A fast decomposition method for polarimetric synthetic aperture radar data based on simplified sorting eigenvalue analytical formula

Abstract

The present invention discloses a method for rapid decomposition of polarimetric synthetic aperture radar data based on a simplified sorting eigenvalue analytical formula, which belongs to the field of radar signal processing technology. The present invention first constructs a polarimetric SAR covariance matrix, and then calculates the eigenvalue using a simplified analytical formula, thereby reducing the calculation of complex cube roots. At the same time, the maximum eigenvalue and its corresponding eigenvector are directly extracted according to a preset sorting rule to characterize the target's dominant scattering mechanism. The present invention is applicable to the correlation matrix of multi-view PolSAR data, and can achieve parallel processing through matrix element-level operations. For data sets with a size of 1×10⁶ to 1×10⁸ covariance matrices or coherence matrices, the computational efficiency is improved by more than 37% compared with the existing technology, and has important application value in fields such as disaster monitoring.

Description

Technical Field

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

[0002] Polarimetric synthetic aperture radar (SPAR) uses multi-polarized electromagnetic waves to acquire target scattering information. Its data processing relies on eigenvalue decomposition of the covariance matrix to extract scattering mechanisms. Traditional methods, such as QR decomposition, suffer from low computational efficiency and struggle to meet real-time processing requirements. Existing techniques, such as the An decomposition method, derive analytical eigenvalue expressions using the Cardano formula but still require complex cube root calculations, leaving room for optimization. Furthermore, unclear eigenvalue sorting rules hinder the rapid extraction of dominant scattering mechanisms. Summary of the Invention

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

[0004] The technical solution for achieving the purpose of the present invention is: a method for rapidly decomposing polarimetric 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 intensities 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 based on the largest analytical eigenvalue.

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

[0009]

[0010] 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 the complex coherence term, where , , , Indicates emission polarization , receiving polarization The scattering coefficient when , H represents horizontal polarization, and V represents vertical polarization.

[0011] Preferably, the polarimetric SAR covariance matrix is ​​solved using the Cardan formula to obtain the analytical eigenvalues ​​of the polarimetric SAR covariance matrix as follows:

[0012] The determinant expansion of the polarimetric SAR covariance matrix yields the characteristic polynomial of the polarimetric SAR covariance matrix:

[0013] ,

[0014] make ,

[0015] 、 、 They are conjugation of;

[0016] The real coefficient cubic equation of the characteristic polynomial of the polarimetric SAR covariance matrix is ​​obtained as follows:

[0017] ,

[0018] The Cardan formula is used to solve the cubic equation with real coefficients and three non-zero analytic eigenvalues ​​are obtained.

[0019] Preferably, the analytical eigenvalues ​​of the polarimetric SAR covariance matrix are specifically:

[0020] ,

[0021] Where, , ,

[0022] .

[0023] Preferably, the linear system is solved using the largest analytical eigenvalue Get the corresponding eigenvector :

[0024] .

[0025] 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 covariance matrix or coherence matrix is ​​calculated, and the computational efficiency is improved by more than 37% compared with the existing technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 A schematic diagram comparing the computation time for data of different sizes.

[0027] Figure 2 Flowchart of the present invention. DETAILED DESCRIPTION

[0028] like Figure 1 As shown in FIG, a method for rapid decomposition of polarimetric synthetic aperture radar data based on a simplified sorting eigenvalue analytical formula is described, wherein the specific steps are as follows:

[0029] Step 1: Construct the polarimetric SAR covariance matrix based on the echo strength of different polarization channels , which has the form:

[0030] (1)

[0031] 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 record file. is the complex coherence term, where , , , Indicates 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.

[0032] Step 2: Calculate the analytical eigenvalues ​​of the polarimetric SAR covariance matrix. The specific process is as follows:

[0033] The determinant expansion of the polarimetric SAR covariance matrix yields the characteristic polynomial of the matrix:

[0034] (2)

[0035] in where is the unknown quantity and represents the eigenvalue to be solved.

[0036] definition

[0037] (3)

[0038] Get the real coefficient cubic equation (here ), which can be solved using the Cardan formula.

[0039] Cardan's formula states that for a cubic equation with real coefficients The root of can be expressed as:

[0040] (4)

[0041] The parameters involved are defined as follows

[0042] (5)

[0043] The properties of the roots of a cubic equation depend on the discriminant ,when When , the three roots are unequal real roots. Let ,but is a conjugate complex number, which can be expressed as

[0044] (6)

[0045] in .

[0046] Then the parameters involved in the roots of the above cubic equation with real coefficients are

[0047] (7)

[0048] Obviously, are conjugates of each other, so the roots solved using the Cardan formula can be simplified to

[0049] (8)

[0050] Further discussion, since there are three real eigenvalues, , we can get and Based on this, the variable Can be rewritten as , the corresponding three eigenvalues ​​can be expressed as

[0051] (9)

[0052] because , we can get .but

[0053] (10)

[0054] Therefore .

[0055] The three-dimensional Pauli or Lexicographic eigenvector can be expressed as The matrix of each multi-view pixel is It can be expressed as

[0056] (11)

[0057] Considering that SAR data always contains additive measurement noise, the eigenvectors are linearly independent, that is, the equation Only when all Established when.

[0058] test The independence of each column, its three column vectors can be written as

[0059] (12)

[0060] If the column vectors are linearly dependent, then there exists satisfy Substituting formula (12) into

[0061] (13)

[0062] Organize each Coefficient and reference have to

[0063] (14)

[0064] The system of equations can be rewritten as

[0065] (15)

[0066] 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 nonzero eigenvalues.

[0067] Therefore, when viewing When the coherence matrix or covariance matrix of the real SAR data containing observation noise is It has three distinct real eigenvalues, which satisfy the simplified root-finding method.

[0068] make , applying the simplified root solution method, the analytical eigenvalue expression of the covariance matrix is ​​derived as:

[0069] (16)

[0070] Where,

[0071] 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 matrix diagonal elements and complex coherent terms, is the intermediate parameter for constructing the eigenvalue calculation expression, and simplifies the complex relationship between matrix elements.

[0072] 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 eigenvector :

[0073] (17)

[0074] 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. 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.

[0075] 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 to 1×10 8 On the R9-7945HX processor, this method processes 1×10 8 The matrix takes 2.64 seconds, which is 38% more efficient than the An decomposition method (4.27 seconds).

[0076] To address the inefficiency of existing numerical calculation methods such as QR decomposition, this paper proposes a simplified analytical eigenvalue expression and optimizes the calculation process by combining it with deterministic sorting rules. Experiments show that this method reduces computation time by approximately 37% compared to the existing optimal method (An decomposition), making it suitable for real-time processing of large-scale PolSAR data. This method can be applied to fields such as disaster monitoring, improving the efficiency of polarimetric 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 intensities of different polarization channels. 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 the complex coherence term, where , , , Indicates launch ,take over The scattering coefficient when , H represents horizontal polarization, V represents vertical polarization; Step 2: Use the Cardan formula to solve the polarimetric SAR covariance matrix and obtain the analytical eigenvalues ​​of the polarimetric SAR covariance matrix. The specific method is: 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 as follows: ， Using the Cardan formula to solve the cubic equation with real coefficients, we obtain three non-zero analytical eigenvalues, specifically: ， Where, , , ； Step 3: Obtain the eigenvector corresponding to the analytical eigenvalue based on the largest analytical eigenvalue. Specifically: Use the largest analytical eigenvalue to solve the linear equations Get the corresponding eigenvector : 。 2. The method for rapid decomposition of polarimetric synthetic aperture radar data based on a simplified sorting eigenvalue analytical formula according to claim 1, characterized in that: is the maximum analytical eigenvalue.

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