A universal fusion method for multi-frequency polarimetric SAR images based on scattering mechanism

Abstract

The present invention discloses a universal fusion method for multi-frequency polarimetric SAR images based on a scattering mechanism. The method uses outlier removal and neighborhood mean replacement methods to process noise in multi-frequency SAR data, and uses the Frobenius norm for normalization to eliminate scale differences between different sensors. The processed matrix is ​​vectorized, and the polarization similarity between the fusion matrix and the standard scattering matrix is ​​calculated based on the Pauli vector. Each combination of multi-frequency data is traversed, and when traversing each combination of multi-frequency data, the weights of the multi-frequency data are iteratively optimized using the SQP algorithm, and the optimal weight configuration is selected to maximize the similarity between the fused data and the standard scattering model. This method can more comprehensively describe the energy and polarization characteristics of ground objects, thereby obtaining more accurate and physically meaningful multi-frequency data fusion results.

Description

Technical Field

[0001] The present invention belongs to the field of Synthetic Aperture Radar (SAR) remote sensing image processing and relates to a method for guiding multi-frequency polarimetric SAR image fusion using a standard scattering model. Specifically, the present invention relates to a method for traversing various combinations of multi-frequency data and calculating the maximum polarimetric similarity between the fused data and the typical scattering model by applying Sequential Quadratic Programming (SQP) to determine the optimal fusion weights of the multi-frequency data. Background Art

[0002] PolSAR can obtain information from different polarization channels, which helps capture the complex electromagnetic scattering characteristics of target objects, thereby accurately describing the geometric structure and physical properties of surface cover, and has significant advantages in areas such as land object recognition and classification.

[0003] Multi-frequency PolSAR combines imagery acquired at different frequencies to more comprehensively capture the electromagnetic scattering characteristics of ground objects. Radar waves in different frequency bands respond differently to ground objects. Low-frequency signals can penetrate vegetation and are suitable for detecting forests and soil, while high-frequency signals are suitable for observing buildings and urban areas.

[0004] Multi-frequency PolSAR data fusion is crucial for improving remote sensing image interpretation and expanding its application. It can be used not only for object classification and identification but also for disaster monitoring, environmental change detection, and urban planning. For example, in disaster monitoring, multi-frequency PolSAR can effectively detect the impacts of disasters like floods and landslides, providing high-resolution information on these changes. In environmental monitoring, multi-frequency data fusion enables more accurate tracking of key parameters such as changes in forest cover and soil moisture. Furthermore, in urban planning, multi-frequency PolSAR can help analyze building distribution and land use, providing a scientific basis for urban development.

[0005] However, existing fusion methods typically use a transformation to extract ground object features from the original scattering matrix and then fuse them together, lacking the ability to fully explore the original data. In reality, the polarization scattering matrix contains the energy, phase, and polarization characteristics of the ground object, providing a relatively complete description of the electromagnetic scattering characteristics of the radar target. Fusion analysis of this matrix facilitates further research. Furthermore, while existing fusion methods can effectively analyze the underlying patterns in the data, the processing lacks clear physical meaning, hindering the full exploration of the scattering characteristics of the pixels.

[0006] In summary, multi-frequency PolSAR fusion technology has important research value in remote sensing image interpretation and practical applications. However, there are many problems in multi-frequency PolSAR data fusion, which can be summarized as insufficient exploration of the original scattering matrix data and a lack of clear physical meaning in the processing process. Summary of the Invention

[0007] This paper addresses the problems of existing methods, such as the lack of interpretability during the fusion process and the difficulty in quantifying the contribution of multi-frequency data. By combining a multi-frequency polarimetric scattering matrix with a standard scattering model with a clear physical interpretation, we propose a universal fusion method for multi-frequency polarimetric SAR imagery based on scattering mechanisms. This method introduces five typical scattering models to guide the fusion of multi-frequency data. By fully accounting for the diversity of scattering from individual pixels, it ensures that the fusion process is physically meaningful, enabling the fusion results to more comprehensively describe the energy and polarimetric characteristics of ground objects, thereby achieving more accurate and physically meaningful multi-frequency data fusion results.

[0008] The purpose of the present invention is achieved through the following technical solutions:

[0009] A universal fusion method for multi-frequency polarimetric SAR images based on scattering mechanism includes the following steps:

[0010] Step 1: Prepare a multi-frequency PolSAR dataset covering the same area;

[0011] Step 2: Resample, geocode, align, and crop the data of each frequency band to keep the same resolution in the study area for subsequent fusion processing;

[0012] Step 3: Remove outliers from the data preprocessed in step 2. Set appropriate percentile thresholds based on the data characteristics to determine the normal fluctuation range of the data. Values ​​outside these ranges are considered outliers and replaced with the neighborhood mean.

[0013] Step 4: Represent the data preprocessed in step 3 in the form of a scattering matrix. Use the Frobenius norm to normalize the scattering matrix to ensure that the scale of the data is uniform while keeping the relative relationships within the data unchanged.

[0014] Step 5: Use weighted combination to define the scattering matrix that fuses different bands and the standard scattering matrix that fuses multiple scattering types;

[0015] Step 6: Calculate the polarization similarity between the fusion matrix obtained in step 5 and the standard scattering matrix;

[0016] Step 7: Traverse each combination of multi-frequency data and use the SQP algorithm to optimize the similarity between the fusion matrix and the standard scattering matrix. Update the weight vector during the optimization process until the convergence condition is met and the optimal weight configuration is found.

[0017] Step 8: After evaluating all multi-frequency combinations, the weight that maximizes the similarity between the multi-frequency fusion data and the standard scattering model is selected as the best configuration.

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] 1. This paper focuses on the original Sinclair scattering matrix and uses a typical scattering model to guide multi-frequency data fusion, ensuring that the fusion process has a clear physical meaning, making the fusion results more interpretable, and being able to quantify the contribution of each frequency band data in the fusion process.

[0020] 2. The present invention performs azimuth compensation on the standard scattering matrix to characterize the target scattering conditions under different incident angles, which can meet the processing requirements of complex objects with various scattering characteristics and has wider applicability.

[0021] 3. During the fusion process, the present invention effectively reduces the scale differences and noise interference caused by different sensors through data normalization and outlier elimination, thereby improving the robustness and stability of the fused data. It is suitable for the fusion research of homogeneous and heterogeneous sensor data, and is also suitable for the fusion application of multiple frequency bands. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 Schematic diagram of a general multi-frequency polarimetric SAR image fusion framework based on scattering mechanism;

[0023] Figure 2 Dual-frequency (C and L band) fully polarimetric SAR images of the San Francisco area, (a) C-band Pauli diagram, (b) L-band Pauli diagram, (c) optical image, (d) ground feature type;

[0024] Figure 3 Multi-frequency polarimetric SAR images after preprocessing, (a) C-band Pauli diagram, (b) L-band Pauli diagram;

[0025] Figure 4 Schematic diagram of the standard scattering model, (a) trihedral angle, (b) dihedral angle, (c) dipole, (d) right-hand spiral scattering, (e) left-hand spiral scattering;

[0026] Figure 5 Results of multi-frequency image fusion: (a) C-band decomposition result, (b) L-band decomposition result, and (c) fused image decomposition result. DETAILED DESCRIPTION

[0027] The technical solution of the present invention is further described below with reference to the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention that does not depart from the spirit and scope of the technical solution of the present invention should be included in the scope of protection of the present invention.

[0028] The present invention provides a universal fusion method for multi-frequency polarimetric SAR images based on a scattering mechanism. The method uses outlier removal and neighborhood mean replacement methods to process the noise in multi-frequency SAR data, and uses the Frobenius norm for normalization to eliminate scale differences between different sensors. The processed matrix is ​​vectorized, and the polarization similarity between the fusion matrix and the standard scattering matrix is ​​calculated based on the Pauli vector. Each combination of multi-frequency data is traversed, and when traversing each combination of multi-frequency data, the weights of the multi-frequency data are iteratively optimized using the SQP algorithm, and the optimal weight configuration is selected to maximize the similarity between the fused data and the standard scattering model. Figure 1 As shown, the specific steps include:

[0029] Step 1: Select multi-frequency datasets covering the same geographic location to ensure spatial consistency of PolSAR data from different frequency bands during the fusion process. Also, consider the imaging time, polarization mode, and resolution of different sensors to ensure data consistency and comparability. The specific steps are as follows:

[0030] Step 1: Select a study area with rich landform types and ensure that there is a multi-frequency dataset with the same coverage in the area.

[0031] Steps 1 and 2: Select appropriate multi-band data based on the research purpose and surface target characteristics. Try to obtain data in different frequency bands at or near the same time.

[0032] Step 13: Select multi-frequency data with a resolution difference of less than 3 meters to ensure that the analysis is performed at the same scale.

[0033] Step 2: Resample, geocode, crop, and register the data of each frequency band to keep the same resolution in the study area for subsequent fusion processing. The specific steps are as follows:

[0034] Step 21: Usually, the resolution of the high-frequency data is used as a benchmark, and the nearest neighbor interpolation method is selected to resample the remaining data to ensure that each data has the same resolution.

[0035] Step 22: Perform coordinate conversion on the resampled multi-frequency data. By reading the sensor parameters and orbit information of the data, project the SAR data from the coordinate system of the imaging platform to the standard geographic coordinate system. Use the geometric positioning algorithm combined with the ground control points to calculate the geographic coordinates of each pixel point, and use the geocoding tool to accurately map the image to a unified geographic space.

[0036] Steps 2 and 3: Select the high-frequency band as the reference image, detect the same ground feature points in the two frequency band images, calculate the offset of these feature points in different images, generate a spatial transformation model, and then use the transformation model to perform geometric correction on the image to be registered so that it is completely consistent with the reference image in geometry.

[0037] Step 24: Determine the cropping range based on the coordinate boundary of the study area, and use SAR image processing software to crop the images of all frequency bands to ensure that the spatial ranges of the two images are completely consistent.

[0038] Step 3: Remove outliers from the data preprocessed in step 2. First, set an appropriate percentile threshold based on the data distribution characteristics to determine the normal fluctuation range of the data. Values ​​outside this range are marked as outliers. Then, the neighborhood mean is used to replace these outliers to reduce their impact on data analysis. The specific steps are as follows:

[0039] Step 31: Perform statistical analysis on the data distribution and define the range of normal data by calculating the percentiles of the data. The 0.5th percentile and the 99.5th percentile are commonly used threshold settings.

[0040] Step 32: Calculate the 0.5th and 99.5th percentiles, and consider data points below or above this range as outliers. Iterate over each data point and check whether it is below or above the specified threshold. If so, mark it as an outlier.

[0041] Step 3: For each data point marked as an outlier, define a 3×3 neighborhood range, calculate the mean of all non-outlier data points in the neighborhood range, replace the outlier with its neighborhood mean, and update the outlier value in the data set to the calculated mean.

[0042] Step 4: Represent the data pre-processed in step 3 in the form of a scattering matrix and normalize the scattering matrix using the Frobenius norm to ensure that data from different sources are compared at the same scale. The specific steps are as follows:

[0043] Step 41: Extract the corresponding Sinclair scattering matrix for each pixel. The scattering matrix is ​​usually a 2×2 complex matrix with the following form:

[0044]

[0045] Among them S HH 、S VV and S HV denote the backscattering coefficients of HH, VV and HV polarization channels, respectively.

[0046] Step 42: Calculate the Frobenius norm of each preprocessed scattering matrix and normalize the scattering matrix using the calculated Frobenius norm:

[0047]

[0048] in is the normalized scattering matrix. This operation can unify the scale of the scattering matrix, thereby eliminating the impact of scale differences between different data sources.

[0049] Step 5: In the multi-frequency polarimetric SAR data fusion process, for matrices of different bands and scattering types, it is necessary to define the scattering matrix for fusing different bands and the standard scattering matrix for fusing multiple scattering types through weighted combination. The specific steps are as follows:

[0050] Step 51: Determine the different frequency bands to be fused, assign weights to the scattering matrix of each frequency band, and the sum of the weights should be 1 to ensure the consistency of the scale of the scattering matrix after weighted combination.

[0051] Step 52: Determine the different scattering type models to be fused. Surface scattering is rotationally invariant. A rotation matrix is ​​introduced to rotate the dihedral angle and volume scattering models to characterize the scattering characteristics of ground objects at different angles.

[0052] Step 53: Assign weights to the matrix of each standard scattering model to reflect its importance in the comprehensive model, and weight the matrix of each scattering type to form the fused standard scattering matrix.

[0053] Step 6: Calculate the polarization similarity between the fusion matrix obtained in step 5 and the standard scattering matrix, and evaluate the quality of the fused data by quantifying the degree of match between the fusion matrix and the known standard scattering matrix. The specific steps are as follows:

[0054] Step 61: Extract the Pauli vectors of each scattering matrix separately for subsequent similarity calculation. The specific formula is as follows:

[0055]

[0056] Step 62: After obtaining the Pauli vectors, first calculate the inner product of the polarization vectors, then perform a modular square operation on the inner product to ensure that the inner product result is non-negative, and then calculate the square of the 2-norm of each vector separately.

[0057] Step 63: Perform a ratio operation on the calculation result of step 62 to obtain the normalized polarization similarity.

[0058] Step 7: Traverse each combination of multi-frequency data and use the SQP algorithm to optimize the similarity between the fusion matrix and the standard scattering matrix. Update the weight vector during the optimization process until the convergence condition is met and the optimal weight configuration is found. The specific steps are as follows:

[0059] Step 71: For each multi-frequency data combination, set the initial weight of the standard scattering matrix as the starting point of the SQP algorithm. Uniform distribution is often used as the initial weight configuration, and the sum of all weights is 1.

[0060] Step 72: Based on step 71, enter the iteration phase. In each iteration, construct and solve an approximate quadratic programming subproblem, and then update the weight vector based on the solution. The SQP algorithm needs to solve the following quadratic programming subproblems:

[0061]

[0062] Where Δf is the increment of the weight vector, which is in the form of It is composed of the difference between the components in the two iterations, where f i Represents the weights corresponding to each standard scattering model, H k is the approximate value of the Hessian matrix of the objective function at the kth iteration, g k is the gradient vector at the kth iteration.

[0063] Step 73: Update the weight vector according to the solution of the subproblem and check whether the convergence condition is met. If so, terminate the algorithm; if not, continue to the next iteration until the optimal weight configuration is found.

[0064] Step 8: After evaluating all multi-frequency combinations, select the weight that maximizes the similarity between the multi-frequency fusion data and the standard scattering model as the optimal configuration. The specific steps are as follows:

[0065] Step 81: Perform similarity evaluation on all multi-frequency data combinations and record the polarization similarity under each combination.

[0066] Step 82: After obtaining the similarity results of all multi-frequency combinations, perform summary analysis and use data comparison method to sort the similarity values ​​of each combination, find the combination with the largest similarity value, and regard its corresponding multi-frequency data combination as the best configuration.

[0067] Example:

[0068] This embodiment provides a dual-frequency polarimetric SAR image fusion method based on the scattering mechanism starting from the original scattering matrix, the method comprising the following steps:

[0069] Step 1: Select C-band data acquired by RADARSAT-2 and L-band data acquired by ALOS-2 for testing. This dataset covers the San Francisco area of ​​the United States. The study area mainly includes four types of land features: mountains, oceans, urban areas, and vegetation. The urban areas can be further divided into high-inclination urban areas, low-inclination urban areas, and orthogonal urban areas according to the radar incident angle. The dual-frequency (C and L band) fully polarized SAR image of the San Francisco area is as follows: Figure 2 shown.

[0070] The C-band RADARSAT-2 data has a spatial resolution of 4.8m × 4.7m and includes four polarization modes (HH / HV / VH / HH). It was collected on April 9, 2008. The L-band ALOS-2 data has a spatial resolution of 3.21m × 2.86m and also includes four polarization channels. It was collected on March 24, 2015.

[0071] The multi-band images selected in this embodiment have the same coverage and are relatively close in spatial resolution, which facilitates subsequent fusion operations. Although there is a certain degree of temporal decoherence between the two images, after comparison, most of the ground objects have not changed significantly under the radar field of view, and fusion research can be carried out.

[0072] Step 2: The lower-resolution RADARSAT-2 data (4.8 m × 4.7 m) were selected as a baseline and the ALOS-2 L-band data were resampled. Bilinear interpolation was used to resize the ALOS-2 data from its original 3.21 m × 2.86 m resolution to 4.8 m × 4.7 m, preserving a smooth transition between features. The geocoding module of the SAR processing tool PolSARpro was then used in conjunction with a digital elevation model (DEM) to geocode both datasets, ensuring they were in the same UTM coordinate system and that each pixel had a clear geographic coordinate. Using a feature-based registration method, significant features in the images, such as road intersections and building edges, were manually annotated to ensure pixel-level spatial alignment between the two images. After registration, the specific geographic coordinates of the study area were confirmed using Google Maps and saved as a .kml file. The ALOS-2 and RADARSAT-2 data were then cropped using the GDAL library in Python to ensure identical spatial extents. After this series of processing, the two sets of data have reached a uniform resolution, geographic coordinate system and spatial range. Figure 3 shown.

[0073] Step 3: Remove outliers from the preprocessed data. The uneven scattering properties of ground objects cause the coherent superposition of echo signals generated by tiny scatterers on the target surface, manifesting as a granular texture in SAR images, known as speckle noise. This noise not only affects the visual quality of SAR images but also interferes with object recognition and power analysis. Removing speckle noise is particularly important for fusing data from different sensors.

[0074] The polarimetric SAR system extracts ground object information by measuring the 2×2 complex scattering matrix associated with each resolution unit:

[0075]

[0076] Among them S HH , S VV and S HV represents the backscatter coefficients for the HH, VV, and HV polarization channels, respectively. Testing has shown that, in the dataset used in this embodiment, outlier detection is most effective when set to the 0.5th and 99.5th percentiles of the data. This prevents valid information from being mistakenly excluded while also adequately filtering out extreme values.

[0077] noise={S i |S i <Q 0.5 or S i >Q 99.5}

[0078] Among them S i ∈{S HH S HV S VV}, Q 0.5 and Q 99.5 Represent the 0.5th percentile and the 99.5th percentile respectively. For each point marked as an outlier, we make full use of the spatial correlation of the data and select a 3×3 pixel matrix around the point as the center. Then, we calculate the mean of all non-outlier pixels in the neighborhood and use this mean to replace the outlier in the center.

[0079] Step 4: Since sensors in different bands differ in data acquisition methods, resolution, polarization channel settings, and radiation characteristics, direct comparison or fusion of data from different sensors may be distorted due to scale differences. Normalization maps data from different sensors to the same scale so that they are processed in the same reference frame, thereby avoiding errors caused by scale differences. In this embodiment, the Frobenius norm is used to normalize the scattering matrix to ensure the magnitude consistency of data in different bands. The normalization process first calculates the Frobenius norm of each scattering matrix. The specific calculation formula is:

[0080]

[0081] Among them, S F is the Frobenius norm of the matrix S, S ij Represents the elements in the scattering matrix. Next, the normalized matrix is ​​obtained by dividing each element in the original scattering matrix by the Frobenius norm of the matrix:

[0082]

[0083] Among them S norm represents the normalized matrix, F Represents the normalized norm of the S matrix. This normalization method ensures that the scale of multi-source data is unified, while the relative relationship within the data remains unchanged, making the fusion between different data sets more reasonable.

[0084] Step 5: Use the similarity parameter to measure the similarity between the fused multi-frequency matrix and the standard scattering matrix. The fusion matrix can be expressed as:

[0085] S f =a·S1+(1-a)·S2

[0086] Where a represents the matrix weight, ranging from 0 to 1. S1 and S2 represent the scattering matrices for different frequency bands, representing RADARSAT-2 and ALOS-2 data, respectively. By adjusting the value of a, the contribution of different frequency bands to the fusion matrix can be controlled, thereby ensuring that the scattering characteristics of the fusion matrix are as consistent as possible with those of the standard scattering matrix.

[0087] Since real-world targets often have complex geometric structures and diverse scattering properties, their scattering responses often exhibit diversity and complexity. The interaction between electromagnetic waves and signals can be characterized by five basic target scattering mechanisms: surface scattering, dihedral scattering, volume scattering, left-handed spiral scattering, and right-handed spiral scattering. The Sinclair matrix for each scattering mechanism is expressed as follows:

[0088]

[0089]

[0090] Among them, surface scattering is used to characterize the interaction process between radar signals and slightly rough surfaces. Dihedral scattering is caused by a pair of orthogonal surfaces with different dielectric constants. Volume scattering is a type of scattering formed by multiple scattering of echo signals and randomly distributed dipoles. It mainly occurs in densely vegetated forests or densely packed building areas. Spiral scattering is mainly caused by complex man-made buildings. Standard scattering models such as Figure 4 shown.

[0091] To further accurately characterize these scattering mechanisms, especially those with complex target scattering characteristics, rotation of the scattering matrix is ​​necessary. Surface scattering is rotationally invariant, meaning that the characteristics of surface scattering remain unchanged regardless of the radar's angle of incidence. By rotating the dihedral angle and volume scattering matrices, these two mechanisms can be incorporated into a broader polarimetric SAR model, facilitating subsequent interpretation. The rotation matrix takes the following form:

[0092]

[0093] Where θ represents the orientation angle of the target. The rotated dihedral scattering matrix can be rotated to a specified position as follows:

[0094]

[0095] Among them S dihedral represents the dihedral angle scattering matrix at θ = 0°, and R(θ) represents the rotation matrix. Similarly, the dipole scattering matrix for each orientation is:

[0096]

[0097] Among them S dipolerepresents the dipole scattering matrix at θ = 0°. According to the common method of target decomposition, the scattering process of a single pixel can be expressed as a linear combination of multiple models. Therefore, the standard scattering matrix can be expressed as:

[0098] S c =f1·S plane +f2·S(θ) dihedral +f3·S(θ) dipole +f4·S r-helix +f5·S l-helix

[0099] Where f1 to f5 represent the weights of the corresponding scattering models.

[0100] Step 6: Polarization similarity mathematically quantifies the degree of similarity between the two polarization statistical matrices. This parameter offers two distinct advantages. First, it is independent of the power of the two scattering matrices. For spherical, planar, and biplane targets, its calculation is unaffected by target size, ensuring consistency across scales. Second, it is azimuth-invariant and therefore remains stable across various observation angles. This robustness makes it widely used in radar target characterization.

[0101] The calculation of polarization similarity relies on the extraction of Pauli vectors, which can be obtained from the S matrix as follows:

[0102]

[0103] Among them, S HH 、S VV and S HV denote the backscattering coefficients of the HH, VV, and HV polarization channels, respectively. The similarity parameter between the above matrices is defined as follows:

[0104]

[0105] Among them, k1 and k2 are two targets corresponding to S f and S c The scattering vector, represents the sum of the absolute squares of the three components of the Pauli vector, represents the conjugate inner product of two Pauli vectors, Represents the inner product of two vectors. This similarity measure reflects the similarity of the polarization features between two targets, and the value ranges from 0 to 1, where 1 means that the two targets are completely similar and 0 means they are completely different.

[0106] Step 7: Sequential quadratic programming is an algorithm for solving nonlinear optimization problems. This method decomposes nonlinear optimization problems into a series of quadratic programming problems. In this embodiment, initial weights are first set as the algorithm's starting point. In each iterative step, an approximate quadratic programming subproblem is constructed and solved. This subproblem is obtained by linearizing the constraint function and the quadratic approximation objective function. The variables of the original problem are updated based on the solution of the subproblem, and a new iteration point is generated. The new iteration point is checked to see if it meets the convergence criteria. If so, the algorithm terminates; otherwise, the iteration continues.

[0107] In each iteration, the SQP algorithm needs to solve the following quadratic programming subproblem:

[0108]

[0109] Where Δf is the increment of the weight vector, which is in the form of It is composed of the difference between the components in the two iterations, where f i Represents the weights corresponding to each standard scattering model, H k It is the approximate value of the Hessian matrix of the objective function at the kth iteration. k is the gradient vector at the kth iteration:

[0110]

[0111] The constraints are as follows:

[0112] A k Δf+b k =0and C k Δf+d k ≥0

[0113] Among them A k and C k are the Jacobian matrices of the equality and inequality constraints, respectively, and b k and d k is the linearization term of the constraint function. After solving the subproblem, the weight vector is updated as:

[0114] f k+1 =f k +Δf

[0115] This updating process gradually adjusts the weight of each frequency band so that the similarity between the fused matrix and the standard scattering model gradually increases.

[0116] After each iteration, the algorithm checks whether the new iteration point meets the convergence criteria. This convergence criterion is typically set as the change in the objective function being less than a preset threshold. If the objective function improves only slightly, it indicates it is close to the optimal solution, and the algorithm terminates. Otherwise, the algorithm proceeds to the next iteration. Through multiple iterations, the SQP algorithm gradually approaches the optimal solution. When the convergence criteria are met, the final optimal weight configuration maximizes the similarity between the multi-frequency fusion data and the standard scattering model:

[0117]

[0118] Step 8: Evaluate the similarity of all multi-frequency data combinations and record the polarization similarity for each combination. After obtaining the similarity results for all multi-frequency combinations, perform a summary analysis. Using a data comparison method, sort the similarity values ​​of each combination and find the combination with the highest similarity value. This corresponding multi-frequency data combination is considered the optimal configuration.

[0119] The result after multi-frequency image fusion is as follows Figure 5 As shown. Figure 5 It can be seen that fused imagery offers advantages over single-band imagery in target interpretation. Specifically, compared to C-band RADARSAT-2 data, the greatest advantage of fused data lies in its more accurate interpretation of mountainous areas. Comparison with optical imagery from the same year reveals the presence of significant bare ground within the mountains. However, due to the shorter wavelength of the C-band, multiple scattering occurs during interaction with the rough surface of the bare ground, resulting in a significant number of echo signals being interpreted as volume scattering. The L-band, with its longer wavelength, is suitable for detecting mountains and forests, and can more accurately characterize the scattering characteristics of mountains. Therefore, the fused imagery can accurately represent bare ground within the mountains.

[0120] Compared to L-band ALOS-2 imagery, the fused imagery offers improved overall visual quality. This is because when generating the color composite image, each image undergoes equalization, redistributing pixel values ​​across the entire pixel range. This results in a more uniform brightness distribution, enhancing image detail and edges and improving overall visual quality. However, due to the longer wavelength of the L-band, it can resonate with large-scale waves on the ocean surface, generating irregular scattering and leading to sea clutter. Furthermore, the L-band has greater penetrating power and can cause multiple scattering with inhomogeneous media in the seawater, increasing clutter intensity and thus reducing image quality. The fused imagery can significantly reduce clutter issues in the original data and better depict the scattering characteristics of the seawater. This also demonstrates that multi-frequency data fusion ensures data stability to a certain extent.

Claims

1. A universal fusion method for multi-frequency polarimetric SAR images based on scattering mechanism, characterized by The method comprises the following steps: Step 1: Prepare a multi-frequency PolSAR dataset covering the same area; Step 2: Resample, geocode, align, and crop the data of each frequency band to keep the same resolution in the study area for subsequent fusion processing; Step 3: Remove outliers from the data preprocessed in step 2. Set appropriate percentile thresholds based on the data characteristics to determine the normal fluctuation range of the data. Values ​​outside these ranges are considered outliers and replaced with the neighborhood mean. Step 4: Represent the data preprocessed in step 3 in the form of a scattering matrix. Use the Frobenius norm to normalize the scattering matrix to ensure that the scale of the data is uniform while keeping the relative relationships within the data unchanged. Step 5: Use weighted combination to define the scattering matrix that fuses different bands and the standard scattering matrix that fuses multiple scattering types. The specific steps are as follows: Step 51: Determine the different frequency bands to be fused, assign weights to the scattering matrix of each frequency band, and the sum of the weights should be 1 to ensure the consistency of the scale of the scattering matrix after weighted combination; Step 52: Determine the different scattering type models to be fused. Surface scattering is rotationally invariant. A rotation matrix is ​​introduced to rotate the dihedral angle and volume scattering models to characterize the scattering characteristics of ground objects at different angles. Step 53: Assign weights to the matrix of each standard scattering model to reflect its importance in the comprehensive model, and weight the matrix of each scattering type to form the fused standard scattering matrix; Step 6: Calculate the polarization similarity between the fusion matrix obtained in step 5 and the standard scattering matrix; Step 7: Traverse each combination of multi-frequency data and use the SQP algorithm to optimize the similarity between the fusion matrix and the standard scattering matrix. Update the weight vector during the optimization process until the convergence condition is met and the optimal weight configuration is found. Step 8: After evaluating all multi-frequency combinations, the weight that maximizes the similarity between the multi-frequency fusion data and the standard scattering model is selected as the best configuration.

2. The universal fusion method of multi-frequency polarimetric SAR images based on scattering mechanism according to claim 1 is characterized in that The specific steps of step one are as follows: Step 1: Select a study area with rich landform types and ensure that the area has a multi-frequency dataset with the same coverage; Step 1 and 2: Select appropriate multi-band data based on the research objectives and surface target characteristics. Try to obtain data from different frequency bands at or near the same time. Step 13: Select multi-frequency data with a resolution difference of less than 3 meters to ensure that the analysis is performed at the same scale.

3. The universal fusion method of multi-frequency polarimetric SAR images based on scattering mechanism according to claim 1 is characterized in that The specific steps of step 2 are as follows: Step 21: Usually, the resolution of high-frequency data is used as a benchmark, and the nearest neighbor interpolation method is selected to resample the remaining data to ensure that each data has the same resolution; Step 22: Perform coordinate conversion on the resampled multi-frequency data. By reading the sensor parameters and orbit information of the data, the SAR data is projected from the coordinate system of the imaging platform to the standard geographic coordinate system. The geographic coordinates of each pixel are calculated using a geometric positioning algorithm combined with ground control points. The image is then accurately mapped to a unified geographic space using geocoding tools. Step 2 and 3: Select the high-frequency band as the reference image, detect the same ground feature points in the two frequency band images, calculate the offset of these feature points in different images, generate a spatial transformation model, and then use the transformation model to perform geometric correction on the image to be registered so that it is completely consistent with the reference image in terms of geometry; Step 24: Determine the cropping range based on the coordinate boundary of the study area, and use SAR image processing software to crop the images of all frequency bands to ensure that the spatial ranges of the two images are completely consistent.

4. The universal fusion method of multi-frequency polarimetric SAR images based on scattering mechanism according to claim 1 is characterized in that The specific steps of step three are as follows: Step 31: Perform statistical analysis on the data distribution and define the range of normal data by calculating the percentile of the data; Step 32: Calculate the 0.5th and 99.5th percentiles, and consider data points below or above this range as outliers. Iterate over each data point and check whether it is below or above the specified threshold. If so, mark it as an outlier. Step 3: For each data point marked as an outlier, define a 3×3 neighborhood range, calculate the mean of all non-outlier data points in the neighborhood range, replace the outlier with its neighborhood mean, and update the outlier value in the data set to the calculated mean.

5. The universal fusion method of multi-frequency polarimetric SAR images based on scattering mechanism according to claim 1 is characterized in that The specific steps are as follows: Step 41: Extract the corresponding Sinclair scattering matrix for each pixel; Step 42: Calculate the Frobenius norm of each preprocessed scattering matrix, and use the calculated Frobenius norm to normalize the scattering matrix.

6. The universal fusion method of multi-frequency polarimetric SAR images based on scattering mechanism according to claim 5 is characterized in that The Sinclair scattering matrix is ​​a 2×2 complex matrix with the following form: in 、 and denote the backscattering coefficients of HH, VV and HV polarization channels respectively; The normalization formula is as follows: in is the normalized scattering matrix.

7. The universal fusion method of multi-frequency polarimetric SAR images based on scattering mechanism according to claim 1 is characterized in that The specific steps of step six are as follows: Step 61: Extract the Pauli vectors of each scattering matrix separately: in 、 and denote the backscattering coefficients of HH, VV and HV polarization channels respectively; Step 62: After obtaining the Pauli vectors, first calculate the inner product of the polarization vectors, then perform a modular square operation on the inner product to ensure that the inner product result is non-negative, and then calculate the square of the 2-norm of each vector separately; Step 63: Perform a ratio operation on the calculation result of step 62 to obtain the normalized polarization similarity.

8. The universal fusion method of multi-frequency polarimetric SAR images based on scattering mechanism according to claim 1 is characterized in that The specific steps of step seven are as follows: Step 71: For each multi-frequency data combination, set the initial weight of the standard scattering matrix as the starting point of the SQP algorithm; Step 72: Based on step 71, enter the iteration phase. In each iteration, construct and solve an approximate quadratic programming subproblem, and then update the weight vector based on the solution. The quadratic programming subproblem is as follows: in is the increment of the weight vector, is the approximate value of the Hessian matrix of the objective function at the kth iteration, is the gradient vector at the kth iteration; Step 73: Update the weight vector according to the solution of the subproblem and check whether the convergence condition is met. If so, terminate the algorithm; if not, continue to the next iteration until the optimal weight configuration is found.

9. The universal fusion method of multi-frequency polarimetric SAR images based on scattering mechanism according to claim 1 is characterized in that The specific steps of step eight are as follows: Step 81: Evaluate the similarity of all multi-frequency data combinations and record the polarization similarity of each combination; Step 82: After obtaining the similarity results of all multi-frequency combinations, perform summary analysis and use data comparison method to sort the similarity values ​​of each combination, find the combination with the largest similarity value, and regard its corresponding multi-frequency data combination as the best configuration.

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