A Polarimetric SAR Speckle Filtering Method Based on Mean Shift

Abstract

The present invention discloses a polarization SAR coherent speckle filtering method based on mean shift, the purpose of which is to solve the problem that current methods are mostly based on statistical correlation between polarization channels, and thus easily filter only the diagonal elements of the polarization covariance matrix / polarization coherence matrix, thereby realizing the processing of non-diagonal elements and improving the filtering effect, and can realize the preservation of boundary features and polarization scattering characteristics, belonging to the field of radar electronic warfare. The technical solution is to estimate the probability density function according to the kernel function; calculate the mean shift vector according to the gradient of the probability density estimate of the kernel function; perform peak iterative search according to the obtained mean shift vector; and obtain the filtering result after the iterative search ends. The present invention is simple to operate, has a strong engineering foundation and application prospects, and can be extended to actual scenarios such as battlefield reconnaissance and detection of local targets in complex electromagnetic environments.

Description

Technical Field

[0001] The present invention belongs to the field of radar information processing, and relates to a filtering method for SAR (Synthetic Aperture Radar), in particular to a polarization SAR coherent speckle filtering method based on mean shift. Background Art

[0002] As a typical imaging system, SAR boasts significant advantages, including all-day, all-weather, and vegetation penetration. It has been widely used in military reconnaissance, topographic mapping, geological monitoring, forest remote sensing, and disaster assessment. In recent years, multi-channel SAR, exemplified by multi-polarization / multi-antenna systems, has significantly expanded SAR applications in areas such as object classification, high-resolution imaging, forward-looking imaging, and moving target imaging, becoming a major trend in SAR development. The acquisition of multi-polarization information, on the one hand, provides richer target scattering information, providing a basis for revealing target scattering mechanisms and inferring target physical and structural characteristics; on the other hand, differences in polarization characteristics provide new information for distinguishing adjacent targets, contributing to improved radar resolution. By utilizing multiple antennas at different spatial locations, SAR can observe the imaging scene from multiple angles, increasing the amount of information in the spatial dimension.

[0003] As an inherent flaw of coherence-based imaging systems, polarimetric SAR images, like SAR images, exhibit speckle noise. This noise causes significant fluctuations in the amplitude and phase of pixels in polarimetric SAR images, severely impacting image interpretability. Over the past few decades, researchers have conducted extensive research on polarimetric SAR speckle filtering, which can be roughly divided into two phases. In the first phase, researchers proposed several speckle filtering algorithms based on the statistical correlation between polarimetric channels. These algorithms suppress speckle noise by combining data from several polarimetric channels. However, these algorithms have inherent drawbacks. First, in theory, all elements of the polarimetric covariance matrix become perfectly correlated after filtering, making the filtered polarimetric covariance matrix undecipherable using a complex Wishart distribution. Second, the filtering process introduces crosstalk between channels, altering polarimetric information. Furthermore, these filtering algorithms often neglect filtering of off-diagonal elements of the polarimetric covariance matrix. The second phase was marked by J.S. Lee's proposal of polarimetric SAR speckle filtering principles, exemplified by the refined Lee polarimetric filtering algorithm proposed by J.S. Lee et al. and the IDAN filtering algorithm proposed by G. Vasil et al. These algorithms began to incorporate the concept of polarimetric scattering characteristics comparison, emphasizing speckle noise suppression while also considering the preservation of polarimetric scattering characteristics.

[0004] However, these algorithms still perform relatively crude comparisons of polarization scattering characteristics, fail to fully utilize the polarization information contained in the polarization covariance matrix / polarization coherence matrix, and thus fail to achieve ideal speckle filtering results. Therefore, to meet the higher requirements of polarimetric SAR image interpretation for image detail information and target polarimetric scattering characteristics, it is necessary to develop new polarimetric SAR speckle filtering methods. Summary of the Invention

[0005] The present invention proposes a polarimetric SAR speckle filtering method based on mean shift, which solves the problem that current methods are mostly based on statistical correlation between polarization channels, thus easily filtering only the diagonal elements of the polarimetric covariance matrix / polarimetric coherence matrix, and realizes the processing of non-diagonal elements. In addition, the present invention also improves the filtering effect and can preserve boundary features and polarimetric scattering characteristics.

[0006] The technical solution of the present invention is a polarization SAR speckle filtering method based on mean shift, comprising the following steps:

[0007] Step 1: Estimate the probability density function based on the kernel function;

[0008] Step 2: Calculate the mean shift vector based on the gradient of the probability density estimate of the kernel function;

[0009] Step 3: Perform peak iterative search according to the obtained mean shift vector;

[0010] Step 4: The iterative search ends and the filtering result is obtained.

[0011] The following beneficial effects can be achieved by adopting the present invention:

[0012] First, information utilization is more comprehensive and effective. The polarimetric SAR speckle filtering method proposed in this paper, based on mean-shift theory, employs joint filtering in the spatial and value domains, fully utilizing both polarization and amplitude information. This satisfies the basic principles of polarimetric SAR speckle filtering and achieves better filtering effects.

[0013] Second, the polarization filtering effect is better. The present invention has good performance in coherent speckle filtering, boundary protection, and preservation of polarization scattering characteristics. The present invention can filter out coherent speckle noise while well preserving image details, boundary information, and polarization scattering characteristics.

[0014] Third, it has important practical value. The implementation steps of the present invention are simple, which overcomes the problem of coherent filtering of polarimetric SAR and provides an effective method for the detection and identification of ground targets by polarimetric SAR. It has important significance and practical value for the detection of targets on modern battlefields, especially in complex electromagnetic environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic diagram of the principle flow of the present invention;

[0016] Figure 2 (a) is the polarimetric SAR pseudo-color image of Lingshui Nationalities Middle School in Hainan Province before filtering;

[0017] Figure 2 (b) is the image after Lee filtering of the polarimetric SAR pseudo-color image of Lingshui Nationalities Middle School in Hainan Province;

[0018] Figure 2 (c) is the polarimetric SAR pseudo-color image of Lingshui Nationalities Middle School in Hainan Province after IDAN filtering by the present invention;

[0019] Figure 2 (d) is a diagram showing the filtering effect of the polarimetric SAR pseudo-color image of Lingshui Nationalities Middle School in Hainan Province according to the present invention;

[0020] Figure 3 (a) is the image of the polarimetric SAR pseudo-color image of the Oberpfaffenhofen test site in Germany before filtering;

[0021] Figure 3 (b) is the image after Lee filtering of the polarimetric SAR pseudo-color image of the Oberpfaffenhofen test site in Germany;

[0022] Figure 3 (c) is the polarimetric SAR pseudo-color image of the Oberpfaffenhofen test site in Germany after IDAN filtering by the present invention;

[0023] Figure 3 (d) is a diagram showing the filtering effect of the polarimetric SAR pseudo-color image of the Oberpfaffenhofen experimental field in Germany according to the present invention;

[0024] Figure 4 (a) is the boundary detection result of the image after the refined Lee polarization filtering is performed on the SAR image of a certain research institute by the present invention;

[0025] Figure 4 (b) is the boundary detection result of the image after IDAN filtering of a SAR image of a certain research institute by the present invention.

[0026] Figure 4 (c) is the boundary detection result of the image after filtering the SAR image of a certain research institute by the present invention. DETAILED DESCRIPTION

[0027] In order to better understand the technical solution of the present invention, the following further describes the embodiments of the present invention in combination with the basic principles of the present invention and the accompanying drawings.

[0028] Figure 1 The schematic diagram of the principle flow of the present invention includes four steps: estimating the probability density function based on the kernel function, calculating the mean shift vector based on the gradient of the kernel function probability density estimate, performing an iterative peak search based on the obtained mean shift vector, and obtaining the filtering result after the iterative search is completed. The specific method is as follows:

[0029] Step 1: For the SAR image, the probability density function is estimated based on the kernel function, which includes the following steps:

[0030] 1.1 Given a d-dimensional Euclidean space R d The n elements x in i , i=1,2,…n, the probability density estimation based on the kernel function K(x) and the d-dimensional bandwidth matrix H is expressed as

[0031]

[0032] in

[0033] K H (x)=|H| -1 / 2 K(H -1 / 2 x) (2)

[0034] x is the independent variable of the defined function;

[0035] 1.2 Take the bandwidth matrix H as

[0036]

[0037] Among them, h k , k=1,2…d are the elements in the bandwidth matrix; if the bandwidth parameter contains only one element h, that is, H=h 2 I form, then The corresponding probability density function is expressed as

[0038]

[0039] 1.3 Expressing the kernel function in a radially symmetric form

[0040] K(x)=c k,d k(||x|| 2 ) (5)

[0041] Where k(·) is the profile function of the kernel function K(x), c k,d is the normalization coefficient, and substituting formula (5) into formula (4) yields

[0042]

[0043] 1.4 Define g(x) = -k′(x), and express the kernel function corresponding to the profile function g(x) as

[0044] G(x)=c g,d g(||x|| 2 ) (7)

[0045] where c g,d is the normalization coefficient, x is the independent variable of the definition function;

[0046] 1.5 According to formula (4), determine The gradient of

[0047]

[0048] Among them, the probability density estimated by part1 and kernel function G(x) is

[0049]

[0050] And in formula (8), part2 is the mean shift vector m to be estimated in step 2 h,G (x)

[0051]

[0052] Step 2: Calculate the mean shift vector based on the gradient of the probability density estimate of the kernel function, including the following steps:

[0053] 2.1 Determine the mean shift vector and and The relationship is

[0054]

[0055] Determine the mean shift vector m by formula (11) h,G (x) is equivalent to the result of the gradient of the probability density estimate based on the kernel function K(x) being normalized by the probability density estimate based on the kernel function G(x); considering the non-negative property of the kernel function, determine m h,G The sign of (x) and Consistent, that is, the maximum rising direction of the estimated probability density;

[0056] Step 3: Perform peak iterative search according to the obtained mean shift vector, including the following steps:

[0057] 3.1 Let y0 = x be the initial value, and set y j, j=1,2,… is recorded as the result of the jth iteration. In the mean shift process, determine y j+1 and y j The relationship between

[0058]

[0059] Among them, y j+1 Is y j is the weighted average of the points in the hypersphere of the center;

[0060] 3.2 According to equations (10) and (12), the final expression of the mean shift vector is:

[0061]

[0062] The mean shift vector also represents the iteration step size;

[0063] Step 4: The iterative search ends and the filtering result is obtained.

[0064] Figure 2 The following are images of the filtering effect of the polarimetric SAR pseudo-color image of Lingshui Nationalities Middle School in Hainan Province using the present invention. (a) The image before filtering; (b) The image after refined Lee polarimetric filtering (filter window 7×7); (c) The image after IDAN polarimetric filtering; and (d) The image after filtering using the method of the present invention. It can be seen that the filtering method of the present invention overcomes many of the shortcomings of the refined Lee polarimetric filtering method and the IDAN filtering algorithm, achieving excellent filtering results. First, in homogeneous areas such as the school playground, the filtering method of the present invention achieves a very smooth filtering effect with no "patching effect," making the two blue goals on the playground appear clearer in the filtered image. Second, the image details and point targets are well preserved. The image texture information is also well preserved, as can be seen from the comparison of the playground area before and after filtering. In summary, it can be seen that the filtering algorithm of the present invention not only filters out coherent speckle noise but also effectively preserves image details.

[0065] Figure 3The figures show the filtering effect of the polarimetric SAR pseudo-color image of the Oberpfaffenhofen experimental field in Germany, (a) shows the image before filtering; (b) shows the image after refined Lee filtering; (c) shows the image after IDAN filtering; (d) shows the image after filtering by the present invention. It can be seen that the filtering effect of the filtering method of the present invention is significantly better than that of refined Lee polarimetric filtering and IDAN filtering. First, in homogeneous areas, the filtering method of the present invention obtains the smoothest filtering effect. After filtering, the interior of the homogeneous area is uniform and delicate, and no "patch effect" occurs. Secondly, the filtering method of the present invention has a good boundary preservation effect. After filtering by the filtering method of the present invention, the boundary can still remain clear, and there is no widening phenomenon.

[0066] Figure 4 The following are the boundary detection results of the CFAR boundary detector after filtering 38 SAR images using the present invention. (a) shows the boundary detection results of the image after refined Lee polarization filtering; (b) shows the boundary detection results of the image after IDAN filtering; and (c) shows the boundary detection results of the image after filtering using the present invention. In the figure, the filtering method of the present invention undoubtedly has the best boundary preservation performance, and the outlines of all roads, runways, and buildings appear continuous and clear. However, the boundaries of the refined Lee polarization filtering show discontinuity, which is particularly evident in the boundary detection results of field roads and runways in the playground. At the same time, the boundaries of many scattering points have become blurred, which is particularly evident in the boundary detection results of scattering points on the upper part of the playground. The boundaries of some scattering points are not even detected. Although the boundary preservation effect of the IDAN filtering method is slightly better than that of the refined Lee polarization filtering method, a large number of noise points appear in the image.

Claims

1. A polarimetric SAR speckle filtering method based on mean shift, comprising the following steps: Step 1: For the SAR image, the probability density function is estimated based on the kernel function, which includes the following steps: 1.1 Given a d-dimensional Euclidean space R d The n elements x in i , i=1,2,…n, the probability density estimation based on the kernel function K(x) and the d-dimensional bandwidth matrix H is expressed as in K H (x)=|H| -12 K(H -12 x) (2) x is the independent variable of the defined function; 1.2 Take the bandwidth matrix H as Among them, h k , k=1,2…d are the elements in the bandwidth matrix; if the bandwidth parameter contains only one element h, that is, H=h 2 I form, then The corresponding probability density function is expressed as 1.3 Expressing the kernel function in a radially symmetric form K(x)=c k,d k(||x|| 2 ) (5) Where k(·) is the profile function of the kernel function K(x), c k,d is the normalization coefficient, and substituting formula (5) into formula (4) yields 1.4 Define g(x) = -k′(x), and express the kernel function corresponding to the profile function g(x) as G(x)=c g,d g(||x|| 2 ) (7) where c g,d is the normalization coefficient, x is the independent variable of the definition function; 1.5 According to formula (4), determine The gradient of Among them, the probability density estimated by part1 and kernel function G(x) is And in formula (8), part2 is the mean shift vector m to be estimated in step 2 h,G (x) Step 2: Calculate the mean shift vector based on the gradient of the probability density estimate of the kernel function, including the following steps: 2.1 Determine the mean shift vector and and The relationship is Determine the mean shift vector m by formula (11) h,G (x) is equivalent to the result of the gradient of the probability density estimate based on the kernel function K(x) being normalized by the probability density estimate based on the kernel function G(x); considering the non-negative property of the kernel function, determine m h,G The sign of (x) and Consistent, that is, the maximum rising direction of the estimated probability density; Step 3: Perform peak iterative search according to the obtained mean shift vector, including the following steps: 3.1 Let y0 = x be the initial value, and set y j , j=1,2,… is recorded as the result of the jth iteration. In the mean shift process, determine y j+1 and y j The relationship between Among them, y j+1 Is y j is the weighted average of the points in the hypersphere of the center; 3.2 According to equations (10) and (12), the final expression of the mean shift vector is: The mean shift vector also represents the iteration step size; Step 4: The iterative search ends and the filtering result is obtained.

Images