channel data together with the original data, and outputs the reconstructed acoustic wave remote exploration data.

[0035] The transformation unit is used to introduce sparse constraints for the hyperbolic Radon transform, and its objective function is expressed by the following equation:

[0036]

[0037] The first term on the right side of the equation is the target expression of conventional inversion, R(m) represents the sparse constraint term, and λ represents the regularization parameter, which is used to adjust the weight between the constraint term and the observed data error.

[0038] The sparse constraint term R(m) is expressed as follows:

[0039]

[0040] Where σ is the scale factor. 1 / 2 The norm promotes the sparsity of the inversion problem, L 2 The norm ensures the stability of the solution and can alleviate the L 1 / 2 The numerical oscillation problem of the norm.

[0041] The objective function of Radon transform based on elastic semi-norm constraint is:

[0042]

[0043] It can ensure the stability and uniqueness of the solution. When σ=0, the elastic semi-norm regularization degenerates into the standard L 1 / 2 Regularization. Formula (3) contains L 1 / 2 norm, so the optimization problem is a non-convex problem. In order to solve the optimization problem, it is necessary to introduce an auxiliary variable T = m, then formula (3) is expressed as:

[0044]

[0045] Its augmented Lagrangian form is:

[0046]

[0047] In the formula, ξ is a non-negative balance term used to control the convergence speed, and c represents the Lagrange multiplier. The optimization problem of formula (5) can be solved by the ADMM algorithm. In the solution process, an intermediate variable z needs to be introduced. By fixing one variable among m, T, z and updating the other two variables, formula (5) is iteratively solved. The iterative update formula of each variable is:

[0048]

[0049] z k+1 =z k +m k+1 -T k+1 (8)

[0051] Where z = c / ξ represents the scaling Lagrange multiplier, and k represents the number of iterations.

[0052]

[0053] Where η = λ / ξ. Using (9), we can iteratively solve formula (5) and finally obtain the Radon model m' with high sparsity.

[0054] In the whole calculation process, only the inverse of a matrix [L T L+(2σ+ε)I] -1 , this matrix has nothing to do with the input data, it is only related to the dimension of the input data and can be reused.

[0055] In a third aspect, an embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of any of the above methods when executed by a processor.

[0056] In a fourth aspect, an embodiment of the present application provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any of the above methods when executing the program.

[0057] The embodiments of the present application are based on the following beneficial effects:

[0058] This application is a fidelity data reconstruction technology based on well logging acoustic wave remote exploration data mapping. Compared with traditional technologies, it has good stability, strong adaptability and good fidelity. Starting from the theory of seismic wave propagation, this scheme uses high-fidelity data mapping operators to reconstruct acoustic wave remote exploration data. The reconstruction results comply with geophysical laws and are highly reasonable. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 This is the flow chart of this program;

[0060] Figure 2 Another flow chart of this scheme is shown below;

[0061] Figure 3 It is part of the common shot point (CSP) gather corresponding to the actual data;

[0062] Figure 4 This is a CSP gather with one missing data and the results before and after processing by this scheme;

[0063] Figure 5 This is a CSP gather with two missing traces and the results before and after processing by this scheme.

[0064] Figure 6 For Figure 4 Comparison of original data and supplementary data of missing tracts;

[0065] Figure 7 For Figure 5 Comparison of original data and supplementary data of missing tracts;

[0066] Figure 8 The flow chart of the acoustic remote exploration data reconstruction device based on high-fidelity data mapping; DETAILED DESCRIPTION

[0067] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of 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.

[0068] In order to solve the problem of fidelity reconstruction based on acoustic sounding data mapping, it is crucial to select and design a suitable data mapping operator. In this study, a high-resolution Radon transform operator with elastic half-norm constraint was used. This operator combines the sparsity of the half-norm and the stability of the 2-norm, showing high resolution and high fidelity. The acoustic sounding data is then reconstructed through the data mapping inverse operator. Figure 1 It is a flowchart of high-fidelity data reconstruction of acoustic exploration data mapping.

[0069] like Figure 2 As shown, the acoustic wave remote exploration data reconstruction technology based on high-fidelity data mapping in this application includes:

[0070] S101, for acoustic remote exploration data with missing or bad tracks, a high-resolution Radon operator is used to transform the data into a mapping domain. If the data has noise, it can be separated and removed in the mapping domain;

[0071] S103, transforming the mapping domain data back to the time domain through a high-resolution inverse Radon mapping operator to obtain reconstructed data corresponding to the missing track or bad track;

[0072] S105, performing energy equalization processing on the reconstructed single-channel data and the original data, and outputting the reconstructed acoustic wave remote sensing data.

[0073] Optionally, in step S101, for the hyperbolic Radon transform, a sparse constraint condition is introduced, and its objective function is expressed by the following equation:

[0074]

[0075] The first term on the right side of the equation is the target expression of conventional inversion, R(m) represents the sparse constraint term, and λ represents the regularization parameter, which is used to adjust the weight between the constraint term and the observed data error.

[0076] The sparse constraint term R(m) is expressed as follows:

[0077]

[0078] Where σ is the scale factor. 1 / 2 The norm promotes the sparsity of the inversion problem, L 2 The norm ensures the stability of the solution and can alleviate the L 1 / 2 The numerical oscillation problem of the norm.

[0079] The objective function of Radon transform based on elastic semi-norm constraint is:

[0080]

[0081] It can ensure the stability and uniqueness of the solution. When σ=0, the elastic semi-norm regularization degenerates into the standard L 1 / 2 Regularization. Formula (3) contains L 1 / 2 norm, so the optimization problem is a non-convex problem. In order to solve the optimization problem, it is necessary to introduce an auxiliary variable T = m, then formula (3) is expressed as:

[0082]

[0083] Its augmented Lagrangian form is:

[0084]

[0085] In the formula, ξ is a non-negative balance term used to control the convergence speed, and c represents the Lagrange multiplier. The optimization problem of formula (5) can be solved by the ADMM algorithm. In the solution process, an intermediate variable z needs to be introduced. By fixing one variable among m, T, z and updating the other two variables, formula (5) is iteratively solved. The iterative update formula of each variable is:

[0086]

[0087] z k+1 =z k +m k+1 -T k+1 (8)

[0089] Where z = c / ξ represents the scaling Lagrange multiplier, and k represents the number of iterations.

[0090]

[0091] Where η = λ / ξ. Using (9), we can iteratively solve formula (5) and finally obtain the Radon model m' with high sparsity.

[0092] In the whole calculation process, only the inverse of a matrix [L T L+(2σ+ε)I] -1 , this matrix has nothing to do with the input data, it is only related to the dimension of the input data and can be reused.

[0093] Optionally, in step S103, the mapping domain data is transformed back to the time domain through a high-resolution inverse Radon mapping operator to obtain reconstructed data corresponding to the missing track or bad track.

[0094] Optionally, in step S105, the reconstructed single-channel data and the original data are subjected to energy equalization processing, and the reconstructed acoustic wave remote exploration data are output.

[0095] This application starts from the theory of seismic wave propagation and uses high-fidelity data mapping operators to reconstruct acoustic wave remote exploration data. The reconstruction results comply with geophysical laws and are highly reasonable.

[0096] The application process is as follows:

[0097] refer to Figure 2 The working process of this program is as follows:

[0098] a) For acoustic remote sounding data with missing or bad channels, a high-resolution Radon operator is used to transform the data into a mapping domain. If the data has noise, it can be separated and removed in the mapping domain;

[0099] b) transforming the mapping domain data back to the time domain through a high-resolution reverse Radon mapping operator to obtain the reconstructed data corresponding to the missing track or bad track;

[0100] c) Performing energy equalization processing on the reconstructed single-channel data together with the original data, and outputting the reconstructed acoustic wave remote detection data.

[0101] Numerical Tests

[0102] This part verifies the correctness and effectiveness of the method of the present invention through actual data testing. Figure 3 It is a partial common shot point (CSP) gather corresponding to the actual data. Figure 4 This is a CSP gather with one missing channel, and the results before and after data mapping. The sixth channel of the CSP gather is extracted as the missing channel for testing. Figure 5 This is a CSP gather with two missing data channels, and the results before and after data mapping. The third and sixth channels of the CSP gather are extracted as missing channels for testing. Figure 6 is for Figure 4 Comparison between the original data of the missing track and the reconstructed data shows that the missing sixth track data has been accurately reconstructed, and the difference ratio of the reconstructed maximum amplitude is controlled within 1%. Figure 7 is for Figure 5 Comparison between the original data of the missing traces and the reconstructed data shows that the missing third and sixth traces are accurately reconstructed, and the difference ratio of the reconstructed maximum amplitude is also controlled within 1%, which verifies the correctness, effectiveness and superiority of the method of the present invention.

[0103] The advantages of this application are as follows:

[0104] 1. This scheme incorporates the idea of ​​geophysical inversion in the reconstruction process, complies with geophysical laws, and the reconstruction results are more in line with reality.

[0105] 2. This scheme introduces the elastic semi-norm constrained inversion algorithm and expands the mapping operator into a high-resolution mapping operator.

[0106] 3. The high-resolution mapping operator introduced in this scheme improves the focusing and resolution of the signal and enhances the fidelity of the reconstruction.

[0107] 4. Compared with traditional methods, this scheme can obtain acoustic wave remote exploration data reconstruction results with higher accuracy and fidelity.

[0108] This patent improves the focusing and resolution of acoustic wave remote sensing data in the mapping space by introducing a high-resolution Radon mapping operator with elastic semi-norm constraints, thereby achieving fidelity data reconstruction.

[0109] like Figure 8 As shown, the present application provides an acoustic wave remote exploration data reconstruction device based on high-fidelity data mapping, including: a transformation unit 201: for acoustic wave remote exploration data with missing tracks or bad tracks, a high-resolution Radon operator is used to transform the data into a mapping domain. If the data has noise, it can be separated and removed in the mapping domain; a return unit 202: the mapping domain data is transformed back to the time domain through a high-resolution inverse Radon mapping operator to obtain the reconstructed data corresponding to the missing tracks or bad tracks; a reconstruction unit 203: the reconstructed single-track data is subjected to energy balancing processing together with the original data, and the reconstructed acoustic wave remote exploration data is output.

[0110] In some embodiments, the transform unit is used to introduce a sparse constraint condition for a hyperbolic Radon transform, and its objective function is expressed by the following equation:

[0111]

[0112] The first term on the right side of the equation is the target expression of conventional inversion, R(m) represents the sparse constraint term, and λ represents the regularization parameter, which is used to adjust the weight between the constraint term and the observed data error.

[0113] The sparse constraint term R(m) is expressed as follows:

[0114]

[0115] Where σ is the scale factor. 1 / 2 The norm promotes the sparsity of the inversion problem, L 2 The norm ensures the stability of the solution and can alleviate the L 1 / 2 The numerical oscillation problem of the norm.

[0116] The objective function of Radon transform based on elastic semi-norm constraint is:

[0117]

[0118] It can ensure the stability and uniqueness of the solution. When σ=0, the elastic semi-norm regularization degenerates into the standard L 1 / 2 Regularization. Formula (3) contains L 1 / 2 norm, so the optimization problem is a non-convex problem. In order to solve the optimization problem, it is necessary to introduce an auxiliary variable T = m, then formula (3) is expressed as:

[0119]

[0120] Its augmented Lagrangian form is:

[0121]

[0122] In the formula, ξ is a non-negative balance term used to control the convergence speed, and c represents the Lagrange multiplier. The optimization problem of formula (5) can be solved by the ADMM algorithm. In the solution process, an intermediate variable z needs to be introduced. By fixing one variable among m, T, z and updating the other two variables, formula (5) is iteratively solved. The iterative update formula of each variable is:

[0123]

[0124]

[0125] z k+1 =z k +m k+1 -T k+1 (8)

[0127] Where z = c / ξ represents the scaling Lagrange multiplier, and k represents the number of iterations.

[0128]

[0129] Where η = λ / ξ. Using (9), we can iteratively solve formula (5) and finally obtain the Radon model m' with high sparsity.

[0130] In the whole calculation process, only the inverse of a matrix [L T L+(2σ+ε)I] -1 , this matrix has nothing to do with the input data, it is only related to the dimension of the input data and can be reused.

[0131] The present application also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the above-mentioned acoustic wave remote exploration data reconstruction technology based on high-fidelity data mapping is implemented.

[0132] The embodiment of the present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the above-mentioned acoustic wave remote exploration data reconstruction technology steps based on high-fidelity data mapping are implemented. The computer-readable storage medium may include, but is not limited to, any type of disk, including a floppy disk, an optical disk, a DVD, a CD-ROM, a micro drive, and a magneto-optical disk, a ROM, a RAM, an EPROM, an EEPROM, a DRAM, a VRAM, a flash memory device, a magnetic card or an optical card, a nanosystem (including a molecular memory IC), or any type of medium or device suitable for storing instructions and / or data.

[0133] The device embodiments described above are merely illustrative. For example, the division of the units is merely a logical function division, and there may be other division methods in actual implementation. The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A technology for reconstructing acoustic wave remote sensing data based on high-fidelity data mapping, characterized in that: include: S101, for acoustic remote exploration data with missing or bad tracks, a high-resolution Radon operator is used to transform the data into a mapping domain. If the data has noise, it can be separated and removed in the mapping domain; S103, transforming the mapping domain data back to the time domain through a high-resolution inverse Radon mapping operator to obtain reconstructed data corresponding to the missing track or bad track; S105, performing energy equalization processing on the reconstructed single-channel data and the original data, and outputting the reconstructed acoustic wave remote sensing data.

2. The acoustic wave remote exploration data reconstruction technology based on high-fidelity data mapping according to claim 1 is characterized in that: In step S101, for the hyperbolic Radon transform, a sparse constraint is introduced, and its objective function is expressed by the following equation: The first term on the right side of the equation is the target expression of conventional inversion, R(m) represents the sparse constraint term, and λ represents the regularization parameter, which is used to adjust the weight between the constraint term and the observed data error. The sparse constraint term R(m) is expressed as follows: Where σ is the scale factor. 1 / 2 The L2 norm promotes the sparsity of the inversion problem, and the L2 norm ensures the stability of the solution, which can alleviate the L 1 / 2 The numerical oscillation problem of the norm. The objective function of Radon transform based on elastic semi-norm constraint is: It can ensure the stability and uniqueness of the solution. When σ=0, the elastic semi-norm regularization degenerates into the standard L 1 / 2 Regularization. Formula (3) contains L 1 / 2 norm, so the optimization problem is a non-convex problem. In order to solve the optimization problem, it is necessary to introduce an auxiliary variable T = m, then formula (3) is expressed as: Its augmented Lagrangian form is: In the formula, ξ is a non-negative balance term used to control the convergence speed, and c represents the Lagrange multiplier. The optimization problem of formula (5) can be solved by the ADMM algorithm. In the solution process, an intermediate variable z needs to be introduced. By fixing one variable among m, T, z and updating the other two variables, formula (5) is iteratively solved. The iterative update formula of each variable is: z k+1 =z k +m k+1 -T k+1 (8) Where z = c / ξ represents the scaling Lagrange multiplier, and k represents the number of iterations. m k+1 =f -1 {[L T L+(2σ+ξ)I] -1 [L T f(d)+ξ(f(T k )-f(z k ))]} T k+1 =H η (m k+1 +z k ) Where η = λ / ξ. Using (9), we can iteratively solve formula (5) and finally obtain the Radon model m' with high sparsity. In the whole calculation process, only the inverse of a matrix [L T L+(2σ+ε)I]- 1 , this matrix has nothing to do with the input data, it is only related to the dimension of the input data and can be reused.

3. The acoustic wave remote exploration data reconstruction technology based on high-fidelity data mapping according to claim 1 or 2 is characterized in that: Separation in the mapping domain removes noise from the data.

4. The acoustic wave remote exploration data reconstruction technology based on high-fidelity data mapping according to claim 1 or 2 is characterized in that In step S103, the mapping domain data is transformed back to the time domain through a high-resolution inverse Radon mapping operator to obtain reconstructed data corresponding to the missing track or bad track.

5. The acoustic wave remote exploration data reconstruction technology based on high-fidelity data mapping according to claim 1 or 2 is characterized in that: Get the reconstruction data corresponding to the missing or bad tracks.

6. The acoustic wave remote exploration data reconstruction technology based on high-fidelity data mapping according to claim 3 is characterized in that S105, performing energy equalization processing on the reconstructed single-channel data and the original data, and outputting the reconstructed acoustic wave remote sensing data.

7. An acoustic wave remote exploration data reconstruction device based on high-fidelity data mapping, characterized in that: include: Transformation unit: For acoustic remote sounding data with missing or bad channels, a high-resolution Radon operator is used to transform the data into a mapping domain. If the data has noise, it can be separated and removed in the mapping domain. Regression unit: transforms the mapping domain data back to the time domain through the high-resolution reverse Radon mapping operator to obtain the reconstructed data corresponding to the missing track or bad track; Reconstruction unit: performs energy balance processing on the reconstructed single-channel data together with the original data, and outputs the reconstructed acoustic wave remote exploration data.

8. The device for reconstructing acoustic wave remote exploration data based on high-fidelity data mapping according to claim 7, characterized in that: The transformation unit is used to introduce a sparse constraint condition for the hyperbolic Radon transform, and its objective function is expressed by the following equation: The first term on the right side of the equation is the target expression of conventional inversion, R(m) represents the sparse constraint term, and λ represents the regularization parameter, which is used to adjust the weight between the constraint term and the observed data error. The sparse constraint term R(m) is expressed as follows: Where σ is the scale factor. 1 / 2 The L2 norm promotes the sparsity of the inversion problem, and the L2 norm ensures the stability of the solution, which can alleviate the L 1 / 2 The numerical oscillation problem of the norm. The objective function of Radon transform based on elastic semi-norm constraint is: It can ensure the stability and uniqueness of the solution. When σ = 0, the elastic semi-norm regularization degenerates into the standard L 1 / 2 Regularization. Formula (3) contains L 1 / 2 norm, so the optimization problem is a non-convex problem. In order to solve the optimization problem, it is necessary to introduce an auxiliary variable T = m, then formula (3) is expressed as: Its augmented Lagrangian form is: In the formula, ξ is a non-negative balance term used to control the convergence speed, and c represents the Lagrange multiplier. The optimization problem of formula (5) can be solved by the ADMM algorithm. In the solution process, an intermediate variable z needs to be introduced. By fixing one variable among m, T, z and updating the other two variables, formula (5) is iteratively solved. The iterative update formula of each variable is: z k+1 =z k +m k+1 -T k+1 (8) Where z = c / ξ represents the scaling Lagrange multiplier, and k represents the number of iterations. m k+1 =f -1 {[L T L+(2σ+ξ)I] -1 [L T f(d)+ξ(f(T k )-f(z k ))]]} T k+1 =H η (m k+1 +z k ) Where η = λ / ξ. Using (9), we can iteratively solve formula (5) and finally obtain the Radon model m' with high sparsity. In the whole calculation process, only the inverse of a matrix [L T L+(2σ+ε)I] -1 , this matrix has nothing to do with the input data, it is only related to the dimension of the input data and can be reused.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method described in any one of claims 1 to 6 are implemented.

10. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the method described in any one of claims 1 to 6 are implemented.

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