Image geometric positioning method and system based on adaptive balance L1-L2 norm regularization

Abstract

The invention discloses an image geometric positioning method and system based on adaptive balance L1-L2 norm regularization, and relates to the technical field of spatial data processing, and the method comprises the following steps: obtaining remote sensing satellite image data, carrying out the radiation and geometric correction of the remote sensing satellite image data, carrying out the image matching through employing SIFT and RANSAC methods, and carrying out the positioning of the remote sensing satellite image data. Obtaining processed remote sensing satellite image data; and the processed remote sensing satellite image data is corrected based on an adaptive balance L1-L2 norm regularization method, so that key positioning parameters are solved, and the re-projection precision and the geometric positioning precision are improved.

Description

Technical Field

[0001] The present invention relates to the field of spatial data processing technology, and in particular to an image geometric positioning method and system based on adaptive balanced L1-L2 norm regularization. Background Art

[0002] Ill-posed problems are often encountered in the geometric positioning method of remote sensing image bundle adjustment. Ill-posed problems are sensitive to observation noise, that is, the observation noise and the ill-posedness of the inversion model system are the reasons for the dramatic fluctuations in parameter estimation, which has a negative impact on the observation and in-depth analysis of spatial data in subsequent work. The parameter solution of the ill-posed problem violates the stability condition of the well-posed solution, that is, the solution of the ill-posed problem exists and is unique but unstable. Parameter estimation of ill-posed problems is a common problem in the fields of geodesy, photogrammetry and remote sensing, especially for the geometric positioning of remote sensing images. Regularization methods are often used to solve ill-posed problems. The essence of the commonly used Tikhonov regularization is to select a reasonable regularization parameter to reduce the influence of small singular values ​​in the coefficient matrix, thereby reducing the condition number and obtaining a more stable solution. However, when the unknown parameter solution is sparse, the result of Tikhonov regularization will be over-smoothed, resulting in the loss of sparse high-frequency information. For example, Patent No. 201610134383.0 implements a high-precision geometric correction method for satellite remote sensing images by micro-correcting RPC parameters. Summary of the invention

[0003] In order to solve the deficiencies mentioned in the above background technology, the purpose of the present invention is to provide an image geometry positioning method and system based on adaptive balanced L1-L2 norm regularization.

[0004] In a first aspect, the purpose of the present invention can be achieved by the following technical solution: an image geometric positioning method based on adaptive balanced L1-L2 norm regularization, the method comprising the following steps: Acquire remote sensing satellite image data, perform radiation and geometric correction on the remote sensing satellite image data, and use SIFT and RANSAC methods for image matching to obtain processed remote sensing satellite image data; The processed remote sensing satellite image data is corrected based on the adaptive balanced L1-L2 norm regularization method to solve the key positioning parameters and improve the reprojection accuracy and geometric positioning accuracy.

[0005] In combination with the first aspect, in some implementations of the first aspect, the method further includes: the regularization method of the adaptive balanced L1-L2 norm includes the following steps: The coefficient matrix constructed by the rational function model and affine transformation is input , ground control points and tie points together form the observation vector , construct a suitable regularization matrix based on prior information and threshold , to initialize the following parameters, including the outer loop index iter , the regularization parameter and balance parameters ; Regularization solution for initialization positioning parameters ; Initialize inner loop index , determine whether the number of iterations is less than the maximum number of iterations; if the condition is met, proceed to the next step and update the outer loop index iter Continue to iterate, otherwise output adaptive regularization solution ; Determine the penalty parameter Is it less than , if the conditions are met, proceed to the next step; otherwise, output the adaptive regularization solution ; Calculate the mixing parameter using the penalty parameter and regularization parameter ; Update auxiliary variables; Update regular solution , unit weight variance ; Judgement set The deviation correction elements in the calculation of the deviation correction solution ; Update auxiliary variables , update the balance parameters ; Based on the minimum mean square error criterion, the regularization parameter is updated using the bisection method ; judge If the inequality is not true, the number of iterations is increased by 1, and the inner loop continues until the inequality is true; otherwise, the outer loop index is updated. iter and update the penalty parameter , and return to the initialization inner loop index to continue iterating; When the outer loop index iter Satisfy the maximum number of times matiter , calculate and output the deviation correction solution of the final result .

[0006] In combination with the first aspect, in some implementations of the first aspect, the method further includes: calculating the mixed parameter using the penalty parameter and the regularization parameter The process is as follows: The expression of the adaptive balanced L1-L2 norm is constructed as follows: (1) in, x represents the parameters to be estimated, is the equilibrium parameter, is a regularized matrix with symmetric and positive and semi-positive definite characteristics; The objective function is constructed as follows: (2) in represents the observation vector; represents the coefficient matrix; is the regularization parameter; The alternating direction multiplier method is used to solve the parameters and introduce intermediate variables The following expression is obtained: (3) in, Indicates the constructed variables x , z, w The objective function; arg min means to find a function parameter value that makes the objective function The result is the smallest; is a positive penalty parameter, is the augmented Lagrangian vector, with superscript T Represents matrix transpose; Defining blending parameters The expression is: (4) in and are the penalty parameter and regularization parameter respectively, is a balance parameter.

[0007] In combination with the first aspect, in some implementations of the first aspect, the method further includes: a calculation formula for updating the auxiliary variable: Auxiliary parameters z The update formula is: (5) in represents the soft threshold function, To update auxiliary variables; Update regular solution , unit weight variance The calculation formula is: parameter The update method is: (6) in , the superscript -1 indicates the inverse operation of the matrix; Unit weight variance The calculation formula is: (7) in, m and n The observation vectors are y The length and estimated parameters of Length.

[0008] In combination with the first aspect, in some implementations of the first aspect, the method further includes: The deviation correction elements in the calculation of the deviation correction solution The process is as follows: Determine the set that meets the deviation correction The expression is as follows: (8) in, Representation Matrix No. i eigenvalues, Indicates the corresponding eigenvalue The eigenvector of Representation Matrix No. i eigenvalues, Indicates the corresponding eigenvalue The eigenvector of . The increase in eigenvalue will decrease, and the value on the left side of formula (6) will increase, then the variance of the selected part of the deviation that satisfies the correction will decrease; Based on this condition, some deviations are removed from the regularized estimation formula (6) to correct the solution deviation The method is: (9) in, represents the bias-corrected regularization solution.

[0009] In combination with the first aspect, in some implementations of the first aspect, the method further includes: updating the auxiliary variable , update the balance parameters The process: The parameters are estimated according to the calculation principle of the alternating direction multiplier method, where the auxiliary variables The update method is: (10) Balance parameters The update method is: (11) in, represents the normalization function, and Represents vectorsx The minimum and maximum values ​​in .

[0010] In combination with the first aspect, in some implementations of the first aspect, the method further includes: obtaining an adaptive regularized solution The mean square error matrix MSE can be expressed as follows: (12) In the formula ; C( ) means The variance matrix of represents the true value of the unknown parameter, bias ( ) indicates a parameter The deviation term, I represents the unit matrix; Regularization parameter pass The optimal By minimizing The expression is obtained by the trace of: (13) in represents the trace of a square matrix; By taking the first-order derivative of equation (13), we can obtain the root whose first-order derivative is zero, which is the regularization parameter result. The expression of the first-order derivative is as follows: (14) Use the binary method to solve the root of equation (14). The approximation of The true value of is not known a priori, and the estimated value of the unknown parameter is used Initialize.

[0011] In combination with the first aspect, in some implementations of the first aspect, the method further includes: updating the penalty parameter The calculation process: judge If not, update , continue the inner loop; otherwise update the outer loop index , and update the solution : (15) Continue to repeatedly initialize the inner loop index, otherwise, finally output the adaptive regularization solution of deviation correction according to formula (9) .

[0012] In a second aspect, in order to achieve the above-mentioned object, the present invention discloses an image geometric positioning system based on adaptive balanced L1-L2 norm regularization, comprising: The data processing module is used to obtain remote sensing satellite image data, perform radiation and geometric correction on the remote sensing satellite image data, and use SIFT and RANSAC methods to perform image matching to obtain processed remote sensing satellite image data; The geometric positioning module is used to correct the processed remote sensing satellite image data based on the adaptive balanced L1-L2 norm regularization method, so as to solve the key positioning parameters and improve the reprojection accuracy and geometric positioning accuracy.

[0013] In another aspect of the present invention, in order to achieve the above-mentioned purpose, a terminal device is disclosed, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the memory stores a computer program capable of running on the processor, and when the processor loads and executes the computer program, the image geometry positioning method based on adaptive balanced L1-L2 norm regularization as described above is adopted.

[0014] Beneficial effects of the present invention: Due to the existence of the L1 norm, the present invention will introduce additional penalty parameters. They increase the difficulty of regularization parameter selection. The present invention focuses on the generalization of regularization parameter selection to reduce the interference of these penalty parameters. Unknown model parameter estimation seriously hinders the deviation calculation based on the L1-L2 norm regularization method, which can usually be calculated iteratively. It can be inferred that reliable initial values ​​of parameters are difficult to obtain and the effects are difficult to define. The present invention analyzes the effects based on approximation theory to overcome this problem. The present invention combines the smoothness of the L2 norm and the sparsity advantages of the L1 norm, overcomes the pathological problems in the geometric positioning process, and can solve the key positioning parameters, thereby improving the reprojection accuracy and geometric positioning accuracy, while also making the regularization-based geometric positioning process more robust and robust. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative work. Figure 1 It is a schematic flow chart of the method of the present invention; Figure 2 It is a schematic diagram of the workflow of the present invention; Figure 3 It is a schematic diagram of the system structure of the present invention; Figure 4 is a scene diagram of experimental data in a certain area of ​​this embodiment; Figure 5Zoomed-in image of the reprojection error distribution calculated using eight different regularization methods for 42 connection points. Figure 6 This is an error distribution analysis diagram of 42 connection points before and after bundle adjustment in this embodiment. DETAILED DESCRIPTION

[0016] 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.

[0017] Embodiment 1: like Figure 1 As shown, the image geometric positioning method based on adaptive balanced L1-L2 norm regularization includes the following steps: S101: Acquire remote sensing satellite image data, perform radiation and geometric correction on the remote sensing satellite image data, and use the scale-invariant feature transformation algorithm SIFT and the random sample consensus algorithm RANSAC method to perform image matching to obtain processed remote sensing satellite image data; S102: Correct the processed remote sensing satellite image data based on the adaptive balanced L1-L2 norm regularization method, so as to solve the key positioning parameters and improve the reprojection accuracy and geometric positioning accuracy.

[0018] Specifically, the remote sensing satellite image and RPC parameter file are obtained by the CCD camera carried by the Resource 3 remote sensing satellite, and the obtained image is subjected to radiation and geometric correction, and then the SIFT and RANSAC methods are used for image matching; in order to obtain high-precision reprojection accuracy and spatial geometric positioning results, the image same-name point pairs and their ground control point data are combined to carry out bundle adjustment. In order to overcome the problem of coefficient matrix morbidity in the bundle adjustment process, the adaptive balanced L1-L2 norm regularization method proposed by the present invention is adopted to achieve stable and efficient solution of key positioning parameters, i.e., connection point position correction parameters and affine transformation parameters, so as to improve the reprojection accuracy and geometric positioning accuracy.

[0019] like Figure 2 As shown, the regularization method of adaptively balancing the L1-L2 norm includes the following steps: The coefficient matrix constructed by the rational function model and affine transformation is input , ground control points and tie points together form the observation vector , construct a suitable regularization matrix based on prior information and threshold , to initialize the following parameters, including the outer loop index iter , the regularization parameter and balance parameters ; Regularization solution for initialization positioning parameters ; Initialize inner loop index , determine whether the number of iterations is less than the maximum number of iterations; if the condition is met, proceed to the next step and update the outer loop index iter , otherwise the output is the adaptive regularization solution ; Determine the penalty parameter Is it less than , if the conditions are met, proceed to the next step; otherwise, output the adaptive regularization solution ; Calculate the mixing parameter using the penalty parameter and regularization parameter ; Update auxiliary variables; Update regular solution , unit weight variance ; Judgement set The deviation correction elements in the calculation of the deviation correction solution ; Update auxiliary variables , update the balance parameters ; Based on the minimum mean square error criterion, the regularization parameter is updated using the bisection method ; judge If the inequality is not true, the number of iterations is increased by 1, and the inner loop continues until the inequality is true; otherwise, the outer loop index is updated. iter and penalty parameters , and return to the initialization inner loop index to continue iterating; When the outer loop index iter Satisfy the maximum number of times matiter , calculate and output the deviation correction solution of the final result .

[0020] Wherein, the hybrid parameter is calculated by using the penalty parameter and the regularization parameter The process is as follows: The expression of the adaptive balanced L1-L2 norm is constructed as follows: (1) in, x represents the parameters to be estimated, is a balance parameter between 0 and 1, is a regularized matrix with symmetric and positive and semi-positive definite characteristics; Objective Function Constructed as follows: (2) in represents the observation vector; represents the coefficient matrix, is the regularization parameter; The alternating direction multiplier method is used to solve the parameters and introduce intermediate variables The following expression is obtained: (3) in, Indicates the constructed variables x , z, w The objective function; arg min means to find a function parameter value that makes the objective function The result is the smallest; is a positive penalty parameter, is the augmented Lagrangian vector, with superscript T Represents matrix transpose; The expression defining the mixing parameters is: (4) in and are the penalty parameter and regularization parameter respectively, is a balance parameter.

[0021] Wherein, the calculation formula for updating the auxiliary variable is: Auxiliary parameters z The update formula is: (5) in represents the soft threshold function, To update auxiliary variables Update regular solution , unit weight variance The calculation formula is: parameter The update method is: (6) in , the superscript -1 indicates the inverse operation of the matrix; Unit weight variance The calculation formula is: (7) in, m and n The observation vectors are y The length and estimated parameters of Length.

[0022] Among them, the judgment set The deviation correction elements in the calculation of the deviation correction solution The process is as follows: Determine the set that meets the deviation correction The expression is as follows: (8) in, Representation Matrix No. i eigenvalues, Indicates the corresponding eigenvalue The eigenvector of Representation Matrix No. i eigenvalues, Indicates the corresponding eigenvalue The eigenvector of . The increase in eigenvalue will decrease, and the value on the left side of formula (6) will increase, then the variance of the selected part of the deviation that satisfies the correction will decrease; based on this condition, part of the deviation is removed from the regularized estimation formula (6) to correct the solution deviation The method is: (9) in, represents the bias-corrected regularization solution.

[0023] Wherein, the updating auxiliary variable , update the balance parameters The process: The parameters are estimated according to the calculation principle of the alternating direction multiplier method, where the auxiliary variables The update method is: (10) Balance parameters The update method is: (11) in, represents the normalization function, and Represents vectors x The minimum and maximum values ​​in .

[0024] In combination with the first aspect, in some implementations of the first aspect, the method further includes: obtaining an adaptive regularized solution The mean square error matrix MSE can be expressed as follows: (12) In the formula ; C( ) means The variance matrix of represents the true value of the unknown parameter, bias ( ) indicates a parameter The deviation term, I represents the unit matrix; Regularization parameter pass The optimal By minimizing The expression is obtained by the trace of: (13) in represents the trace of a square matrix; By taking the first-order derivative of equation (13), we can obtain the root whose first-order derivative is zero, which is the regularization parameter result. The expression of the first-order derivative is as follows: (14) Use the binary method to solve the root of equation (14). The approximation of The true value of is not known a priori, and the estimated value of the unknown parameter is used Initialize.

[0025] In combination with the first aspect, in some implementations of the first aspect, the method further includes: updating the penalty parameter The calculation process: judge If not, update , continue the inner loop; otherwise update the outer loop index , and update the solution : (15) Continue to repeatedly initialize the inner loop index, otherwise, finally output the adaptive regularization solution of deviation correction according to formula (9) .

[0026] Specifically, the present invention is further described below by way of embodiments: In this experiment, the left image is used as the reference image. Therefore, the reprojection error of the right image is used to evaluate the relative accuracy of the bundle adjustment solution. u and v The distribution in direction is Figure 5Compared with other similar algorithms, the BL1L2N algorithm proposed in this invention has the shortest arrow length, which means that the proposed BL1L2N has the smallest reprojection error, that is, it has the highest relative positioning accuracy. Specifically, the reprojection error of the LS solution is biased towards u -direction, and v- In contrast, the arrows of ElasticNet move in both directions. v - Direction and u -direction tilt. The above results are consistent with the results in Table 2. As shown in Table 2, the relative accuracy is qualitatively evaluated. In terms of the relative positioning accuracy, the improvement rates of the results of different regularization methods relative to the relative positioning accuracy of LS are 94.827%, 94.445%, 98.287%, 94.837%, 94.827%, 98.193%, 99.428% and 99.428%, respectively. It can be seen that the regularization method is an effective method to improve the relative accuracy of satellite image geometric positioning. In addition, the improvement rates of the relative positioning accuracy of BL1L2N proposed in the present invention relative to other regularization methods except LS are 4.601%, 4.983%, 1.142%, 4.591%, 4.601%, 1.235% and 0.0006%, respectively, which strongly proves the superiority of BL1L2N proposed in this paper in the accuracy of remote sensing image reprojection.

[0027] Table 1: RMSE of the right image reprojection error of 42 tie points Table 2: Geometric positioning accuracy residuals of the 42 connection points after adjustment To further evaluate the geometric positioning accuracy of BL1L2N, the absolute geometric positioning accuracy (as the RMSE of the residuals of 42 connection points) of different regularization methods is listed in Table 2. As can be seen from Table 2, L1 and ElasticNet cannot obtain reasonable geometric positioning accuracy, and the geometric positioning accuracy is consistent with that of direct forward intersection without adjustment. The absolute geometric positioning accuracy of the LS method is XY The plane accuracy reached 10.754m in the direction. Z The elevation accuracy of the proposed BL1L2N method is 13.471m, far exceeding other regularization methods. The root mean square error of the plane accuracy and elevation accuracy of the proposed BL1L2N method is almost equal, that is, about 5.3m and 5.8m respectively, but this is a substantial improvement over the similar L1 and ElasticNet spatial positioning methods. Although the geometric positioning accuracy is determined by the accuracy of the camera calibration parameters, the accuracy of the control points, and the accuracy of the spatial data processing algorithm; but by comparing the absolute positioning accuracy of LS (such as Figure 6As shown in Figure 3): Regularization methods improve the relative accuracy of reprojection and can potentially improve the absolute geometric positioning accuracy.

[0028] Example: The purpose of the present invention is to explore the generalization of regularization parameter selection to reduce the penalty parameter interference caused by the alternating direction multiplier method. On the basis of the deviation analysis in the process of solving the bundle adjustment model, the judgment condition for judging the deviation removal range is derived to ensure its rationality. In order to achieve the above-mentioned purpose, the present invention discloses an image geometry positioning method based on adaptive balanced L1-L2 norm regularization. Since the normal equation of the bundle adjustment of image geometry positioning belongs to an ill-posed problem, the traditional least squares method cannot obtain a convergent solution in the absence of ground control points (GCPs). In the case of terrain correlation, the rational polynomial coefficient parameters (RPCs) can be estimated by using at least 40 GCPs. And due to a large number of high correlation coefficients, the normal matrix of the rational function model is also ill-posed. The proposed BL1L2N can be used to solve these two problems.

[0029] In this example, if Figure 4 As shown in the figure, a ZY-3 stereo satellite image located in a certain area is selected, covering the range of (112.83°E~113.57°E, 34.33°W~34.95°W). In order to obtain high-precision spatial geometric positions from high-resolution satellite images, a bundle adjustment model based on the rational function model (RFM) is used, and its basic form can be expressed as: (16) in are the normalized image point coordinates in the u and v directions, and represents the normalized ground point coordinates. In addition, is a third-order polynomial, and each polynomial has 20 RPCs. They are and The system error correction parameter in the direction is expressed as: (17) in are the compensation parameters of these system errors. The error equations can be obtained by using the first-order Taylor linearization equation to obtain the series expansion, which can be expressed in matrix form: (18) in and is the residual error vector of the ground control point and tie point measurements in the u and v directions. A and B are the corresponding coefficient matrices; x is the correction vector of the ground control point coordinates corresponding to the tie point; t is the vector of systematic errors, or the parameters of the affine transformation; l is the constant vector calculated from the initial value; the subscripts cp and tp are the GCP and tie point, respectively. Due to the presence of many unknown parameters in the bundle adjustment process, the affine transformation coefficient t is separated from the coordinate correction of the ground point x. After linear transformation, the expression of t can be obtained as follows: (19) in is the corresponding weight matrix. is the Schur complement matrix, which can be obtained by reducing the normal matrix The dimension of is used to reduce the computational complexity. However, similar, It is still severely ill-posed, with a condition number exceeding 3.009×1013, so a regularization method should be applied to obtain a stable solution.

[0030] Second, as Figure 3 As shown, in order to achieve the above-mentioned purpose, the present invention discloses an image geometric positioning system based on adaptive balanced L1-L2 norm regularization, comprising: The data processing module 11 is used to obtain remote sensing satellite image data, perform radiation and geometric correction on the remote sensing satellite image data, and use SIFT and RANSAC methods to perform image matching to obtain processed remote sensing satellite image data; The geometric positioning module 12 is used to correct the processed remote sensing satellite image data based on the adaptive balanced L1-L2 norm regularization method, so as to solve the key positioning parameters and improve the reprojection accuracy and geometric positioning accuracy.

[0031] Based on the same inventive concept, the present invention also provides a computer device, which includes: one or more processors, and a memory for storing one or more computer programs; the program includes program instructions, and the processor is used to execute the program instructions stored in the memory. The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is used to implement one or more instructions, specifically for loading and executing one or more instructions in a computer storage medium to implement the above method.

[0032] It should be further explained that, based on the same inventive concept, the present invention also provides a computer storage medium, on which a computer program is stored, and the computer program is executed by the processor to execute the above method. The storage medium can adopt any combination of one or more computer-readable media. The computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electrical, magnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples (non-exhaustive list) of computer-readable storage media include: an electrical connection with one or more wires, a portable computer 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. In the present invention, a computer-readable storage medium can be any tangible medium containing or storing a program, which can be used by an instruction execution system, device or device or used in combination with it.

[0033] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present disclosure. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0034] The above shows and describes the basic principles, main features and advantages of the present disclosure. Those skilled in the art should understand that the present disclosure is not limited by the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present disclosure. Without departing from the spirit and scope of the present disclosure, the present disclosure may have various changes and improvements, and these changes and improvements fall within the scope of the present disclosure to be protected.

Claims

1. An image geometric positioning method based on adaptive balanced L1-L2 norm regularization, characterized in that: The method comprises the following steps: Acquire remote sensing satellite image data, perform radiation and geometric correction on the remote sensing satellite image data, and use SIFT and RANSAC methods for image matching to obtain processed remote sensing satellite image data; The processed remote sensing satellite image data is corrected based on the adaptive balanced L1-L2 norm regularization method to solve the key positioning parameters and improve the reprojection accuracy and geometric positioning accuracy.

2. The image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to claim 1, characterized in that: The regularization method of the adaptive balanced L1-L2 norm comprises the following steps: The coefficient matrix constructed by the rational function model and affine transformation is input , ground control points and tie points together form the observation vector , construct a regularization matrix based on prior information and threshold , to initialize the following parameters, including the outer loop index iter , the regularization parameter and balance parameters ; Regularization solution for initialization positioning parameters ; Initialize inner loop index , determine whether the number of iterations is less than the maximum number of iterations; if the condition is met, proceed to the next step and update the outer loop index iter Continue to iterate, otherwise output adaptive regularization solution ; Determine the penalty parameter Is it less than ; If the conditions are met: , then proceed to the next step; otherwise, output the adaptive regularization solution ; Calculate the mixing parameter using the penalty parameter and regularization parameter ; Update auxiliary variables; Update regular solution , unit weight variance ; Judgement set The deviation correction elements in the calculation of the deviation correction solution ; Update auxiliary variables , update the balance parameters ; Based on the minimum mean square error criterion, the regularization parameter is updated using the bisection method ; judge If the inequality is not true, the number of iterations is increased by 1, and the inner loop continues until the inequality is true; otherwise, the outer loop index is updated. iter and penalty parameters , and return to the initialization inner loop index to continue iterating; When the outer loop index iter Satisfy the maximum number of times matiter , calculate and output the deviation correction solution of the final result .

3. The image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to claim 2, characterized in that: The penalty parameter and the regularization parameter are used to calculate the mixing parameter The process is as follows: The expression of the adaptive balanced L1-L2 norm is constructed as follows: (1) in, x represents the parameters to be estimated, is the equilibrium parameter, is a regularized matrix with symmetric and positive and semi-positive definite characteristics; The objective function is constructed as follows: (2) in, represents the observation vector; represents the coefficient matrix; is the regularization parameter; The alternating direction multiplier method is used to solve the parameters and introduce intermediate variables The following expression is obtained: (3) in, Indicates the constructed variables x , z, w The objective function; arg min means to find a function parameter value that makes the objective function The result is the smallest; is a positive penalty parameter, is the augmented Lagrangian vector, with superscript T Represents matrix transpose; Defining blending parameters The expression is: (4) in and are the penalty parameter and regularization parameter respectively, is a balance parameter.

4. The image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to claim 3, characterized in that: The calculation formula for updating the auxiliary variable is: Auxiliary parameters z The update formula is: (5) in represents the soft threshold function, To update auxiliary variables; Update regular solution , unit weight variance The calculation formula is: parameter The update method is: (6) in , the superscript -1 indicates the inverse operation of the matrix; Unit weight variance The calculation formula is: (7) in, m and n The observation vectors are y The length and estimated parameters of Length.

5. The image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to claim 4, characterized in that: The judgment set The deviation correction elements in the calculation of the deviation correction solution The process is as follows: Determine the set that meets the deviation correction The expression is as follows: (8) in, Representation Matrix No. i eigenvalues, Indicates the corresponding eigenvalue The eigenvector of Representation Matrix No. i eigenvalues, Indicates the corresponding eigenvalue The eigenvector of The increase in eigenvalue will decrease, and the value on the left side of formula (6) will increase, then the variance of the selected part of the deviation that satisfies the correction will decrease; Based on this condition, some deviations are removed from the regularized estimation formula (6) to correct the solution deviation The method is: (9) in, represents the bias-corrected regularization solution.

6. The image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to claim 5, characterized in that: The updating auxiliary variable , update the balance parameters The process: The parameters are estimated according to the calculation principle of the alternating direction multiplier method, where the auxiliary variables The update method is: (10) Balance parameters The update method is: (11) in, represents the normalization function, and Represents vectors x The minimum and maximum values ​​in .

7. The image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to claim 6, characterized in that: The adaptive regularized solution is obtained The mean square error matrix MSE can be expressed as follows: (12) In the formula , C( ) represents The variance matrix of represents the true value of the unknown parameter, bias ( ) indicates the parameter The deviation term, I represents the unit matrix; Regularization parameter pass The optimal By minimizing The expression is obtained by the trace of: (13) in represents the trace of a square matrix; By taking the first-order derivative of equation (13), we can obtain the root whose first-order derivative is zero, which is the regularization parameter result. The expression of the first-order derivative is as follows: (14) Use the binary method to solve the root of equation (14). The approximation of The true value of is not known a priori, and the estimated value of the unknown parameter is used Initialize.

8. The image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to claim 7, characterized in that: The updated penalty parameter The calculation process: judge If not, update , continue the inner loop; otherwise update the outer loop index , and update the solution : (15) Continue to repeatedly initialize the inner loop index, otherwise, finally output the adaptive regularization solution of deviation correction according to formula (9) .

9. An image geometric positioning system based on adaptive balanced L1-L2 norm regularization, which adopts the image geometric positioning method based on adaptive balanced L1-L2 norm regularization according to any one of claims 1 to 8, characterized in that: include: The data processing module is used to obtain remote sensing satellite image data, perform radiation and geometric correction on the remote sensing satellite image data, and use SIFT and RANSAC methods to perform image matching to obtain processed remote sensing satellite image data; The geometric positioning module is used to correct the processed remote sensing satellite image data based on the adaptive balanced L1-L2 norm regularization method, so as to solve the key positioning parameters and improve the reprojection accuracy and geometric positioning accuracy.

10. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that: The memory stores a computer program that can be run on a processor. When the processor loads and executes the computer program, the image geometry positioning method based on adaptive balanced L1-L2 norm regularization described in any one of claims 1 to 8 is adopted.

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