A high-performance density or magnetic susceptibility imaging method, electronic device and storage medium

Abstract

The invention discloses a high-performance density or magnetic susceptibility imaging method, electronic device and storage medium. The method comprises: dividing a coefficient matrix into a plurality of sub-matrices by column, and storing all of them in a computer hard disk; cyclically reading the sub-matrix, calculating the current iteration fitting residual vector; judging whether the iteration continues; cyclically reading the sub-matrix again, calculating the vector of the steepest ascent mapping in the model space of the current iteration and the vector of the conjugate gradient ascent mapping in the model space of the previous iteration; calculating the steepest ascent vector of the current iteration and the conjugate gradient ascent vector of the current iteration; calculating the current iteration coefficient, and updating the density or magnetic susceptibility vector. The invention reduces the three-cycle loading of the sub-matrix to two-cycle loading of the sub-matrix by introducing the calculation of the vector of the steepest ascent mapping in the model space and the vector of the conjugate gradient ascent mapping in the model space, and simultaneously achieves the purpose of reducing the memory space consumption in the imaging process and improving the imaging efficiency.

Description

Technical Field

[0001] The present invention relates to the field of electrical digital data processing, and in particular to a high-performance density or magnetic susceptibility imaging method, electronic equipment and storage medium. Background Art

[0002] In the field of electrical digital data processing, density and magnetic susceptibility imaging technology of gravity and magnetic exploration plays a vital role. This technology constructs density or magnetic anomaly images of underground media by minimizing the objective function, thereby providing key data support for fields such as mineral resource exploration and earth science research.

[0003] However, with the advancement of science and technology and the rapid growth of exploration needs, the amount of observed gravity or magnetic anomaly data has also increased. This trend has brought a significant challenge: the size of the coefficient matrix has increased dramatically, resulting in a sharp increase in the consumption of computer memory resources during the imaging process, low imaging efficiency, and even the inability to complete the imaging task on ordinary computers.

[0004] To meet this challenge, researchers have proposed and developed a variety of technical strategies. Among them, coefficient matrix compression technology (e.g., published by Portniaguine and Zhdanov in 2002; Li and Oldenburg in 2003) attempts to reduce memory usage by reducing redundant data, but this technology may be accompanied by the risk of information loss, and as the observed gravity or magnetic anomaly data continues to increase, its effect of reducing memory usage gradually weakens. Equivalent geometric grid technology (e.g., published by Yao Changli et al. in 2003) uses the regular distribution of measurement points and the regular layout of model units to reduce memory usage through equivalence, but this technology cannot handle irregular distribution of measurement points. Based on the conjugate gradient minimization objective function (e.g., published by Zhdanov in 2002 and 2015 respectively; Rezaie in 2023), it avoids large-scale operations such as matrix inversion and matrix-matrix product, thereby improving imaging efficiency to a certain extent, but this technology still involves the problem of severe memory consumption caused by the direct participation of large-scale coefficient matrices in operations. For ordinary computers, due to limited memory, this technology even has difficulty completing the imaging task of about 10,000 observation points.

[0005] Matrix blocking technology (e.g., Liang Shengxian published in 2018, 2019, and 2023) is an effective way to reduce memory usage and is not limited by the regularity of the distribution of measurement points, while ensuring the integrity of the coefficient matrix information. Therefore, if the matrix blocking technology is incorporated into the conjugate gradient minimization objective function, the computer memory usage of the imaging process can be significantly reduced and the imaging efficiency can be improved. However, if the matrix blocking technology is directly used in the conjugate gradient algorithm, there is a phenomenon of three-fold loop loading of sub-matrices. The process of three-fold loop loading of sub-matrices in turn reduces the imaging speed.

[0006] Therefore, it is necessary to improve the conjugate gradient minimization objective function algorithm to better integrate matrix blocks into it, reduce the number of sub-matrix loading times while reducing memory usage, and improve imaging efficiency. Summary of the invention

[0007] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a high-performance density or magnetic susceptibility imaging method, electronic device and storage medium.

[0008] The objective of the present invention is achieved through the following technical solutions:

[0009] A first aspect of the present invention provides a high performance density or magnetic susceptibility imaging method, comprising the following steps:

[0010] S01: Split the coefficient matrix into multiple sub-matrices by column, and store all of them in the computer hard disk;

[0011]

[0012] In the formula, represents a coefficient matrix, which represents the geometric relationship between the measurement points of gravity or magnetic anomaly data and the model units; is a submatrix, with the superscript is the submatrix number, is the number of sub-matrices;

[0013] S02: Circularly read the submatrix from the computer hard disk to the memory and calculate the current iterative fitting residual vector:

[0014] S0201: Start executing a number of The loop:

[0015] Load the Sub-matrices to memory and accumulate the fitted data vector according to the following formula:

[0016]

[0017] In the formula, is the fitted gravity or magnetic anomaly data vector, is the current density or susceptibility subvector, with the subscript Represents the current iteration number; and before loading the next sub-matrix, clear the sub-matrix currently loaded in the memory;

[0018] S0202: After the loop is executed, the fitting residual vector of the current iteration is calculated according to the following formula:

[0019]

[0020] In the formula, is the fitting residual vector of the current iteration, Represents the observed gravity or magnetic anomaly data vector;

[0021] S03: Determine whether to continue the iteration. If the current number of iterations is Less than the maximum number of iterations , and the fitted residual vector of the current iteration The corresponding current fitting residual Greater than the residual threshold , then execute the subsequent steps, otherwise terminate the iteration and output the current density or magnetic susceptibility vector As imaging results; represents the 2-norm; where, ;

[0022] S04: Read the submatrix from the computer hard disk to the memory again, and calculate the vector of the steepest ascent mapping of the current iteration in the model space. and the vector of the conjugate gradient ascent mapping of the previous iteration in the model space :Start executing a number of The loop:

[0023] Load the Sub-matrices to memory, and calculate the vector of the steepest ascent mapping of the current iteration in the model space according to the following formulas and the vector of the conjugate gradient ascent mapping of the previous iteration in the model space :

[0024]

[0025]

[0026] when hour, ;in,

[0027]

[0028] and They represent the steepest ascent subvector of the current iteration and the vector of the steepest ascent mapping of the current iteration in the model space respectively; and They represent the conjugate gradient ascent subvector of the previous iteration and the vector of the conjugate gradient ascent mapping of the previous iteration in the model space respectively. The conjugate gradient ascent subvector of the previous iteration is obtained in the previous iteration; is the regularization factor, is the reference density or susceptibility subvector, with the subscript is the current iteration number, with a superscript represents matrix transpose; if n=0, then ; and before loading the next sub-matrix, clear the currently loaded sub-matrix in memory;

[0029] S05: Calculate the steepest ascent vector of the current iteration and the conjugate gradient ascent vector of the current iteration :

[0030]

[0031]

[0032] In the formula, is the conjugate coefficient, which is calculated as follows:

[0033]

[0034] is the steepest ascent vector of the previous iteration;

[0035] S06: Calculate the current iteration coefficient , update the density or susceptibility vector:

[0036]

[0037]

[0038] In the formula, is the updated density or susceptibility vector;

[0039] S07: Return to step S02.

[0040] A second aspect of the present invention provides an electronic device, comprising a storage unit and a processing unit, wherein the storage unit stores computer instructions that can be executed on the processing unit, and when the processing unit executes the computer instructions, the steps of the high-performance density or magnetic susceptibility imaging method as described in the first aspect are performed.

[0041] According to a third aspect of the present invention, there is provided a storage medium having computer instructions stored thereon, which, when executed, execute the steps of the high performance density or magnetic susceptibility imaging method as described in the first aspect.

[0042] The beneficial effects of the present invention are:

[0043] In an exemplary embodiment of the present invention, by introducing a vector for calculating the steepest ascent mapping in the model space and a vector for calculating the conjugate gradient ascent mapping in the model space, three-loop sub-matrix loading is reduced to two-loop sub-matrix loading, thereby achieving the purpose of reducing the memory space consumption in the imaging process and improving the imaging efficiency at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A flowchart of a high performance density or magnetic susceptibility imaging method provided in an exemplary embodiment of the present invention;

[0045] Figure 2 A schematic diagram comparing the computer memory occupied by the technology of the present invention and the traditional technology provided in an exemplary embodiment of the present invention;

[0046] Figure 3 It is a schematic diagram of time consumption comparison of the technology of the present invention, the simple superposition technology and the traditional technology provided in an exemplary embodiment of the present invention on a computer 1;

[0047] Figure 4 It is a schematic diagram of time consumption comparison of the technology of the present invention, the simple superposition technology and the traditional technology provided in an exemplary embodiment of the present invention on a computer 2;

[0048] Figure 5 It is a schematic diagram showing the times by which the imaging speed of the technology of the present invention and the simple superposition technology provided in an exemplary embodiment of the present invention on a computer 1 is increased compared with the conventional technology;

[0049] Figure 6 It is a schematic diagram showing the times by which the imaging speed of the technology of the present invention and the simple overlay technology provided in an exemplary embodiment of the present invention is increased on a computer 2 compared with the conventional technology. DETAILED DESCRIPTION

[0050] The technical solution of the present invention is described clearly and completely below in conjunction with the accompanying drawings. 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.

[0051] In the description of the present invention, it should be noted that the directions or positional relationships indicated by "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside", etc. are directions or positional relationships based on the drawings, which are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0052] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0053] In addition, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0054] Before introducing the exemplary embodiments of the present invention, the conjugate gradient minimization objective function, matrix blocking, the technical steps of the conjugate gradient minimization objective function, and the technical steps after the simple superposition of the matrix blocking and the conjugate gradient minimization objective function are first introduced.

[0055] 1. Conjugate gradient minimization objective function

[0056] The objective function here Written as:

[0057] (1)

[0058] in, is a coefficient matrix, which is determined by the geometric relationship between the measurement points of gravity or magnetic anomaly data and the model units. Its calculation method can be found in references (e.g., Guan Zhining, 2005; Zeng Hualin, 2005); is the gravity or magnetic anomaly data vector; is the density or magnetic susceptibility vector to be solved, i.e., the imaging result; is the reference density or magnetic susceptibility vector; represents the 2-norm; is the regularization factor, which can be calculated by (e.g. Zhdanov, 2002 and 2015).

[0059] For the conjugate gradient algorithm, given the current density or susceptibility vector In the case of It can be expressed as:

[0060] (2)

[0061] in, is the conjugate gradient ascent vector for the current iteration; is the current iteration coefficient; subscript Represents the current iteration number.

[0062] In formula (2), It is expressed as:

[0063] (3)

[0064] in is the current fastest ascent vector, is a linear factor, is the conjugate gradient ascent vector of the previous step. When the density or magnetic susceptibility vector is In the case of By minimizing the objective function (1), we can obtain:

[0065] (4)

[0066] in The residual vector for the current iteration fit is written as:

[0067] (5)

[0068] The linear factor in formula (3) Calculate it by the following formula:

[0069] (6)

[0070] when hour, .

[0071] In formula (2) Then the density or magnetic susceptibility vector is In the case of , minimizing the objective function (1) yields:

[0072] (7)

[0073] From the above conjugate gradient minimization objective function, it can be seen that formula (4), formula (5) and formula (7) all involve Related operations. Usually, it is a large matrix with a total number of elements that may reach hundreds of millions, tens of billions or even higher. If double precision (each element takes up 8 bytes) is used to store them in memory, then 1 billion elements will consume about 7.5GB of memory, 10 billion elements will consume up to 75GB of memory, and so on. The memory space consumed will increase with the increase in the number of elements. Therefore, if the If it is processed, it may cause serious memory consumption and even cause memory overflow.

[0074] 2. Matrix Blocking

[0075] If the coefficient matrix is ​​divided into multiple sub-matrices by column, it can be written as:

[0076] (8)

[0077] in, coefficient matrix; is a submatrix; the superscript is the submatrix number; is the number of submatrices. Then formula (5) can be written as:

[0078] (9)

[0079] in, is the current density or susceptibility subvector. Accordingly, formula (4) can be written as:

[0080] (10)

[0081] in, is the reference density or magnetic susceptibility vector. and back, The solution formula (7) can be written as:

[0082] (11)

[0083] in, is the conjugate gradient ascent subvector for the current iteration.

[0084] From formula (9) to formula (11), it can be seen that after the matrix partitioning and the conjugate gradient minimization objective function are simply superimposed, the sub-matrix reading operation needs to be performed three times, which undoubtedly increases the I / O overhead in the imaging process and thus reduces the imaging speed. In addition, the calculation of formula (11) is highly dependent on and , which makes formula (10) and formula (11) unable to be effectively integrated.

[0085] 3. Technical steps for conjugate gradient minimization objective function

[0086] Step 1: Calculate the current iteration fitting residual vector using formula (5):

[0087] Step 2: Determine whether to continue the iteration. If the current number of iterations is less than the maximum number of iterations and the current fitting residual is greater than the residual threshold, then execute the subsequent steps. Otherwise, terminate the iteration and output the imaging result, i.e., the density or magnetic susceptibility vector.

[0088] Step 3: Calculate the current iteration's steepest ascent vector and conjugate gradient ascent vector by using formula (4) and formula (3) respectively;

[0089] Step 4: Calculate the current iteration coefficient using formula (7) and update the density or magnetic susceptibility vector using formula (2);

[0090] Step 5: Replace the density or susceptibility vector of the current iteration with the updated density or susceptibility vector, and repeat steps 1 to 5.

[0091] Disadvantage analysis: It can be seen that a significant disadvantage of the traditional conjugate gradient minimization objective function is the direct operation of large-scale coefficient matrices in the key steps (steps 1, 3, and 4). If the large-scale coefficient matrix is ​​not processed, it will cause serious memory consumption and may even cause memory overflow.

[0092] 4. Technical steps after simple superposition of matrix partitioning and conjugate gradient minimization objective function

[0093] Step 1: Divide the coefficient matrix into multiple sub-matrices by column according to formula (8), and store all of them in the computer hard disk;

[0094] Step 2: Read the submatrix from the computer hard disk cyclically and calculate the current iterative fitting residual vector according to formula (9);

[0095] Step 3: Determine whether to continue the iteration. If the current number of iterations is less than the maximum number of iterations and the current fitting residual is greater than the residual threshold, then execute the subsequent steps. Otherwise, terminate the iteration and output the imaging result.

[0096] Step 4: Circularly read the submatrix from the computer hard disk again, calculate the current iteration's steepest ascent vector according to formula (10), and then calculate the current iteration's conjugate gradient ascent vector according to formula (3);

[0097] Step 5: once again, the sub-matrix is ​​read from the computer hard disk in a loop, the current iteration coefficient is calculated according to formula (11), and the density or magnetic susceptibility vector is updated according to formula (2);

[0098] Step 6: Replace the density or susceptibility vector of the current iteration with the updated density or susceptibility vector, and repeat steps 2 to 6.

[0099] Disadvantage Analysis: It can be seen that the simple superposition technique of matrix partitioning and conjugate gradient minimization objective function requires repeated execution of sub-matrix cyclic loading in steps 2, 4, and 5, a total of three times, which undoubtedly increases the I / O overhead in the imaging process. Although the memory usage is optimized, the frequent sub-matrix loading becomes a key factor restricting the imaging speed. In addition, the execution of step 5 is highly dependent on the output of step 4. and ,This dependency makes the sub-matrix loop loading in steps 4 and 5 cannot be effectively integrated.

[0100] In summary, simply superimposing matrix partitioning with the conjugate gradient algorithm weakens the overall imaging efficiency due to the cubic sub-matrix cyclic loading.

[0101] See also Figure 1 , Figure 1 A flowchart of a high-performance density or magnetic susceptibility imaging method provided in an exemplary embodiment of the present invention is shown, comprising the following steps:

[0102] S01: dividing the coefficient matrix into multiple sub-matrices by column, and storing all of them in a computer hard disk, wherein all sub-matrices are stored in the computer hard disk, thereby releasing content space;

[0103] (12)

[0104] In the formula, represents a coefficient matrix, which represents the geometric relationship between the measurement points of gravity or magnetic anomaly data and the model units. The calculation method is the existing technology and can be found in references (e.g., Guan Zhining published in 2005; Zeng Hualin published in 2005); is a submatrix, with the superscript is the submatrix number, is the number of sub-matrices;

[0105] S02: Circularly read the submatrix from the computer hard disk to the memory and calculate the current iterative fitting residual vector:

[0106] S0201: Start executing a number of The loop is based on looping all sub-matrices:

[0107] Load the Sub-matrices to memory and accumulate the fitted data vector according to the following formula:

[0108] (13)

[0109] In the formula, is the fitted gravity or magnetic anomaly data vector, is the current density or susceptibility subvector, with the subscript Represents the current iteration number; and before loading the next sub-matrix, clear the sub-matrix currently loaded in the memory; this ensures that there is only one sub-matrix in the memory space, thereby reducing memory consumption;

[0110] S0202: After the loop is executed, the fitting residual vector of the current iteration is calculated according to the following formula:

[0111] (14)

[0112] In the formula, is the fitting residual vector of the current iteration, Represents the observed gravity or magnetic anomaly data vector;

[0113] S03: Determine whether to continue the iteration. If the current number of iterations is Less than the maximum number of iterations , and the fitted residual vector of the current iteration The corresponding current fitting residual Greater than the residual threshold , then execute the subsequent steps, otherwise terminate the iteration and output the current density or magnetic susceptibility vector As imaging results; represents the 2-norm; where, ;

[0114] S04: Read the submatrix from the computer hard disk to the memory again, and calculate the vector of the steepest ascent mapping of the current iteration in the model space. and the vector of the conjugate gradient ascent mapping of the previous iteration in the model space :Start executing a number of The loop:

[0115] Load the Sub-matrices to memory, and calculate the vector of the steepest ascent mapping of the current iteration in the model space according to the following formulas and the vector of the conjugate gradient ascent mapping of the previous iteration in the model space :

[0116] (15)

[0117] (16)

[0118] when hour, ;in,

[0119] (17) (18)

[0121] and They represent the steepest ascent subvector of the current iteration and the vector of the steepest ascent mapping of the current iteration in the model space respectively; and They represent the conjugate gradient ascent subvector of the previous iteration and the vector of the conjugate gradient ascent mapping of the previous iteration in the model space. The conjugate gradient ascent subvector of the previous iteration is obtained in the previous iteration ( ); is the regularization factor, which reflects the weight between model constraints and data fitting; is the reference density or susceptibility subvector, with the subscript is the current iteration number, with a superscript represents matrix transpose; if n=0, then ; And before loading the next sub-matrix, clear the sub-matrix currently loaded in the memory; this ensures that there is only one sub-matrix in the memory space, thereby reducing memory consumption;

[0122] S05: Calculate the steepest ascent vector of the current iteration and the conjugate gradient ascent vector of the current iteration :

[0123] (19)

[0124] (20)

[0125] In the formula, is the conjugate coefficient, which is calculated as follows:

[0126] (twenty one)

[0127] is the steepest ascent vector of the previous iteration;

[0128] S06: Calculate the current iteration coefficient , update the density or susceptibility vector:

[0129] (twenty two)

[0130] (twenty three)

[0131] In the formula, is the updated density or susceptibility vector;

[0132] S07: Return to step S02.

[0133] Specifically, in this exemplary embodiment, by introducing the vector of the steepest ascent map in the model space and the vector of the conjugate gradient ascent map in model space , reducing the three-loop sub-matrix loading to two-loop sub-matrix loading, thereby achieving the purpose of reducing the memory space consumption in the imaging process and improving the imaging efficiency at the same time.

[0134] In order to fully demonstrate the effect of this exemplary embodiment in reducing computer memory usage and improving imaging efficiency, we demonstrated three imaging comparison experiments of different data scale examples. The specific experimental settings are as follows:

[0135] 1. Experimental Data

[0136] Example 1: The amount of observation data is 861, and the number of model units is 17,600 (corresponding to Model 1).

[0137] Example 2: The amount of observation data increases to 1681, and the number of model units increases accordingly to 35200 (corresponding to Model 2).

[0138] Example 3: The amount of observation data further increases to 3321, and the number of model units jumps to 140,800 (corresponding to Model 3).

[0139] 2. Experimental Equipment

[0140] Computer 1 (basic configuration): ThinkPad E490, equipped with a mechanical hard drive, equipped with a 4th Gen Intel(R)Core(TM) i5-8265U CPU, with a main frequency of 1.60GHz to 1.80GHz, and a memory capacity of 8.00 GB.

[0141] Computer 2 (high configuration): Legion Y9000P IAH7H, with SSD, 12th Gen Intel(R) Core(TM) i9-12900H processor, 2.50 GHz, and 16GB of memory.

[0142] 3. Experimental Methods

[0143] On two laptops with different configurations, the three data examples were imaged using the traditional technology (conjugate gradient minimization objective function), the simple superposition technology (matrix block division and simple superposition of conjugate gradient minimization objective function) and the technology of the present invention. During the experiment, the coefficient matrix was evenly divided into 10 sub-matrices by column. The effect of the technology of the present invention was evaluated by comparing and analyzing the memory usage and imaging speed of the three technologies during the imaging process.

[0144] 4. Memory usage comparison

[0145] Figure 2 The comparison of memory usage between the technology of the present invention and the traditional technology when imaging the above three example data is demonstrated. Figure 2 The first column of each model is the traditional technology, and the second column of each model is the technology of the present invention. The data clearly shows that the memory consumed by the technology of the present invention is only about one tenth of the traditional technology, indicating that the technology of the present invention effectively saves memory space.

[0146] It is worth mentioning that when processing the data of Example 3, if the traditional technology is used, the memory required for the imaging process is as high as 3.5GB, which is close to the memory limit of Computer 1, indicating that when the data scale further increases, the traditional technology will face the risk of memory overflow and cannot successfully complete the imaging task on Computer 1. In contrast, the technical advantages of the present invention are more prominent, providing strong support for processing large-scale data.

[0147] 5. Comparison results of imaging efficiency

[0148] Figure 3 and Figure 4 The time consumption comparison of the technology of the present invention, the simple superposition technology and the traditional technology when performing imaging tasks on computer 1 and computer 2 is respectively shown. Figure 3 and Figure 4 In the figure, the first column of each model is the traditional technology, the second column of each model is the simple superposition technology, and the third column of each model is the technology of the present invention. The two charts clearly show that no matter on which hardware platform, compared with the traditional technology and the simple superposition technology, the technology of the present invention has greatly improved the imaging efficiency.

[0149] also, Figure 5 and Figure 6 The imaging speed improvement times of the technology of the present invention, the simple superposition technology and the traditional technology on computer 1 and computer 2 are respectively. Figure 5 and Figure 6In the figure, the first column of each model is the simple superposition technology, and the second column of each model is the technology of the present invention. For computer 1 equipped with a mechanical hard disk, the imaging speed of the technology of the present invention is improved by about 2 times compared with the traditional technology; while the simple superposition technology only improves it by about 1.5 times. For computer 2 equipped with a solid-state hard disk and with more powerful performance, the imaging speed of the technology of the present invention is up to more than 7 times that of the traditional technology; while the simple superposition technology is only 4.5 times. This shows that the technology of the present invention effectively improves the imaging speed.

[0150] It is worth noting that Figure 3 , Figure 4 , Figure 5 and Figure 6 It shows that as the amount of data continues to increase, the efficiency improvement effect of the technology of the present invention becomes more obvious. This shows that the technology of the present invention has shown good performance in dealing with large-scale data processing and provides strong technical support for large-scale data imaging tasks.

[0151] Having the same inventive concept as the above exemplary embodiment, another exemplary embodiment of the present invention provides an electronic device, including a storage unit and a processing unit, wherein the storage unit stores computer instructions that can be executed on the processing unit, and the processing unit executes the steps of the high-performance density or magnetic susceptibility imaging method when running the computer instructions.

[0152] The electronic device is presented in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: the at least one processing unit, the at least one storage unit, and a bus connecting different system components (including the storage unit and the processing unit).

[0153] The storage unit stores program codes, which can be executed by the processing unit, so that the processing unit performs the steps according to various exemplary embodiments of the present invention described in the above “Exemplary Method” section of this specification. For example, the processing unit can perform the following steps: Figure 1 The method shown in .

[0154] The storage unit may include a readable medium in the form of a volatile memory unit, such as a random access memory unit (RAM) and / or a cache memory unit, and may further include a read-only memory unit (ROM).

[0155] The storage unit may also include a program / utility having a set (at least one) of program modules, such program modules including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0156] The bus may represent one or more of several types of bus structures, including a memory unit bus or memory unit controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

[0157] The electronic device may also communicate with one or more external devices (e.g., keyboards, pointing devices, Bluetooth devices, etc.), may communicate with one or more devices that enable a user to interact with the electronic device, and / or may communicate with any device that enables the electronic device to communicate with one or more other computing devices (e.g., routers, modems, etc.). Such communication may be performed through an input / output (I / O) interface. Furthermore, the electronic device may also communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) through a network adapter. The network adapter communicates with other modules of the electronic device through a bus. It should be understood that other hardware and / or software modules may be used in conjunction with the electronic device, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, etc.

[0158] Through the above description, it is easy for those skilled in the art to understand that the example implementation described here can be implemented by software or by combining software with necessary hardware. Therefore, the technical solution according to this exemplary embodiment can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which can be a personal computer, a server, a terminal device, or a network device, etc.) to execute the method according to this exemplary embodiment.

[0159] With the same inventive concept as the above exemplary embodiment, another exemplary embodiment of the present invention provides a storage medium having computer instructions stored thereon, which when executed execute the steps of the high performance density or magnetic susceptibility imaging method as described in the first aspect.

[0160] Based on such understanding, the technical solution of this embodiment can essentially or the part that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product (program product). The computer software product is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention.

[0161] The program product may use any combination of one or more readable media. The readable medium may be a readable signal medium or a readable storage medium. The readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples (non-exhaustive list) of readable storage media include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0162] Computer readable signal media may include data signals propagated in baseband or as part of a carrier wave, in which readable program code is carried. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. Readable signal media may also be any readable medium other than a readable storage medium, which may send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0163] The program code embodied on the readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination of the foregoing.

[0164] Program code for performing the operations of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a separate software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving a remote computing device, the remote computing device may be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., through the Internet using an Internet service provider).

[0165] Obviously, the above embodiments are merely examples for clear explanation, and are not intended to limit the implementation methods. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived from them are still within the protection scope of the invention.

Claims

1. A high performance density or magnetic susceptibility imaging method, characterized in that: The following steps are involved: S01: Split the coefficient matrix into multiple sub-matrices by column, and store all of them in the computer hard disk; ; In the formula, represents a coefficient matrix, which represents the geometric relationship between the measurement points of gravity or magnetic anomaly data and the model units; is a submatrix, with the superscript is the submatrix number, is the number of sub-matrices; S02: Circularly read the submatrix from the computer hard disk to the memory and calculate the current iterative fitting residual vector: S0201: Start executing a number of The loop: Load the Sub-matrices to memory and accumulate the fitted data vector according to the following formula: ； In the formula, is the fitted gravity or magnetic anomaly data vector, is the current density or susceptibility subvector, with the subscript Represents the current iteration number; and before loading the next sub-matrix, clear the sub-matrix currently loaded in the memory; S0202: After the loop is executed, the fitting residual vector of the current iteration is calculated according to the following formula: ； In the formula, is the fitting residual vector of the current iteration, Represents the observed gravity or magnetic anomaly data vector; S03: Determine whether to continue the iteration. If the current number of iterations is Less than the maximum number of iterations , and the fitted residual vector of the current iteration The corresponding current fitting residual Greater than the residual threshold , then execute the subsequent steps, otherwise terminate the iteration and output the current density or magnetic susceptibility vector As imaging results; represents the 2-norm; where, ; S04: Read the submatrix from the computer hard disk to the memory again, and calculate the vector of the steepest ascent mapping of the current iteration in the model space. and the vector of the conjugate gradient ascent mapping of the previous iteration in the model space :Start executing a number of The loop: Load the Sub-matrices to memory, and calculate the vector of the steepest ascent mapping of the current iteration in the model space according to the following formulas and the vector of the conjugate gradient ascent mapping of the previous iteration in the model space : ； ； when hour, ;in, ； and They represent the steepest ascent subvector of the current iteration and the vector of the steepest ascent mapping of the current iteration in the model space respectively; and They represent the conjugate gradient ascent subvector of the previous iteration and the vector of the conjugate gradient ascent mapping of the previous iteration in the model space respectively. The conjugate gradient ascent subvector of the previous iteration is obtained in the previous iteration; is the regularization factor, is the reference density or susceptibility subvector, with the subscript is the current iteration number, with a superscript represents matrix transpose; if n=0, then ; And before loading the next sub-matrix, clear the currently loaded sub-matrix in memory; S05: Calculate the steepest ascent vector of the current iteration and the conjugate gradient ascent vector of the current iteration : ； ； In the formula, is the conjugate coefficient, which is calculated as follows: ； is the steepest ascent vector of the previous iteration; S06: Calculate the current iteration coefficient , update the density or susceptibility vector: ； ； In the formula, is the updated density or susceptibility vector; S07: Return to step S02.

2. An electronic device, comprising a storage unit and a processing unit, wherein the storage unit stores computer instructions that can be executed on the processing unit, characterized in that: The processing unit executes the steps of the high performance density or susceptibility imaging method according to claim 1 when executing the computer instructions.

3. A storage medium having computer instructions stored thereon, characterized in that: The computer instructions execute the steps of the high performance density or susceptibility imaging method as claimed in claim 1 when executed.

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