CN108303740B - Aviation electromagnetic data noise suppression method and device - Google Patents
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Abstract
The invention relates to the field of aviation electromagnetic data processing, in particular to an aviation electromagnetic data noise suppression method and device, which are used for decomposing profile data into principal components arranged according to variance on the basis of principal component analysis; residual noise in the low-order principal component is removed using a minimum noise separation transform. Aiming at the problems that profile data of an aviation electromagnetic late track is high in noise level and difficult to extract abnormity, a theory of statistical analysis is introduced, so that residual noise in a low-order principal component can be removed comprehensively, abnormal information annihilated by noise in the low-order principal component is extracted effectively, the problem that the abnormal information of the late track is influenced by the early track due to direct implementation of minimum noise separation transformation is avoided, and the noise of the late track is suppressed effectively.
Description
Technical Field
The invention relates to the field of aviation electromagnetic data processing, in particular to an aviation electromagnetic data noise suppression method and device.
Background
The time domain aviation electromagnetic detection technology adopts an airborne mode, realizes the geophysical detection with large depth and high efficiency according to the electromagnetic induction principle, has the advantages of high speed, low cost, good trafficability, large-area coverage and the like, and is widely applied to the fields of basic geological investigation, mineral resource investigation, oil gas investigation, hydrology, engineering, environmental investigation and the like. The aviation electromagnetic detection system is influenced by environmental noise, system noise, motion noise and the like in the flight detection process, interferes with the observation of aviation electromagnetic data and the extraction of effective signals, seriously influences the deep detection capability of the system, and is an important index for restricting the development of aviation electromagnetic detection technology.
A noise removal method for filtering and reconstructing a principal component of aviation electromagnetic data in an article such as Zhukelong and the like is J geophysical report 2015,58(08):2803-2811, the principal component is used for analyzing and extracting characteristics of the aviation electromagnetic data, and residual noise of a section of the aviation electromagnetic data is effectively suppressed; an article such as an old and the like is a time domain aviation electromagnetic denoising method [ J ] based on kernel principal component analysis, geophysical science and newspaper 2014,57(01): 295-; wanglingqu et al, "aviation electromagnetic data noise removing method based on principal component analysis" [ J ]. Chinese non ferrous metals academic newspaper, 2013,23(09): 2430-; li Yue et al, entitled "Noise removal for airborne time based on minor Noise fraction" explicit geomatics, 2016, Online Early, suppress Noise in airborne electromagnetic profile data using minimum Noise separation transform.
Chinese patent publication No. CN106094046A discloses a "time domain airborne electromagnetic data denoising method based on singular value decomposition and wavelet analysis". According to the method, singular value decomposition and wavelet analysis are combined, time domain and space domain filtering processing is carried out on time domain aviation electromagnetic detection profile data, and human noise and celestial electric noise in signals are suppressed. However, the residual noise of the late trace of the aviation electromagnetic profile data cannot be effectively removed, and the abnormal information can be extracted under the condition that the late trace noise submerges the signal.
Disclosure of Invention
The embodiment of the invention provides a method and a device for suppressing noise of aviation electromagnetic data, which solve the problem that abnormal information is difficult to extract under the condition that signals are drowned by late-stage noise.
The present invention is achieved in such a way that,
in a first aspect of the present invention, there is provided an airborne electromagnetic data noise suppression method, including:
calculating an aviation electromagnetic profile data covariance matrix, decomposing eigenvalues of the aviation electromagnetic profile data covariance matrix, and arranging the eigenvalues and eigenvectors obtained by decomposition in a descending order to form an eigenvector matrix;
obtaining a rotation matrix according to the eigenvector matrix, and linearly transforming the aviation electromagnetic profile data into principal component data;
performing noise estimation on low-order principal component data of the principal component data;
calculating a low-order principal component data noise covariance matrix, decomposing the eigenvalues of the low-order principal component data noise covariance matrix, and arranging the eigenvalues and eigenvectors obtained by decomposition in a descending order;
calculating a low-order principal component data covariance matrix and constructing an adjustment matrix to adjust the low-order principal component data covariance matrix;
performing eigenvalue decomposition on the adjusted low-order principal component covariance matrix, and performing descending order arrangement on the eigenvalues and eigenvectors obtained by decomposition;
constructing a transformation matrix, and transforming the low-order principal component data into a minimum noise separation transformation component;
selecting a low-order minimum noise separation transformation component to reconstruct low-order principal component data;
and reconstructing profile data by using the low-order principal component data.
With reference to the first aspect, in a first possible implementation manner, the covariance matrix of the airborne electromagnetic profile data is calculated, and preprocessing is performed on the airborne electromagnetic raw data before the eigenvalue decomposition is performed on the airborne electromagnetic profile data, where the preprocessing includes performing zero-mean processing on each piece of data of the survey line to obtain the airborne electromagnetic profile data, and the airborne electromagnetic profile data is used for the next calculation.
With reference to the first aspect, in a first possible implementation manner, the element α in the covariance matrix of the airborne electromagnetic profile datakqThe calculation expression of (a) is as follows:
in the formula, xk(j) Represents the j-th measuring point data of the k-th track, wherein j is 1, 2.
And
respectively, carrying out eigenvalue decomposition on the covariance matrix of the aviation electromagnetic profile data, wherein the average values of the k-th track and the q-th track of the aviation electromagnetic profile data are k and q are 1, 2.
C＝VDVT，
Wherein C is a covariance matrix of the aviation electromagnetic profile data, D is a diagonal matrix in which eigenvalues of the covariance matrix of the aviation electromagnetic profile data are arranged in descending order, V is an eigenvector matrix corresponding to the eigenvalues of the covariance matrix of the aviation electromagnetic profile data, and V is a linear matrix of the eigenvectorsTIs a rotation matrix.
With reference to the first possible implementation manner of the first aspect, in a second implementation manner, a rotation matrix is obtained according to an eigenvector matrix corresponding to an eigenvalue of a covariance matrix of the aviation electromagnetic profile data, and the aviation electromagnetic profile data is linearly transformed into principal component data, where an adopted formula is as follows: phi ═ VTX，VTThe matrix is a rotation matrix, X is aviation electromagnetic profile data, and phi (m multiplied by n) is main component data.
With reference to the first aspect, in a third implementable manner, an accumulated contribution rate of the previous p-order principal component data is calculated, and when the accumulated contribution rate of the current p-order principal component data is higher than 90%, the previous p-order principal component data is taken as the low-order principal component data, and the remaining high-order principal components contain a large amount of uncorrelated noise.
With reference to the first aspect, in a third implementable manner, in a fourth implementable manner, noise estimation is performed on the previous p-th order principal component data by using an adaptive window width filtering algorithm.
With reference to the first aspect, in a third implementable manner, in a fifth implementable manner, calculating a covariance matrix of low-order principal component data and constructing an adjustment matrix to adjust the covariance matrix includes: converting the noise variance in each minimum noise separation transformation component into unit variance by constructing an adjustment matrix, wherein the expression of the adjustment matrix is as follows: p is UNDN -0.5Where P is the adjustment matrix, DNIs a diagonal matrix with characteristic values of low-order principal component data noise covariance matrix arranged in descending order, UNThe method is characterized in that the method is an eigenvector matrix corresponding to eigenvalues of a low-order principal component data noise covariance matrix, and the covariance matrix of the low-order principal component data is adjusted, wherein the expression is as follows:
wherein C isDTo the adjusted front p-th order principal component data covariance matrix,
the covariance matrix of the first p-th order principal component data.
With reference to the first aspect, in a sixth implementable manner, performing eigenvalue decomposition on the adjusted low-order principal component covariance matrix includes: the expression used is: cD＝VDDDVD TIn the formula, DDIs a diagonal matrix, V, in which the adjusted low-order principal component covariance matrices are arranged in descending orderDIs an eigenvector matrix corresponding to eigenvalues of the adjusted low-order principal component covariance matrix, CDIs the adjusted low-order principal component covariance matrix.
With reference to the first aspect, in a seventh implementable manner, constructing the transformation matrix includes using the expression: r ═ PVDP is an adjustment matrix, VDThe feature vector matrix corresponding to the eigenvalue of the adjusted low-order principal component covariance matrix, R is a transformation matrix, wherein the low-order principal component data is linearly transformed into a minimum noise separation transformation component through the transformation matrix R, and the matrix formed by the minimum noise separation transformation component is represented as follows:
in the formula,
separating the transformed component for minimum noise by psi as low-order principal component data, DNIs a diagonal matrix with characteristic values of low-order principal component data noise covariance matrix arranged in descending order, UNThe method is characterized in that the method is an eigenvector matrix corresponding to eigenvalues of a low-order principal component data noise covariance matrix, minimum noise separation transformation components are arranged from large to small according to signal-to-noise ratio, the low-order components comprise main signal parts of electromagnetic profile data, and the minimum noise separation transformation of the front L (L is more than 1 and less than p) is selectedAnd reconstructing low-order principal component data by component conversion.
With reference to the first aspect, in an eighth implementable manner, the reconstructing the profile data from the low-order principal component data includes: zero padding is carried out on the reconstruction principal component data matrix to form an m multiplied by n matrix, and the reconstruction section data expression is as follows:
in the formula, B (m × m) is a truncated matrix in which the first p rows have 1 element and the remaining elements have 0 elements.
In a second aspect, the present invention provides an airborne electromagnetic data noise suppression apparatus, the apparatus comprising: the memory is in communication connection with the processor, the output module retrieves the data of the memory for output,
the memory is used for storing the aeroelectromagnetic profile data;
the processor is used for calculating the covariance matrix of the aviation electromagnetic profile data after the data of the memory is taken, decomposing the eigenvalues of the covariance matrix, arranging the eigenvalues and the eigenvectors obtained by decomposition in a descending order, forming an eigenvector matrix and storing the eigenvector matrix in the memory;
the processor is used for obtaining a rotation matrix according to the characteristic vector matrix and linearly transforming the aviation electromagnetic profile data into principal component data;
the processor is used for carrying out noise estimation on low-order principal component data of the principal component data;
the processor is used for calculating a low-order principal component data noise covariance matrix, decomposing the eigenvalue of the low-order principal component data noise covariance matrix, and performing descending order arrangement on the eigenvalue and the eigenvector obtained by decomposition;
the processor is used for calculating a low-order principal component data covariance matrix and constructing an adjustment matrix to adjust the low-order principal component data covariance matrix;
the processor is used for decomposing the eigenvalues of the adjusted low-order principal component covariance matrix and arranging the eigenvalues and eigenvectors obtained by decomposition in a descending order;
the processor is used for constructing a transformation matrix and transforming the low-order principal component data into a minimum noise separation transformation component;
the processor is used for selecting a low-order minimum noise separation transformation component to reconstruct low-order principal component data;
the processor is used for reconstructing profile data from the low-order principal component data;
and the output module outputs a noise suppression result to the data processed by the processor and forms a graph.
A further aspect of the invention provides a computer program having a program code for running on a processor on which the method of the possible implementation of the first aspect is performed.
Compared with the prior art, the invention has the beneficial effects that:
the noise suppression method of the invention firstly decomposes profile data into principal components arranged according to variance based on Principal Component Analysis (PCA); second, residual noise in the low-order principal component is removed using a minimum noise separation transform (MNF). Aiming at the problems that profile data of an aviation electromagnetic late track is high in noise level and difficult to extract abnormity, the method introduces a theory of statistical analysis, can completely remove residual noise in a low-order principal component, effectively extracts abnormal information annihilated by noise in the low-order principal component, avoids the problem that the abnormal information of the late track is influenced by an early track due to direct implementation of minimum noise separation transformation, and realizes effective suppression of the noise of the late track. The method can effectively extract the late track data abnormality annihilated by noise, and the noise suppression effect of the method is superior to the principal component analysis noise suppression effect and the minimum noise separation transformation noise suppression effect.
Drawings
FIG. 1 is a flow chart of an aviation electromagnetic data noise suppression method based on a PCA and MNF combined algorithm according to an embodiment of the present invention;
FIG. 2 is a block diagram of a structure of an aviation electromagnetic data noise suppression device based on a PCA and MNF combined algorithm according to an embodiment of the present invention;
FIG. 3 is a cross-sectional view of airborne electromagnetic data in an embodiment provided by an embodiment of the present invention;
FIG. 4a is a cross-sectional view of a late trace of airborne electromagnetic data in an embodiment provided by an embodiment of the present invention;
FIG. 4b is a cross-sectional view of a late trace of a noise suppression result based on principal component analysis according to an embodiment of the present invention;
FIG. 4c is a cross-sectional diagram of a late trace of a noise suppression result based on a minimum noise separation transform according to an embodiment of the present invention;
fig. 4d is a cross-sectional view of a late trace of a noise suppression result based on a joint algorithm of PCA and MNF according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
According to the aviation electromagnetic data noise suppression method provided by the embodiment of the invention, profile data is decomposed into principal components arranged according to the variance based on a principal component analysis algorithm (PCA); second, residual noise in the low-order principal component is removed using a minimum noise separation transform (MNF). The method comprises the following steps:
based on certain input data, the data is original data after being collected, and the aviation electromagnetic original data is preprocessed after being input to obtain survey line profile data. Specifically, a measuring line X (n multiplied by m) is provided with m data of n measuring points, each data is subjected to zero-crossing equalization processing, and the measuring line section data, namely the aviation electromagnetic section data, is expressed as follows:
in the formula, xk(j) Represents the jth measuring point data of the kth track, wherein k is 1, 2. j is 1, 2.
Calculating and carrying out covariance matrix on aviation electromagnetic profile dataDecomposing the eigenvalue, and arranging the eigenvalue and the eigenvector obtained by decomposition in a descending order to form an eigenvector matrix; in the process, the element alpha in the covariance matrix C of the aeroelectromagnetic profile datakqThe calculation expression of (a) is as follows:
in the formula,
and
the mean values of the k-th track and the q-th track of the aeronautical electromagnetic profile data, k and q being 1, 2. And (3) carrying out eigenvalue decomposition on the aviation electromagnetic profile data covariance matrix C, wherein the expression is as follows:
C＝VDVT，
wherein D is a diagonal matrix with characteristic values of the covariance matrix of the aviation electromagnetic profile data arranged in descending order, V is an eigenvector matrix corresponding to the characteristic values of the covariance matrix of the aviation electromagnetic profile data, and V is a diagonal matrixTIs a rotation matrix.
After a rotation matrix is obtained, linearly converting the aviation electromagnetic profile data into principal component data; in the process, a rotation matrix V is usedTThe profile data X is linearly converted into principal component data Φ (m × n) by the following formula: phi ═ VTX，VTIs a rotation matrix and X is the aeronautical electromagnetic profile data.
Performing noise estimation on low-order principal component data of the principal component data; preferably, the cumulative contribution Δ of the pre-p-th order principal component is calculatedp，
In the formula, λjIs the characteristic value corresponding to the j-th order principal component data. When the accumulated contribution rate of the current p-order principal component data is higher than 90%, taking the previous p-order principal component data as
The remaining higher order principal components contain a significant amount of uncorrelated noise.
Using self-adaptive window width filtering algorithm to carry out pre-p-order principal component
And carrying out noise estimation. With the k-th data in the data
For example, the adaptive window width filtering algorithm process is as follows:
assuming a window width of WL-WU，WLAnd WURepresenting the minimum window width and the maximum window width, respectively.
Is the maximum window width smoothing filter result of the k-th order,
the second order difference calculation expression of (1) is as follows:
wherein, the [ alpha ], [ beta ]]Is a calculation of rounding down to the nearest integer,
is that
The element of the jth measuring point of (1), namely the maximum window width filtered data of each measuring point. Adaptive window width W of each measurement pointk(j) Included in the minimum window width WLAnd maximum window width WUWithin the range, the expression is as follows:
wherein, DeltarIs the threshold for the second order difference.
The data of the first p-th order principal component after the k-th order principal component is subjected to adaptive window width filtering is represented as follows:
the noise estimated after the k-th order principal component is filtered by the adaptive window width is represented as follows:
calculating a noise covariance matrix of low-order principal component data (namely the previous p-order principal component data), decomposing the eigenvalue of the noise covariance matrix, and arranging the eigenvalue and the eigenvector obtained by decomposition in a descending order; noise covariance matrix C of pre-p-order principal component dataNMiddle element gammakqThe calculation expression of (a) is as follows:
wherein,
and
mean values, k, q ═ 1,2,.. times, m, for the k-th and q-th traces, respectively, of the noisy data, the noise covariance matrix is subjected to eigenvalue decomposition, the expression being as follows:
CN＝UNDNUN T，
in the formula, DNIs a diagonal matrix with noise covariance matrix eigenvalues arranged in descending order, UNIs a matrix of eigenvectors corresponding to the eigenvalues.
Calculating a low-order principal component data covariance matrix and constructing an adjustment matrix to adjust the low-order principal component data covariance matrix; front p-order principal component data covariance matrix
Beta of middle elementkqThe calculation expression of (a) is as follows:
in the formula,
and
the average values of the k-th track and the q-th track of the previous p-order principal component data, k, q are 1,2,.
The adjustment matrix is constructed so that the noise variance in each of the minimum noise separation transformation components is converted into a unit variance, wherein the adjustment matrix P satisfies the equation PTCNAnd E is an identity matrix. The adjustment matrix expression is as follows: p is UNDN -0.5. Where P is the adjustment matrix, UNIs an eigenvector matrix corresponding to eigenvalues of a low-order principal component data noise covariance matrix, DNThe covariance matrix of the low-order principal component data is adjusted by a diagonal matrix in which eigenvalues of the low-order principal component data noise covariance matrix are arranged in a descending order.
Covariance matrix of pre-p-order principal component data
The adjustment is made, the expression is as follows:
wherein C isDTo the adjusted front p-th order principal component data covariance matrix,
the covariance matrix of the first p-th order principal component data.
Performing eigenvalue decomposition on the adjusted low-order principal component covariance matrix, and performing eigenvalue decomposition on the decomposed characteristicsThe values and feature vectors are arranged in descending order; the expression used is: cD＝VDDDVD TIn the formula, DDIs a diagonal matrix, V, in which the adjusted low-order principal component covariance matrices are arranged in descending orderDIs an eigenvector matrix corresponding to eigenvalues of the adjusted low-order principal component covariance matrix, CDIs the adjusted low-order principal component covariance matrix.
Constructing a transformation matrix, and transforming the low-order principal component data into a minimum noise separation transformation component; constructing the transformation matrix includes using the expression: r ═ PVDP is an adjustment matrix, VDThe feature vector matrix corresponding to the eigenvalue of the adjusted low-order principal component covariance matrix, R is a transformation matrix, wherein the low-order principal component data is linearly transformed into a minimum noise separation transformation component through the transformation matrix R, and the matrix formed by the minimum noise separation transformation component is represented as follows:
in the formula,
separating the transformed component for minimum noise by psi as low-order principal component data, DNIs a diagonal matrix with characteristic values of low-order principal component data noise covariance matrix arranged in descending order, UNThe minimum noise separation transformation component is arranged from large to small according to the signal-to-noise ratio, the low-order component comprises a main signal part of the electromagnetic profile data, and the low-order component is reconstructed by selecting the front L (L is more than 1 and less than p) minimum noise separation transformation component.
Selecting a low-order minimum noise separation transformation component to reconstruct low-order principal component data; the reconstructed principal component data expression is as follows:
reconstructing profile data from low-order principal component data, wherein reconstructing electromagnetic profile data requires reconstructing a principal component data matrix
Zero padding is carried out to form an m multiplied by n matrix, and the reconstructed section data expression is as follows:
in the formula, B (m × m) is a truncated matrix in which the first p rows have 1 element and the remaining elements have 0 elements.
The invention also provides an airborne electromagnetic data noise suppression device, referring to fig. 2, the device comprising: the memory is in communication connection with the processor, the output module retrieves the data of the memory for output,
the memory is used for storing the aeronautical electromagnetic profile data;
the processor is used for calculating the covariance matrix of the aviation electromagnetic profile data after the data of the memory is called, decomposing the eigenvalues of the covariance matrix, arranging the eigenvalues and the eigenvectors obtained by decomposition in a descending order, forming an eigenvector matrix and storing the eigenvector matrix in the memory;
the processor is used for obtaining a rotation matrix according to the characteristic vector matrix and linearly transforming the aviation electromagnetic profile data into principal component data;
the processor is used for carrying out noise estimation on low-order principal component data of the principal component data;
the processor is used for calculating a low-order principal component data noise covariance matrix, decomposing the eigenvalue of the low-order principal component data noise covariance matrix, and performing descending order arrangement on the eigenvalue and the eigenvector obtained by decomposition;
the processor is used for calculating a low-order principal component data covariance matrix and constructing an adjustment matrix to adjust the low-order principal component data covariance matrix;
the processor is used for decomposing the eigenvalues of the adjusted low-order principal component covariance matrix and arranging the eigenvalues and eigenvectors obtained by decomposition in a descending order;
the processor is used for constructing a transformation matrix and transforming the low-order principal component data into a minimum noise separation transformation component;
the processor is used for selecting a low-order minimum noise separation transformation component to reconstruct low-order principal component data;
the processor is used for reconstructing the profile data from the low-order principal component data;
the output module outputs the noise suppression result through the data processed by the processor and forms a graph.
The processor also comprises a preprocessing unit which is used for calculating the covariance matrix of the aviation electromagnetic profile data, preprocessing the aviation electromagnetic original data before decomposing the eigenvalue of the covariance matrix, and carrying out zero-crossing averaging processing on each data of the measuring line to obtain the aviation electromagnetic profile data.
Element alpha in covariance matrix of aviation electromagnetic profile datakqThe calculation expression of (a) is as follows:
in the formula, xk(j) Represents the j-th measuring point data of the k-th track, wherein j is 1, 2.
And
the processor further includes a decomposition module for performing eigenvalue decomposition on the covariance matrix of the aviation electromagnetic profile data, where the expression is as follows:
C＝VDVT，
wherein C is a covariance matrix of the aviation electromagnetic profile data, D is a diagonal matrix in which eigenvalues of the covariance matrix of the aviation electromagnetic profile data are arranged in descending order, V is an eigenvector matrix corresponding to the eigenvalues of the covariance matrix of the aviation electromagnetic profile data, and V is a linear matrix of the eigenvectorsTIs a rotation matrix.
The processor also includes a computationThe unit is used for obtaining a rotation matrix according to an eigenvector matrix corresponding to the covariance matrix eigenvalue of the aviation electromagnetic profile data, and linearly transforming the aviation electromagnetic profile data into principal component data by adopting a formula as follows: phi ═ VTX，VTThe matrix is a rotation matrix, X is aviation electromagnetic profile data, and phi (m multiplied by n) is main component data.
The processor adopts a noise estimation unit to calculate the cumulative contribution rate of the previous p-order principal component data, when the cumulative contribution rate of the current p-order principal component data is higher than 90%, the previous p-order principal component data is taken as the low-order principal component data, and the rest high-order principal components contain a large amount of uncorrelated noise. And noise estimation is carried out on the previous p-order principal component data by adopting a self-adaptive window width filtering algorithm.
The processor further comprises an adjusting unit for calculating the covariance matrix of the low-order principal component data and constructing an adjusting matrix to adjust the covariance matrix, wherein the adjusting unit comprises: converting the noise variance in each minimum noise separation transformation component into unit variance by constructing an adjustment matrix, wherein the expression of the adjustment matrix is as follows: p is UNDN -0.5Where P is the adjustment matrix, UNIs an eigenvector matrix corresponding to eigenvalues of a low-order principal component data noise covariance matrix, DNThe covariance matrix of the low-order principal component data is adjusted by a diagonal matrix in which eigenvalues of the low-order principal component data noise covariance matrix are arranged in a descending order, and the expression is as follows:
wherein C isDTo the adjusted front p-th order principal component data covariance matrix,
the covariance matrix of the first p-th order principal component data.
The processor adopts a calculation module to carry out eigenvalue decomposition on the adjusted low-order principal component covariance matrix, and the eigenvalue decomposition comprises the following steps: the expression used is: cD＝VDDDVD TIn the formula, DDThe adjusted low-order principal component covariance matrix is sorted according to descending orderDiagonal matrix of columns, VDIs an eigenvector matrix corresponding to eigenvalues of the adjusted low-order principal component covariance matrix, CDIs the adjusted low-order principal component covariance matrix.
The processor further comprises a construction unit for constructing the transformation matrix comprising the following expressions: r ═ PVDP is an adjustment matrix, VDThe feature vector matrix corresponding to the eigenvalue of the adjusted low-order principal component covariance matrix, R is a transformation matrix, wherein the low-order principal component data is linearly transformed into a minimum noise separation transformation component through the transformation matrix R, and the matrix formed by the minimum noise separation transformation component is represented as follows:
in the formula,
separating the transformed component for minimum noise by psi as low-order principal component data, DNIs a diagonal matrix with characteristic values of low-order principal component data noise covariance matrix arranged in descending order, UNThe minimum noise separation transformation component is arranged from large to small according to the signal-to-noise ratio, the low-order component comprises a main signal part of the electromagnetic profile data, and the low-order component is reconstructed by selecting the front L (L is more than 1 and less than p) minimum noise separation transformation component.
The processor further includes a reconstruction unit for reconstructing profile data from the low-order principal component data, including: zero padding is carried out on the reconstruction principal component data matrix to form an m multiplied by n matrix, and the reconstruction section data expression is as follows:
in the formula, B (m × m) is a truncated matrix in which the first p rows have 1 element and the remaining elements have 0 elements.
The embodiments described above may be implemented in whole or in part by software, hardware, firmware, or any combination thereof, and when implemented using software, may be implemented in whole or in part in the form of a computer program product. The program code is used for the computer program to execute the program code of the above-mentioned embodiment method on the processor, and the computer program can be stored in a computer readable storage medium, where the readable storage medium can be a hard disk, an optical disk and a read-only form memory.
The invention is composed of
The system takes the aviation electromagnetic profile data in northwest of the nice waterfall, ontario, canada as an example. Describing the above mentioned method, the line contains 3500 stations.
Step a, reading time domain aviation electromagnetic profile data, and marking as X, as shown in FIG. 3.
Step b, element alpha in covariance matrix C of section datakqComprises the following steps:
in the formula,
and
the mean values of the k-th and q-th traces of the profile data, k, q being 1, 2. The covariance matrix C of the profile data is subjected to eigenvalue decomposition,
C＝VDVT，
wherein D is a diagonal matrix in which eigenvalues of the covariance matrix of the profile data are arranged in descending order, V is an eigenvector matrix corresponding to the eigenvalues, and V is a diagonal matrix in which eigenvalues of the covariance matrix of the profile data are arranged in descending orderTIs a rotation matrix.
Step c, utilizing the rotation matrix VTThe section data X is linearly converted into a principal component phi (31X 3500),
Φ＝VTX。
step d, calculating the cumulative contribution rate delta of the former p-order principal componentp，
In the formula, λjIs the corresponding eigenvalue of the j-th order principal component. The accumulated contribution rate of the first 3-order principal component is higher than 90%, and the first 3-order principal component is taken as
The remaining higher order principal components contain a significant amount of uncorrelated noise.
Adopting self-adaptive window width filtering algorithm to carry out filtering on the first 3-order principal component
And carrying out noise estimation. By the k-th principal component in the data
For example, the window width range is WL-WU。
Is the maximum window width smoothing filter result of the k-th order,
the second order difference of (d) is:
wherein, the [ alpha ], [ beta ]]Is a calculation of rounding down to the nearest integer,
is that
The element of the jth measuring point of (1), namely the maximum window width filtered data of each measuring point. Adaptive window width W of each measurement pointk(j) Comprises the following steps:
wherein, DeltarIs the threshold for the second order difference.
The first 3-order principal component data of the kth-order principal component after being subjected to self-adaptive window width filtering is as follows:
then the estimated noise of the k-th order principal component after adaptive window width filtering is:
step e, noise covariance matrix C of first 3-order principal component dataNMiddle element gammakqComprises the following steps:
wherein,
and
are the means of the k and q traces, respectively, of the noisy data, k, q being 1, 2. The noise covariance matrix is subjected to eigenvalue decomposition,
CN＝UNDNUN T，
in the formula, DNIs a diagonal matrix with noise covariance matrix eigenvalues arranged in descending order, UNIs a matrix of eigenvectors corresponding to the eigenvalues.
Step f, covariance matrix of first 3-order principal component data
Beta of middle elementkqComprises the following steps:
in the formula,
and
the average values of the k-th track and the q-th track of the first 3-order principal component data, k, q, 1, 2.
Constructing an adjustment matrix, wherein the adjustment matrix is composed of a plurality of adjustment matrixes,
P＝UNDN -0.5。
covariance matrix for first 3 th order principal component data
The adjustment is carried out, and the adjustment is carried out,
step g, covariance matrix C of the adjusted first 3-order principal component dataDThe decomposition of the characteristic value is carried out,
CD＝VDDDVD T，
in the formula, DDIs a diagonal matrix V with characteristic values of the adjusted profile data covariance matrix arranged in descending orderDIs a matrix of eigenvectors corresponding to the eigenvalues.
Step h, constructing a transformation matrix,
R＝PVD。
first 3 principal component data
The transformed components can be linearly transformed by a transformation matrix R, the matrix formed by the components being represented as:
as the minimum noise separation transformation components are arranged from large to small according to the signal-to-noise ratio, and the low-order components comprise the main signal part of the electromagnetic profile data, the first 2-order minimum noise separation transformation components are selected to reconstruct the first 3-order principal component data.
Step i, reconstructing the main component data,
step j, reconstructing electromagnetic profile data and reconstructing a principal component data matrix
Zero padding becomes a matrix of 31 x 3500,
in the formula, B (31 × 31) is a truncated matrix with the first 3 rows having 1 element and 0 remaining elements.
And k, outputting a noise suppression result and forming a graph. 4 a-4 d are airborne electromagnetic data noise suppression result analyses. Fig. 4d shows a cross-sectional view of the noise suppression result based on the PCA and MNF combined algorithm, and this example shows the airborne electromagnetic late track data, such as fig. 4a, the noise suppression result based on the principal component analysis, such as fig. 4b, and the noise suppression result based on the minimum noise separation transformation, such as fig. 4c, for comparison of the noise suppression results. The PCA and MNF combined algorithm adds minimum noise separation transformation processing on the low-order principal component on the basis of principal component analysis, effectively suppresses abnormal information submerged by noise in the low-order principal component, avoids the problem of abnormal form disorder of a late channel caused by direct MNF processing, and is more favorable for noise suppression and abnormal extraction of aviation electromagnetic data. Comparing the figures 4a, 4b, 4c and 4d, it can be seen that the method is superior to the method for separately processing the principal component analysis method and the minimum noise separation transformation method in the noise suppression effect of the aviation electromagnetic profile data, and has certain effectiveness and practicability.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (11)
1. An airborne electromagnetic data noise suppression method, the method comprising:
calculating an aviation electromagnetic profile data covariance matrix, decomposing eigenvalues of the aviation electromagnetic profile data covariance matrix, and arranging the eigenvalues and eigenvectors obtained by decomposition in a descending order to form an eigenvector matrix;
obtaining a rotation matrix according to the eigenvector matrix, and linearly transforming the aviation electromagnetic profile data into principal component data;
performing noise estimation on low-order principal component data of the principal component data;
calculating a low-order principal component data noise covariance matrix, decomposing the eigenvalues of the low-order principal component data noise covariance matrix, and arranging the eigenvalues and eigenvectors obtained by decomposition in a descending order;
calculating a low-order principal component data covariance matrix and constructing an adjustment matrix to adjust the low-order principal component data covariance matrix;
performing eigenvalue decomposition on the adjusted low-order principal component covariance matrix, and performing descending order arrangement on the eigenvalues and eigenvectors obtained by decomposition;
constructing a transformation matrix, and transforming the low-order principal component data into a minimum noise separation transformation component;
selecting a low-order minimum noise separation transformation component to reconstruct low-order principal component data;
and reconstructing profile data by using the low-order principal component data.
2. The method as claimed in claim 1, wherein the covariance matrix of the airborne electromagnetic profile data is calculated and the airborne electromagnetic raw data is preprocessed before eigenvalue decomposition, and zero-mean processing is performed on each data of the survey line to obtain the airborne electromagnetic profile data.
3. The method of claim 1, wherein the covariance matrix of the aeroelectromagnetic profile data comprises the element αkqThe calculation expression of (a) is as follows:
in the formula, xk(j) Represents the j-th measuring point data of the k-th track, wherein j is 1, 2.
And
respectively, carrying out eigenvalue decomposition on the covariance matrix of the aviation electromagnetic profile data, wherein the average values of the k-th track and the q-th track of the aviation electromagnetic profile data are k and q are 1, 2.
C＝VDVT，
Wherein C is a covariance matrix of the aviation electromagnetic profile data, D is a diagonal matrix in which eigenvalues of the covariance matrix of the aviation electromagnetic profile data are arranged in descending order, V is an eigenvector matrix corresponding to the eigenvalues of the covariance matrix of the aviation electromagnetic profile data, and V is a linear matrix of the eigenvectorsTIs a rotation matrix.
4. The method of claim 2,
obtaining a rotation matrix according to an eigenvector matrix corresponding to the eigenvalue of the covariance matrix of the aviation electromagnetic profile data, and linearly transforming the aviation electromagnetic profile data into principal component data by adopting a formula as follows: phi ═ VTX，VTThe matrix is a rotation matrix, X is aviation electromagnetic profile data, and phi (m multiplied by n) is main component data.
5. The method according to claim 1, wherein the cumulative contribution rate of the previous p-order principal component data is calculated, and when the cumulative contribution rate of the current p-order principal component data is higher than 90%, the previous p-order principal component data is taken as the lower-order principal component data, and the remaining high-order principal components contain a large amount of uncorrelated noise.
6. The method of claim 5, wherein the pre-p order principal component data is noise estimated using an adaptive window width filtering algorithm.
7. The method of claim 1 or 5, wherein computing the covariance matrix of the low-order principal component data and constructing an adjustment matrix to adjust the covariance matrix comprises: converting the noise variance in each minimum noise separation transformation component into unit variance by constructing an adjustment matrix, wherein the expression of the adjustment matrix is as follows: p is UNDN -0.5Where P is the adjustment matrix, DNIs a diagonal matrix with characteristic values of low-order principal component data noise covariance matrix arranged in descending order, UNThe method is characterized in that the method is an eigenvector matrix corresponding to eigenvalues of a low-order principal component data noise covariance matrix, and the covariance matrix of the low-order principal component data is adjusted, wherein the expression is as follows:
wherein C isDTo the adjusted front p-th order principal component data covariance matrix,
the covariance matrix of the first p-th order principal component data.
8. The method of claim 1, wherein performing eigenvalue decomposition on the adjusted low-order principal component covariance matrix comprises: the expression used is: cD＝VDDDVD TIn the formula, DDIs a diagonal matrix with the adjusted low-order principal component covariance matrix eigenvalues arranged in descending order, VDIs an eigenvector matrix corresponding to eigenvalues of the adjusted low-order principal component covariance matrix, CDFor adjusted low-order principal componentsAnd (4) dividing a covariance matrix.
9. The method of claim 1, wherein constructing a transformation matrix comprises using the expression: r ═ PVDP is an adjustment matrix, VDThe feature vector matrix corresponding to the eigenvalue of the adjusted low-order principal component covariance matrix, R is a transformation matrix, wherein the low-order principal component data is linearly transformed into a minimum noise separation transformation component through the transformation matrix R, and the matrix formed by the minimum noise separation transformation component is represented as follows:
in the formula,
separating the transformed component for minimum noise by psi as low-order principal component data, DNIs a diagonal matrix with characteristic values of low-order principal component data noise covariance matrix arranged in descending order, UNThe minimum noise separation transformation component is arranged from large to small according to the signal-to-noise ratio, the low-order component comprises a main signal part of the electromagnetic profile data, the former L minimum noise separation transformation component is selected to reconstruct the low-order principal component data, wherein L is more than 1 and less than p.
10. The method of claim 1, wherein reconstructing profile data from the low-order principal component data comprises: zero padding is carried out on the reconstruction principal component data matrix to form an m multiplied by n matrix, and the reconstruction section data expression is as follows:
in the formula, B (m × m) is a truncated matrix in which the first p rows have 1 element and the remaining elements have 0 elements.
11. An airborne electromagnetic data noise suppression apparatus, the apparatus comprising: the device comprises a memory, a processor and an output module, wherein the memory is in communication connection with the processor, the output module retrieves the data of the memory for output,
the memory is used for storing the aeroelectromagnetic profile data;
the processor is used for calculating the covariance matrix of the aviation electromagnetic profile data after the data of the memory is taken, decomposing the eigenvalues of the covariance matrix, arranging the eigenvalues and the eigenvectors obtained by decomposition in a descending order, forming an eigenvector matrix and storing the eigenvector matrix in the memory;
the processor is used for obtaining a rotation matrix according to the characteristic vector matrix and linearly transforming the aviation electromagnetic profile data into principal component data;
the processor is used for carrying out noise estimation on low-order principal component data of the principal component data;
the processor is used for calculating a low-order principal component data noise covariance matrix, decomposing the eigenvalue of the low-order principal component data noise covariance matrix, and performing descending order arrangement on the eigenvalue and the eigenvector obtained by decomposition;
the processor is used for calculating a low-order principal component data covariance matrix and constructing an adjustment matrix to adjust the low-order principal component data covariance matrix;
the processor is used for decomposing the eigenvalues of the adjusted low-order principal component covariance matrix and arranging the eigenvalues and eigenvectors obtained by decomposition in a descending order;
the processor is used for constructing a transformation matrix and transforming the low-order principal component data into a minimum noise separation transformation component;
the processor is used for selecting a low-order minimum noise separation transformation component to reconstruct low-order principal component data;
the processor is used for reconstructing profile data from the low-order principal component data;
and the output module outputs a noise suppression result to the data processed by the processor and forms a graph.
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