Method for quickly decomposing polarized synthetic aperture radar data based on simplified sorting eigenvalue analytic expression

Abstract

The invention discloses a polarized synthetic aperture radar data rapid decomposition method based on a simplified sorting eigenvalue analytic expression, and belongs to the technical field of radar signal processing. According to the method, the polarimetric SAR covariance matrix is firstly constructed, then the feature values are calculated by using the simplified analytic expression, complex cubic root calculation is reduced, and meanwhile, the maximum feature value and the feature vector corresponding to the maximum feature value are directly extracted according to the preset sorting rule and are used for representing the target dominant scattering mechanism. The method is suitable for correlation matrixes of multi-view PolSAR data, parallel processing can be achieved through matrix element level operation, the calculation efficiency is improved by 37% or above compared with the prior art for covariance matrixes or coherence matrixes with the data set scale being 1 * 10-1 * 10, and the method has important application value in the field of disaster monitoring and the like.

Description

Technical Field

[0001] The invention relates to radar signal processing technology, in particular to a polarization synthetic aperture radar data rapid decomposition method based on a simplified sorting eigenvalue analytical formula, which is suitable for target feature extraction of large-scale PolSAR images. Background Art

[0002] Polarimetric synthetic aperture radar obtains target scattering information through multi-polarized electromagnetic waves, and its data processing relies on the eigenvalue decomposition of the covariance matrix to extract the scattering mechanism. Traditional methods such as QR decomposition have low computational efficiency and are difficult to meet real-time processing requirements. Although existing technologies (such as the An decomposition method) derive analytical eigenvalue expressions through the Cardano formula, they still require complex cube root calculations, leaving room for optimization. In addition, the eigenvalue sorting rules are unclear, which affects the rapid extraction of the dominant scattering mechanism. Summary of the invention

[0003] The invention proposes a polarization synthetic aperture radar data rapid decomposition method based on a simplified sorting eigenvalue analytical formula.

[0004] The technical solution to achieve the purpose of the present invention is: a method for rapid decomposition of polarization synthetic aperture radar data based on a simplified sorting eigenvalue analytical formula, comprising the following steps:

[0005] Step 1: Construct the polarimetric SAR covariance matrix based on the echo strength of different polarization channels;

[0006] Step 2: Use the Cardan formula to solve the polarimetric SAR covariance matrix and obtain the analytical eigenvalues ​​of the polarimetric SAR covariance matrix;

[0007] Step 3: Obtain the eigenvector corresponding to the analytical eigenvalue according to the largest analytical eigenvalue.

[0008] Preferably, the constructed polarization SAR covariance matrix is ​​specifically:

[0009] in, is the number of views, They are the echo intensity information of the horizontal polarization transmission-horizontal polarization reception channel HH, the horizontal polarization transmission-vertical polarization reception channel HV, and the vertical polarization transmission-vertical polarization reception channel VV, is the polarization measurement vector, is a complex coherent term, where , , , Indicates the emission polarization , receiving polarization The scattering coefficient when , H represents horizontal polarization, and V represents vertical polarization.

[0010] Preferably, the polarimetric SAR covariance matrix is ​​solved using the Cardan formula, and the specific method for obtaining the analytical eigenvalues ​​of the polarimetric SAR covariance matrix is:

[0011] The determinant expansion of the polarimetric SAR covariance matrix yields the characteristic polynomial of the polarimetric SAR covariance matrix:

[0012] ,

[0013] make ,

[0014] , , They are conjugation of;

[0015] The real coefficient cubic equation of the characteristic polynomial of the polarimetric SAR covariance matrix is ​​obtained, specifically:

[0016] ,

[0017] The Cardan formula is used to solve the cubic equation with real coefficients and three non-zero analytic eigenvalues ​​are obtained.

[0018] Preferably, the analytical eigenvalues ​​of the polarimetric SAR covariance matrix are specifically:

[0019] ,

[0020] In the formula, , ,

[0021] .

[0022] Preferably, the linear system is solved using the largest analytical eigenvalue Get the corresponding feature vector :

[0023] .

[0024] Compared with the prior art, the present invention has the following significant advantages: the present invention is applicable to the covariance matrix and coherence matrix of multi-view PolSAR data, and realizes parallel processing through matrix element-level operations. to The computational efficiency is improved by more than 37% compared with the existing technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1This is a schematic diagram comparing the computing time for data of different scales.

[0026] Figure 2 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0027] like Figure 1 As shown, a method for rapid decomposition of polarization synthetic aperture radar data based on a simplified sorting eigenvalue analytical formula is described, and the specific steps are as follows:

[0028] Step 1: Construct the polarimetric SAR covariance matrix based on the echo strength of different polarization channels , which is of the form:

[0029] (1)

[0030] in, is the number of views, are real diagonal elements, which are the echo intensity information of the horizontal polarization transmission-horizontal polarization reception channel (HH), the horizontal polarization transmission-vertical polarization reception channel (HV), and the vertical polarization transmission-vertical polarization reception channel (VV). They are directly measured by the polarimetric SAR system and can be extracted from the radar system data recording file. is a complex coherent term, where , , , Indicates the emission polarization , receiving polarization The scattering coefficient when The scattering coefficient is obtained by inverting the signal received by the radar. The superscript * indicates the conjugate of the complex number. Represents the correlation between different polarization channels. This correlation contains the scattering characteristics of the target, such as the target's geometric structure, dielectric properties and other information.

[0031] Step 2: Calculate the analytical eigenvalues ​​of the polarimetric SAR covariance matrix. The specific process is:

[0032] The determinant expansion of the polarimetric SAR covariance matrix yields the characteristic polynomial of the matrix:

[0033] (2)

[0034] in where is the unknown quantity and represents the eigenvalue to be solved.

[0035] definition

[0036] (3)

[0037] Get the real coefficient cubic equation (here ), which can be solved using Cardan's formula.

[0038] Cardan's formula states that for a cubic equation with real coefficients The root of can be expressed as:

[0039] (4)

[0040] The parameters involved are defined as follows

[0041] (5)

[0042] The properties of the roots of a cubic equation depend on the discriminant ,when When , the three roots are unequal real roots. ,but is a conjugate complex number, which can be expressed as

[0043] (6)

[0044] in .

[0045] Then the parameters involved in the roots of the above cubic equation with real coefficients are

[0046] (7)

[0047] Obviously, are conjugates of each other, so the roots solved using the Cardan formula can be simplified to

[0048] (8)

[0049] Further discussion, since there are three real eigenvalues, , can be obtained and Based on this, the variable can be rewritten as , the corresponding three eigenvalues ​​can be expressed as

[0050] (9)

[0051] because , can be obtained .but

[0052] (10)

[0053] Therefore .

[0054] The three-dimensional Pauli or Lexicographic eigenvector can be expressed as The matrix for each multi-view pixel is It can be expressed as

[0055] (11)

[0056] Considering that SAR data always contains additive measurement noise, the eigenvectors are linearly independent, that is, the equation Only when all Established at that time.

[0057] test The independence of each column, its three column vectors can be written as

[0058] (12)

[0059] If the column vectors are linearly dependent, then there exists satisfy Substituting formula (12) into

[0060] (13)

[0061] Organize each Coefficient and reference have to

[0062] (14)

[0063] This system of equations can be rewritten as

[0064] (15)

[0065] This is a homogeneous linear system of equations. Linearly independent, coefficient matrix The rank of is 3 (equal to the number of columns), so the system of equations has only zero solutions. The columns are linearly independent and have three non-zero eigenvalues.

[0066] Therefore, when the number of When the coherence matrix or covariance matrix of the real SAR data containing observation noise is It has three distinct eigenvalues, and the eigenvalues ​​are real numbers, which satisfy the simplified root-finding method.

[0067] make , applying the simplified root solution method, the analytical eigenvalue expression of the covariance matrix is ​​derived as:

[0068] (16)

[0069] In the formula,

[0070] Among them, Re means taking the real part of the complex number, Im means taking the imaginary part, is an intermediate variable used to calculate the eigenvalue; It integrates the information of the diagonal elements and complex coherent terms of the matrix, is the intermediate parameter for constructing the eigenvalue calculation expression, and simplifies the complex relationship between the matrix elements.

[0071] Step 3: According to the preset sorting rules Directly extract the maximum eigenvalue . Solve the linear system using the largest analytical eigenvalue Get the corresponding feature vector :

[0072] (17)

[0073] In polarimetric synthetic aperture radar data processing, the maximum eigenvalue extracted and its corresponding eigenvector It is mainly used to characterize the dominant scattering mechanism of the target. This is because in practical applications, the scattering mechanism of the target is complex and diverse, but there is often one scattering mechanism that dominates. Maximum eigenvalue Represents the part with the greatest intensity or the most prominent contribution among all scattering mechanisms. and , we can understand the main scattering characteristics of the target more clearly.

[0074] like Figure 1 As shown, the horizontal axis is the number of third-order covariance matrices, and the vertical axis is the calculation time (seconds). Curve 1: the method of the present invention; Curve 2: An decomposition method. For the simulated data set (1×10 6 Up to 1×10 8 On the R9-7945HX processor, this method can process 1×10 8 The matrix takes 2.64 seconds, which is 38% more efficient than the An decomposition method (4.27 seconds).

[0075] In view of the low efficiency of numerical calculation methods such as QR decomposition in the prior art, the present invention proposes a simplified analytical eigenvalue expression and optimizes the calculation process in combination with deterministic sorting rules. Experiments show that the present invention reduces the calculation time by about 37% compared with the existing optimal method (An decomposition method), and is suitable for real-time processing of large-scale PolSAR data. The present invention can be applied to fields such as disaster monitoring to improve the efficiency of polarization decomposition.

Claims

1. A method for rapid decomposition of polarimetric synthetic aperture radar data based on a simplified sorting eigenvalue analytical formula, characterized in that: The following steps are involved: Step 1: Construct the polarimetric SAR covariance matrix based on the echo strength of different polarization channels; Step 2: Use the Cardan formula to solve the polarimetric SAR covariance matrix and obtain the analytical eigenvalues ​​of the polarimetric SAR covariance matrix; Step 3: Obtain the eigenvector corresponding to the analytical eigenvalue according to the largest analytical eigenvalue.

2. The method for rapid decomposition of polarimetric synthetic aperture radar data based on simplified sorting eigenvalue analytical formula according to claim 1, characterized in that: The constructed polarimetric SAR covariance matrix is ​​specifically: ， in, is the number of views, They are the echo intensity information of the horizontal polarization transmission-horizontal polarization reception channel HH, the horizontal polarization transmission-vertical polarization reception channel HV, and the vertical polarization transmission-vertical polarization reception channel VV, is the polarization measurement vector, is a complex coherent term, where , , , Indicates emission ,take over The scattering coefficient when , H represents horizontal polarization, and V represents vertical polarization.

3. The method for rapid decomposition of polarimetric synthetic aperture radar data based on simplified sorting eigenvalue analytical formula according to claim 1, characterized in that: The specific method of solving the polarimetric SAR covariance matrix using the Cardan formula and obtaining the analytical eigenvalues ​​of the polarimetric SAR covariance matrix is ​​as follows: The determinant expansion of the polarimetric SAR covariance matrix yields the characteristic polynomial of the polarimetric SAR covariance matrix: ， make , , , They are conjugation of; The real coefficient cubic equation of the characteristic polynomial of the polarimetric SAR covariance matrix is ​​obtained, specifically: ， The Cardan formula is used to solve the cubic equation with real coefficients and three non-zero analytic eigenvalues ​​are obtained.

4. The method for rapid decomposition of polarization synthetic aperture radar data based on simplified sorting eigenvalue analytical formula according to claim 3, characterized in that: The analytical eigenvalues ​​of the polarimetric SAR covariance matrix are: ， In the formula, , , 。 5. The method for rapid decomposition of polarimetric synthetic aperture radar data based on simplified sorting eigenvalue analytical formula according to claim 4, characterized in that: is the maximum analytic eigenvalue.

6. The method for rapid decomposition of polarization synthetic aperture radar data based on simplified sorting eigenvalue analytical formula according to claim 5, characterized in that: Solve a system of linear equations using the largest analytical eigenvalue Get the corresponding feature vector : 。

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