CN115421212B - Synchronous processing method and system for heavy magnetic map complement and denoising - Google Patents
Synchronous processing method and system for heavy magnetic map complement and denoising Download PDFInfo
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- 230000001360 synchronised effect Effects 0.000 title claims abstract description 17
- 238000003672 processing method Methods 0.000 title claims abstract description 9
- 230000000295 complement effect Effects 0.000 title claims description 11
- 238000005457 optimization Methods 0.000 claims abstract description 39
- 238000012545 processing Methods 0.000 claims abstract description 22
- 102000008297 Nuclear Matrix-Associated Proteins Human genes 0.000 claims abstract description 12
- 108010035916 Nuclear Matrix-Associated Proteins Proteins 0.000 claims abstract description 12
- 210000000299 nuclear matrix Anatomy 0.000 claims abstract description 12
- 239000011159 matrix material Substances 0.000 claims description 26
- 238000000034 method Methods 0.000 claims description 9
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- 238000013507 mapping Methods 0.000 claims description 2
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- 238000011478 gradient descent method Methods 0.000 description 2
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Abstract
The invention discloses a synchronous processing method for the completion and denoising of a heavy magnetic map, which comprises the steps of firstly collecting heavy magnetic data and forming an original heavy magnetic map, then defining an optimization problem of synchronous processing of the completion and denoising of the heavy magnetic map, and finally solving the optimization problem to obtain a processed reconstructed heavy magnetic map. The invention can synchronously complete the completion and denoising of the heavy magnetic map, and further improves the processing precision of the heavy magnetic map by using global information; the nuclear matrix is adopted to project the original heavy magnetic data into a high-dimensional data space, so that the nonlinear processing capacity is improved; the optimization problem containing the Schatten norm is converted into the optimization problem containing the trace norm, and the optimization problem is easy to solve.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to a processing method and a system for synchronizing heavy magnetic map piece completion and denoising.
Background
The gravity magnetic exploration is carried out on the earth, and generally takes the gravitational field of the earth as the gravitational field of the detected object and the magnetic field of the earth as the magnetization field of the detected object, so that gravity anomaly generated by the attraction of the earth to the detected object and magnetic anomaly generated by the magnetization of the earth magnetic field are observed by using a gravity and magnetic instrument to achieve the detection purpose, and the gravity magnetic exploration has important roles in the fields of geological exploration, underground military target detection and the like.
The original measured heavy magnetic data can contain some measurement errors and random interference before processing, even some local data are missing, and preprocessing is needed before interpretation to eliminate some errors in the data. Common methods for preprocessing include lagrangian polynomial interpolation for data loss, kriging interpolation, etc., and linear rounding and quadratic curve rounding methods for data noise. These methods have two problems: firstly, global information is not used, so that the precision is difficult to further improve; secondly, there is no recognition that data missing can be regarded as an extreme case of data noise, and the two can be essentially completed synchronously.
Disclosure of Invention
The invention aims to solve the technical problem of providing a processing method and a processing system for synchronously completing and denoising a heavy magnetic drawing, which synchronously complete the completion and denoising of the heavy magnetic drawing and further improve the processing precision of the heavy magnetic drawing.
The technical scheme of the invention is as follows:
the synchronous processing method for the complement and the denoising of the heavy magnetic map comprises the following steps:
(1) First, the heavy magnetic data is collected and the original heavy magnetic image is formedn and m are respectively the number of transverse and longitudinal pixels of the preset original heavy magnetic drawing piece;
(2) Defining an optimization problem, wherein the formula of the optimization problem is shown in a formula (1):
wherein, as indicated by Hadamard multiplier; II and tr (·) are the F norm and trace norm, respectively; x is a reconstructed magnetic map; u is a pixel weighting matrix, and its element U E [0,1 ]]；λ>0, a weight factor;in the form of a matrix of nuclei,κ(x i ,x j ) A kernel function representing an ith row vector and a jth column vector in X; p epsilon (0, 1), which is the p factor of Schatten norm;
(3) And solving the optimization problem of the formula (1) to obtain the processed reconstructed magnetic map.
The pixel point D of the ith row and the jth column in the original heavy magnetic drawing piece D ij When missing, the ith row and jth column element U in U ij =0; when the pixel point d ij U when contaminated by noise ij E (0, 1), pixel point d ij The higher the signal-to-noise ratio, the u ij Correspondingly larger; when the pixel point d ij U when no noise pollution is generated ij ＝1。
The core matrixMiddle kappa (x) i ,x j ) The polynomial kernel function is adopted, and the formula of the polynomial kernel function is shown as formula (2):
wherein q>0, which is the degree of the polynomial;transposed symbols representing a transposed matrix; b>0, is the bias parameter.
The core matrixMiddle kappa (x) i ,x j ) The Gaussian kernel function is adopted, and the formula of the Gaussian kernel function is shown as a formula (3):
wherein σ >0 is the kernel smoothness parameter.
The system comprises an original drawing acquisition module, a pixel weighting matrix generation module, a nuclear matrix generation module, an optimization problem definition module and a training module;
the original image acquisition module is used for acquiring the heavy magnetic data and forming an original heavy magnetic image
The pixel weighting matrix generation module is used for determining a pixel weight according to noise pollution and missing conditions of each pixel point in the original heavy magnetic map;
the nuclear matrix generation module is used for projecting the collected heavy magnetic data into a high-dimensional data space;
the optimization problem definition module is used for constructing optimization problems of the synchronous processing of the remaking and denoising of the magnetic map;
the training module is used for solving the optimization problem.
The optimization problem definition module is used for constructing an optimization problem based on the original drawing acquisition module, the pixel weighting matrix generation module and the nuclear matrix generation module.
The invention has the advantages that:
(1) The invention can synchronously complete the completion and the denoising of the heavy magnetic map, and further improves the processing precision of the heavy magnetic map by using global information.
(2) According to the invention, the nuclear matrix is adopted to project the original heavy magnetic data into a high-dimensional data space, so that the nonlinear processing capacity is improved.
(3) The invention converts the optimization problem containing Schatten norms into the optimization problem containing trace norms, and is easy to solve.
Drawings
FIG. 1 is a flow chart of the method for synchronous processing of the completion and denoising of the heavy magnetic map.
FIG. 2 is a schematic diagram of a method for synchronous processing of heavy magnetic pattern completion and denoising according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in FIG. 1, the synchronous processing method for the completion and denoising of the heavy magnetic map comprises the following steps:
(1) First, the heavy magnetic data is collected and the original heavy magnetic image is formedn and m are respectively the number of transverse and longitudinal pixels of the preset original heavy magnetic drawing piece;
(2) Defining an optimization problem, wherein the formula of the optimization problem is shown in a formula (1):
wherein, as indicated by Hadamard multiplier; II and tr (·) are the F norm and trace norm, respectively; x is a reconstructed magnetic map; u is a pixel weighting matrix, and its element U E [0,1 ]]Pixel point D of ith row and jth column in original heavy magnetic map D ij When missing, the ith row and jth column element U in U ij =0; when the pixel point d ij U when contaminated by noise ij E (0, 1), pixel point d ij The higher the signal-to-noise ratio, the u ij Correspondingly larger; when the pixel point d ij U when no noise pollution is generated ij =1; lambda E (0, 100), is a weight factor;is a nuclear matrix> κ(x i ,x j ) A kernel function representing an ith row vector and a jth column vector in X; p epsilon (0, 1), which is the p factor of Schatten norm;
kappa (x) in the kernel matrix Z i ,x j ) A polynomial kernel function may be used, where the formula of the polynomial kernel function is shown in formula (2):
wherein q is E [1,10 ]]Is the degree of a polynomial; />Transposed symbols representing a transposed matrix; b E [ -10,10]Is a bias parameter;
nuclear matrixMiddle kappa (x) i ,x j ) A gaussian kernel function can be used, and the formula of the gaussian kernel function is shown in formula (3):
wherein σ ε [0.1,10] is the kernel smoothness parameter;
(3) Solving the optimization problem of the formula (1) to obtain a processed reconstructed magnetic map; the gradient descent method can be adopted to solve, and the gradient of the gradient descent method for solving the optimization problem is as follows:
wherein,
wherein delta is rs Represents the r-th row and s-th column element in delta,representation->The j-th column element of row i,the j-th column element of the i-th row of (2) is +.>
A simple derivation of the optimization problem is given below in connection with fig. 2:
for the denoising and complement problem of the graph, the following optimization problem is usually solved by using the low rank assumption:
where rank represents the rank norm, however, the rank norm is difficult to solve, and therefore, the most convex relaxation of rank norms is used instead of the kernel norms, i.e. with II X II * Replacement rank (X); more precisely, the non-convex relaxed Schatten norm using the rank norm, i.eWherein delta i (X) represents the kth singular value of X; it is easy to see that,
further, the original heavy magnetic data is projected to a high-dimensional space, so that the nonlinear processing capacity is improved, namely, a nonlinear function is adoptedMapping D to feature space by row +.>Wherein (1)>Is an inner product space, and its dimension l can be arbitrarily large or even infinite, forming a mapped heavy magnetic map +.> Without the display structure phi (, a) a kernel matrix can be used> And->And (3) taking the power of the rank as a rank measure, and bringing the power into a formula (4) to obtain a formula (1). Therefore, the nuclear matrix not only can improve the nonlinear processing capacity, but also can simplify the solution of Schatten, and X obtained after optimization solution is the reconstructed magnetic map.
The system comprises an original drawing acquisition module, a pixel weighting matrix generation module, a nuclear matrix generation module, an optimization problem definition module and a training module;
the original image acquisition module is used for acquiring the heavy magnetic data and forming an original heavy magnetic image
The pixel weighting matrix generation module is used for determining a pixel weight according to noise pollution and missing conditions of each pixel point in the original heavy magnetic drawing;
the nuclear matrix generation module is used for projecting the collected heavy magnetic data into a high-dimensional data space;
the optimization problem definition module is used for constructing an optimization problem of the synchronous processing of the remagnet map piece completion and the denoising, and the optimization problem definition module is used for constructing the optimization problem based on the original map piece acquisition module, the pixel weighting matrix generation module and the nuclear matrix generation module;
the training module is used for solving the optimization problem.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (6)
1. The synchronous processing method for the completion and denoising of the heavy magnetic map is characterized by comprising the following steps of: the method specifically comprises the following steps:
(1) First, the heavy magnetic data is collected and the original heavy magnetic image is formedn and m are respectively the number of transverse and longitudinal pixels of the preset original heavy magnetic drawing piece;
(2) Defining an optimization problem, wherein the formula of the optimization problem is shown in a formula (1):
wherein, as indicated by Hadamard multiplier; II and tr (·) are the F norm and trace norm, respectively; x is a reconstructed magnetic map; u is a pixel weighting matrix, and its element U E [0,1 ]]；λ>0, a weight factor;in the form of a matrix of nuclei,κ(x i ,x j ) A kernel function representing an ith row vector and a jth column vector in X; p epsilon (0, 1), which is the p factor of Schatten norm;
the original heavy magnetic data in the original heavy magnetic drawing piece is projected to a high-dimensional space, so that the nonlinear processing capacity is improved, namely, a nonlinear function phi (.):mapping D into feature space by row/>Wherein (1)>Is an inner product space, and its dimension l is arbitrarily large or infinite, forming a mapped heavy magnetic mapWithout explicit construction of phi (,), a kernel matrix is employedAnd->As a rank metric;
(3) And solving the optimization problem of the formula (1) to obtain the processed reconstructed magnetic map.
2. The method for synchronous processing of heavy magnetic map complement and denoising according to claim 1, wherein: the pixel point D of the ith row and the jth column in the original heavy magnetic drawing piece D ij When missing, the ith row and jth column element U in U ij =0; when the pixel point d ij U when contaminated by noise ij E (0, 1), pixel point d ij The higher the signal-to-noise ratio, the u ij Correspondingly larger; when the pixel point d ij U when no noise pollution is generated ij ＝1。
3. The method for synchronous processing of heavy magnetic map complement and denoising according to claim 1, wherein: the core matrixMiddle kappa (x) i ,x j ) The polynomial kernel function is adopted, and the formula of the polynomial kernel function is shown as formula (2):
wherein q>0, which is the degree of the polynomial;transposed symbols representing a transposed matrix; b>0, is the bias parameter.
4. The method for synchronous processing of heavy magnetic map complement and denoising according to claim 1, wherein: the core matrixMiddle kappa (x) i ,x j ) The Gaussian kernel function is adopted, and the formula of the Gaussian kernel function is shown as a formula (3):
wherein σ >0 is the kernel smoothness parameter.
5. The heavy magnetic pattern complement and denoising synchronous processing system for realizing the heavy magnetic pattern complement and denoising synchronous processing method of claim 1, which is characterized in that: the system comprises an original drawing acquisition module, a pixel weighting matrix generation module, a kernel matrix generation module, an optimization problem definition module and a training module;
the original image acquisition module is used for acquiring the heavy magnetic data and forming an original heavy magnetic image
The pixel weighting matrix generation module is used for determining a pixel weight according to noise pollution and missing conditions of each pixel point in the original heavy magnetic map;
the nuclear matrix generation module is used for projecting the collected heavy magnetic data into a high-dimensional data space;
the optimization problem definition module is used for constructing an optimization problem of the synchronous processing of the heavy magnetic map piece complement and the denoising, and the formula of the optimization problem is shown in a formula (1);
the training module is used for solving the optimization problem.
6. The heavy magnetic pattern complement and denoising synchronization processing system of claim 5, wherein: the optimization problem definition module is used for constructing an optimization problem based on the original drawing acquisition module, the pixel weighting matrix generation module and the nuclear matrix generation module.
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