A parameterized constant false alarm processing method for any PolSAR detector

Abstract

The present invention provides a parameterized constant false alarm rate processing method applicable to any PolSAR detector, comprising the following steps: obtaining clutter samples on a PolSAR image, and calculating the ensemble mean of the clutter polarization covariance matrix of the clutter samples; using any PolSAR detector to process input data to obtain a detection transformation matrix; calculating the eigenvalue of the product of the detection transformation matrix and the ensemble mean; converting the output of the PolSAR detector into a characteristic function based on the eigenvalue and the Imhof law; performing cumulative distribution function processing on the characteristic function to obtain the relationship between the false alarm probability and the detection threshold, and obtaining the constant false alarm rate after inversely solving the detection threshold. By adopting a parameterized modeling method, any PolSAR detector can be accurately fitted, and no matter whether its detection transformation matrix is ​​positive definite or negative definite, an effective probability density function and cumulative distribution function can be obtained, and the detection threshold can be calculated according to the setting.

Description

Technical Field

[0001] The invention relates to the technical field of polarization synthetic aperture radar detection, and in particular to a parameterized constant false alarm processing method suitable for any PolSAR detector. Background Art

[0002] Synthetic aperture radar (SAR) achieves high-resolution ground scene inversion through two-dimensional matched filtering of echo signals, and plays an important role in wide-area target detection tasks. Compared with optical imaging systems, the unique advantage of SAR is that it can observe the earth all day and all weather, without being restricted by weather and lighting conditions. At the same time, it has a certain degree of penetration and can detect hidden information under the surface. Based on SAR technology, polarimetric synthetic aperture radar (PolSAR) further improves the performance of target detection by introducing multi-polarization channels. Multi-polarization channels can capture the scattering characteristics of targets in different polarization states, providing richer and more accurate information for target classification, identification and monitoring, thereby enhancing the interpretation effect and application value of SAR images.

[0003] Although the current deep learning-based target detection methods have attracted much attention due to their powerful feature extraction capabilities, their performance is not ideal in practical applications, especially in the absence of a large amount of high-quality sample data support. In addition, the interpretability of deep learning-based target detection methods still needs further study. In this context, for radar images, the traditional constant false alarm rate (CFAR) detection method is still an important means to effectively detect targets of interest. CFAR detection originated from the Neyman-Pearson criterion in signal detection theory and is applicable to situations where both the error loss cost and the target prior distribution are unknown. To achieve CFAR detection, the distribution type and parameters of clutter are generally estimated by analyzing the accumulated clutter data; then, a specific false alarm probability (PFA) is set, and the detection threshold is reversely derived based on this; finally, the detection threshold is used to determine whether the pixel to be detected belongs to the target or clutter.

[0004] In the current CFAR detection method, when the detection transformation matrix is ​​obtained in a data-driven manner, it is no longer necessarily a positive definite matrix. This situation will cause the output of the polarization detector to be non-positive. In this case, the traditional statistical modeling method fails and CFAR detection cannot be performed. There are already some non-parametric statistical modeling methods, such as Parzen window and Gaussian mixture model (GMM), but these non-parametric methods are completely dependent on data and are not satisfactory in terms of anti-interference, robustness and accuracy. Summary of the invention

[0005] The present invention proposes a parameterized constant false alarm processing method applicable to any PolSAR detector to solve the technical problem that when the output of the polarization detector is not a positive value, the existing CFAR detection method is difficult to perform constant false alarm processing.

[0006] In order to solve the above technical problems, the present invention provides a parameterized constant false alarm processing method applicable to any PolSAR detector, comprising the following steps:

[0007] Step S1: obtaining clutter samples on the PolSAR image, and calculating the ensemble average of the clutter polarization covariance matrix of the clutter samples;

[0008] Step S2: using any PolSAR detector to process the input data and obtain a detection transformation matrix;

[0009] Step S3: Calculate the eigenvalue of the product of the detection transformation matrix and the ensemble mean;

[0010] Step S4: converting the output of the PolSAR detector into a characteristic function based on the eigenvalue and the Imhof law;

[0011] Step S5: Process the characteristic function with a cumulative distribution function to obtain the false alarm probability PFA and the detection threshold The relationship between the detection threshold and the constant false alarm rate can be obtained by inversely solving the detection threshold.

[0012] Preferably, the method for obtaining the clutter sample comprises:

[0013] 1) Obtained using sliding window method;

[0014] 2) Extract from accumulated data;

[0015] 3) Based on historical data, select a large area of ​​pixels that do not contain the target area for acquisition.

[0016] Preferably, the expression of step S1 is:

[0017] ;

[0018] In the formula, is the ensemble mean of the clutter polarization covariance matrix, is the polarization covariance matrix of the clutter region.

[0019] Preferably, step S3 comprises: obtaining an eigenvalue according to the product of the ensemble mean and the detection transformation matrix of the PolSAR detector, i.e., an eigenvector:

[0020] ;

[0021] In the formula, For the matrix The eigenvector of For the matrix The characteristic value of .

[0022] Preferably, step S4 comprises the following steps:

[0023] Step S41: Using the Imhof law, the output of the PolSAR detector is converted into It is equivalent to the mixed chi-square distribution function;

[0024] Step S42: converting the mixed chi-square distribution function into a characteristic function.

[0025] Preferably, the expression of step S41 is:

[0026] ;

[0027] In the formula, The degree of freedom is 2 Chi-square distribution of ; is the number of views of the PolSAR image.

[0028] Preferably, the expression of step S42 is:

[0029] ;

[0030] In the formula, is the characteristic function output by the PolSAR detector; t represents the real variable of the characteristic function; i is the imaginary unit.

[0031] Preferably, the false alarm probability PFA and the detection threshold in step S5 The expression of the relationship is:

[0032] ;

[0033] In the formula, represents the false alarm probability under the detection threshold T; CDF represents the cumulative distribution function; Re represents the real part operation; exp represents the exponential function; is the characteristic function output by the PolSAR detector; t represents the real variable of the characteristic function; i represents the imaginary unit.

[0034] The beneficial effects of the present invention include at least: the method of the present invention can accurately fit any PolSAR detector, whether its detection transformation matrix is ​​positive or negative, can obtain an effective probability density function (PDF) and cumulative distribution function (CDF), and calculate the detection threshold according to the set PFA. It solves the problem that traditional Gamma distribution, generalized Gamma distribution, lognormal distribution and other models cannot handle negative values; on the other hand, compared with non-parametric methods such as Parzen window or GMM that are completely dependent on samples, the statistical modeling method proposed by the present invention is parametric, and through the processing of Imhof's law and eigenvalues, the number of samples required is smaller, and it has better resistance to abnormal samples. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A schematic diagram of a method flow of an embodiment of the present invention;

[0036] Figure 2 This is a schematic diagram of a PolSAR image to be detected according to an embodiment of the present invention;

[0037] Figure 3 A schematic diagram of probability density fitting of the polarization detector output according to an embodiment of the present invention;

[0038] Figure 4 It is a schematic diagram of the CFAR performance test results of an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the protection scope of the present invention.

[0040] PolSAR data are generally stored in the format of multi-view polarization covariance matrix. At present, there are various detectors that directly act on PolSAR multi-view polarization covariance matrix data. They obtain the detection transformation matrix based on different optimization objectives, scattering mechanisms, etc. Ultimately, the output of each detector can be expressed as the trace of the product of the detection transformation matrix and the multi-view polarization covariance matrix, as shown in equation (1):

[0041] (1)

[0042] In the above formula is the output of the polarization detector; is the detection transformation matrix of the polarization detector, which is a Hermitian matrix; is the multi-view polarization covariance matrix of the pixels to be detected in the PolSAR image.

[0043] Most polarization detectors, such as polarization notch filter (PNF), optimal polarization detector (OPD), polarization matched filter (PMF), polarization whitening filter (PWF), have positive definite matrices for their detection transformation matrices. Therefore, the output of the polarization detector in any case is When the polarization scattering vector obeys a zero-mean complex Gaussian distribution, the Gamma distribution can be used. Statistical modeling was performed and the detection threshold was then back-derived from PFA.

[0044] However, when detecting the transformation matrix When obtained by data-driven method, it is no longer necessarily a positive definite matrix. This situation will cause the output of the polarization detector to be is not a positive value. In view of this situation, the traditional statistical modeling method fails and CFAR detection cannot be performed. At present, there are some non-parametric statistical modeling methods, such as Parzen window and Gaussian mixture model (GMM), but these non-parametric methods are completely dependent on data and are not satisfactory in terms of anti-interference, robustness and accuracy.

[0045] Therefore, in order to make the feature map constructed by any PolSAR detector able to smoothly perform CFAR detection, no matter whether its detection transformation matrix is ​​positive definite or negative definite, the embodiment of the present invention provides a parameterized constant false alarm processing method applicable to any PolSAR detector, such as Figure 1 As shown, the following steps are included:

[0046] Step S1: Obtain clutter samples on the PolSAR image and calculate the ensemble average of the clutter polarization covariance matrix of the clutter samples;

[0047] Step S2: using any PolSAR detector to process the input data and obtain a detection transformation matrix;

[0048] Step S3: Calculate the eigenvalue of the product of the detection transformation matrix and the ensemble mean;

[0049] Step S4: converting the output of the PolSAR detector into a characteristic function based on the eigenvalue and Imhof's law;

[0050] Step S5: Process the characteristic function with the cumulative distribution function to obtain the false alarm probability PFA and the detection threshold The relationship between the detection threshold and the constant false alarm rate can be obtained by inversely solving the detection threshold.

[0051] Specifically, step S1 obtains clutter samples on the input PolSAR image based on prior information. Clutter samples can be obtained using the classic sliding window method, or extracted from accumulated data, or by selecting a large area of ​​pixels that do not contain the target area based on prior intelligence. The ensemble mean of the clutter polarization covariance matrix is ​​obtained using formula (2):

[0052] (2)

[0053] In the above formula, is the ensemble mean of the clutter polarization covariance matrix, is the polarization covariance matrix of the clutter region.

[0054] Exemplarily, step S2 utilizes a PolSAR detector to process the input data. The detector here may be a physical mechanism, such as the previously mentioned polarization notch filter (PNF), optimal polarization detector (OPD), polarization matched filter (PMF), polarization whitening filter (PWF), etc., or it may be obtained by data optimization.

[0055] Specifically, in step S3, the eigenvalue of the product of the estimated clutter polarization covariance matrix and the detection transformation matrix of the PolSAR detector is obtained. The eigenvalue satisfies formula (3):

[0056] (3)

[0057] In the above formula For the matrix The characteristic vector of For the matrix The characteristic value of .

[0058] Then, the PolSAR detector output is converted to Equivalent to a mixed chi-square distribution:

[0059] (4)

[0060] Its characteristic function is obtained as:

[0061] (5)

[0062] In the formula, The degree of freedom is 2 Chi-square distribution of ; is the number of views of the PolSAR image; is the characteristic function output by the PolSAR detector; t represents the real variable of the characteristic function; i is the imaginary unit.

[0063] Finally, we get the false alarm probability PFA and detection threshold The relationship is:

[0064] (6)

[0065] Finally, through the dichotomy method, the detection threshold is reversed under the setting of PFA .

[0066] Through the transformation of formulas (4), (5) and (6), the statistical modeling method in the embodiment of the present invention is parameterized, which requires a smaller number of samples and has better resistance to abnormal samples. The CFAR detection form of the PolSAR detector is unified, and all the The exported feature maps can all be used to implement CFAR detection using this technology.

[0067] The following describes the embodiments of the present invention through specific implementation procedures.

[0068] The PolSAR image to be detected is as follows: Figure 2 As shown, the clutter region is first extracted, and the ensemble mean of the clutter polarization covariance matrix is ​​calculated using formula (2). Then, the ensemble mean of the target polarization covariance matrix is ​​obtained based on prior knowledge. .

[0069] This embodiment uses a data-driven algorithm, such as a pocket sensor algorithm, as an example to construct a detection transformation matrix At this time, the output of the polarization detector is It is no longer limited to positive values. Traditional statistical models such as Gamma distribution, generalized Gamma distribution, and lognormal distribution are invalid and cannot be fitted.

[0070] Using the modeling method shown in formula (4), the output of the PolSAR detector can be is equivalent to a mixed chi-square distribution, such as Figure 3 As shown in the figure, it can be seen that the output contains negative values ​​and the statistical model has good fitting performance.

[0071] By substituting formula (5) into formula (6), we can calculate the result of PFA with the change of strength. Figure 3 As in the case of FIG, the relationship between the derived constant false alarm rate and the actual threshold fits well, indicating that the method proposed in the present invention can provide good CFAR detection performance.

[0072] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. Only the preferred embodiments of the present invention are expressed. The description is more specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. As long as there is no contradiction in the combination of these technical features, they should be considered as the scope recorded in this specification.

[0073] It should be noted that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these modifications and improvements all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A parameterized constant false alarm processing method applicable to any PolSAR detector, characterized by: The following steps are involved: Step S1: obtaining clutter samples on the PolSAR image, and calculating the ensemble average of the clutter polarization covariance matrix of the clutter samples; Step S2: using any PolSAR detector to process the input data and obtain a detection transformation matrix; Step S3: Calculate the eigenvalue of the product of the detection transformation matrix and the ensemble mean; Step S4: converting the output of the PolSAR detector into a characteristic function based on the eigenvalue and the Imhof law; Step S5: Process the characteristic function with a cumulative distribution function to obtain the false alarm probability PFA and the detection threshold After reversing the detection threshold, the constant false alarm rate is obtained. Step S4 includes the following steps: Step S41: Using the Imhof law, the output of the PolSAR detector is converted into It is equivalent to the mixed chi-square distribution function; Step S42: converting the mixed chi-square distribution function into a characteristic function; The expression of step S41 is: ； In the formula, The degree of freedom is 2 Chi-square distribution of ; is the number of views of the PolSAR image, For the matrix The characteristic value of represents the detection transformation matrix, represents the ensemble mean of the clutter polarization covariance matrix.

2. A parameterized constant false alarm processing method applicable to any PolSAR detector according to claim 1, characterized in that: The method for obtaining the clutter sample comprises: 1) Obtained using sliding window method; 2) Extract from accumulated data; 3) Based on historical data, select a large area of ​​pixels that do not contain the target area for acquisition.

3. A parameterized constant false alarm processing method applicable to any PolSAR detector according to claim 1, characterized in that: The expression of step S1 is: ； In the formula, is the ensemble mean of the clutter polarization covariance matrix, is the polarization covariance matrix of the clutter region.

4. A parameterized constant false alarm processing method applicable to any PolSAR detector according to claim 1, characterized in that: Step S3 includes: obtaining an eigenvalue according to the product of the ensemble average and the detection transformation matrix of the PolSAR detector, that is, an eigenvector: ； In the formula, For the matrix The eigenvector of For the matrix The characteristic value of .

5. The parameterized constant false alarm processing method applicable to any PolSAR detector according to claim 1, characterized in that: The expression of step S42 is: ； In the formula, is the characteristic function output by the PolSAR detector; t represents the real variable of the characteristic function; i is the imaginary unit.

6. A parameterized constant false alarm processing method applicable to any PolSAR detector according to claim 1, characterized in that: The false alarm probability PFA and the detection threshold in step S5 The expression of the relationship is: ； In the formula, represents the false alarm probability under the detection threshold T; CDF represents the cumulative distribution function; Re represents the real part operation; exp represents the exponential function; is the characteristic function output by the PolSAR detector; t represents the real variable of the characteristic function; i represents the imaginary unit.

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