Multiband SAR (Synthetic Aperture Radar) inter-spectrum feature extraction method for ground feature classification
By constructing inter-spectral co-occurrence tensors and combining them with local non-negative tensor decomposition, compact discriminative features of multi-band SAR images are extracted, solving the problem of unmined inter-band features in existing technologies and improving the accuracy and robustness of ground cover classification.
Patent Information
- Application Number
- CN202511275781.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-08
- Publication Date
- 2025-11-28
AI Technical Summary
Existing multi-band SAR image feature extraction methods have failed to effectively mine the inherent spectral features between bands, resulting in insufficient accuracy and robustness in ground cover classification.
We employ a method based on the construction of inter-spectral co-occurrence features and non-negative tensor decomposition. By constructing inter-spectral co-occurrence tensors and combining them with the idea of local preservation for dimensionality reduction, we can extract compact and discriminative multi-band SAR inter-spectral features.
It improves the accuracy and robustness of land cover classification in multi-band SAR images, effectively overcomes the limitations of feature stitching in traditional methods, enhances adaptability to multi-band registration errors, and is applicable to land classification, target detection, and recognition tasks of multi-band SAR.
Smart Images
Figure CN121033438A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of SAR image feature extraction, and relates to a multi-band SAR interspectral feature extraction method for ground cover classification. Background Technology
[0002] Synthetic Aperture Radar (SAR) has wide applications in both civilian and military fields due to its all-weather, all-day imaging capabilities. Multiband SAR, by transmitting signals with different center frequencies, can acquire richer information on the scattering characteristics of ground targets, thereby improving target perception accuracy. However, the effective utilization of multiband SAR data depends on reasonable feature extraction methods. How to fully mine multiband information and construct robust feature representations is the key to multiband SAR image processing applications.
[0003] Traditional multiband SAR feature extraction methods typically involve directly stitching together features extracted from single-band images along the band dimension to obtain multiband features. Commonly used SAR feature extraction methods include gray-level co-occurrence matrix (GLCM) for texture features, Gabor filters for structural features, local binary modes for local pattern features, and polarization decomposition for scattering characteristics. Directly stitching these features along the multiband dimension reveals the variations of each feature across different bands, reflecting the interspectral information of ground objects to some extent. This is a computationally simple and easy-to-implement multiband SAR feature extraction method. However, this method merely stitches together features calculated independently in each band, ignoring interspectral correlations and failing to uncover deeper interspectral features.
[0004] In recent years, tensor representation-based methods have been increasingly introduced into the field of multi-band SAR image feature extraction. These methods characterize a large number of features in multi-band SAR images using tensor forms containing high-dimensional, high-order data, and then remove redundant information through tensor decomposition or subspace projection methods to achieve further feature mining. Most tensor-based feature extraction methods focus on how to extract compact features from high-dimensional, multi-order feature tensors. These methods can be divided into three categories: subspace projection methods, such as multilinear principal component analysis, local preservative projection, and linear discriminant analysis, map the original tensor data to a low-dimensional subspace using a projection matrix; tensor decomposition methods, such as Tucker decomposition and CP decomposition, decompose feature tensors into combinations of low-rank basis tensors, suitable for tensor features with sparse data structures; and deep learning methods are emerging feature mining methods in recent years, which automatically learn compact features using large amounts of data by constructing neural networks. While these methods can extract compact features from large amounts of feature data, their discriminative information is still limited by the construction method of the original high-dimensional tensor—existing methods stack polarization, texture, and structural features extracted from images of each band in the neighborhood and band dimensions to form a high-order tensor. Although this tensor representation contains a large amount of feature data, its essence is still a simple stacking of single-band spatial dimension features, failing to extract the inherent inter-spectral features determined by the backscattering characteristics of ground objects with varying frequencies. Therefore, for multi-band SAR image applications, especially for ground object classification, it is necessary to conduct research on multi-band inter-spectral feature extraction methods targeting the spectral dimension constituted by transmission frequencies. Summary of the Invention
[0005] The purpose of this invention is to overcome the problems of existing multi-band SAR image feature extraction methods, which simply stitch together single-band features and lack the ability to mine spectral spatial features composed of multiple bands. This invention proposes a multi-band SAR inter-spectral feature extraction method based on inter-spectral co-occurrence feature construction and non-negative tensor decomposition (NTF) to improve the accuracy and robustness of ground cover classification. This method constructs a high-dimensional inter-spectral feature tensor by utilizing the statistical properties of pixel vectors composed of salient points in multi-band SAR images. Then, it performs dimensionality reduction through NTF, incorporating locality-preserving principles, to construct highly discriminative and compact inter-spectral features.
[0006] A method for extracting interspectral features of multi-band SAR for land cover classification, specifically including the following steps:
[0007] Step 1: For the given registered... For each pixel in a SAR image across all bands, a set of significant pixels is constructed in its neighborhood space using the Otsu threshold.
[0008] The specific process is as follows:
[0009] First, use a size of Sliding windows in multi-band images Slide the slider on top to construct the pixels to be classified. Neighborhood image patch .in and Represents the horizontal and vertical coordinates of the image plane. This indicates the center frequency of the acquisition system corresponding to this image.
[0010] Secondly, the saliency threshold for each band is selected using the Ostu method. For each image patch in a band, all possible grayscale thresholds are traversed within the image's grayscale range. Pixels greater than the current threshold are classified as salient target pixels, and pixels less than the threshold are classified as background pixels. The mean and variance of the pixels in the two categories are calculated separately, and then the inter-class variance is calculated. The threshold that maximizes the inter-class variance is selected as the saliency threshold for that band.
[0011] Next, the proportion of target pixels corresponding to the saliency threshold of each band is defined as the saliency proportion coefficient. The saliency proportion coefficient of a multi-band image patch is the mean of the saliency proportion coefficients of each band, denoted as . .
[0012] Finally, the pixel values of the image blocks in each band are arranged from largest to smallest, and the first pixel of each band is selected. The proportion of pixels as the salient pixel set:
[0013]
[0014] in ,and .
[0015] Step 2: Extract the Spectral Co-occurrence Tensor (SCT) features of the pixels to be detected using the significant pixel set, and form a feature sample set.
[0016] The specific steps are as follows:
[0017] First, initialize the interspectral co-occurrence tensor to Zero-order tensors.
[0018] For those with A multi-band SAR image of the nth band, if the nth band The gray levels of the image in each band are , No. The interspectral co-occurrence tensor of each pixel to be detected is represented as Initialized to Zero-order tensors.
[0019] Secondly, salient pixels from each band are selected sequentially from the salient pixel set to form the interspectral salient pixel vector as follows:
[0020]
[0021] Calculate the distance coefficient of the spectral salient pixel vector based on the position of the selected pixel in each band image:
[0022]
[0023] Add the distance coefficient to The corresponding position, which is composed of The grayscale values of pixels in each band determine the grayscale value.
[0024]
[0025] So
[0026]
[0027] Next, iterate through all The combination, repeated and The final interspectral co-occurrence tensor of the pixel to be detected is obtained. .
[0028] Finally, spectral co-occurrence tensor features are extracted from all pixels to be detected to construct a feature sample set. ,in Let be the number of samples, and , .
[0029] Step 3: Apply local preserving nonnegative tensor decomposition to the above feature sample set. Construct a low-dimensional feature optimization objective function.
[0030] The specific steps are as follows:
[0031] First, the feature sample set in the original space is calculated based on the idea of k-adjacency matrix. Similarity matrix .
[0032] Next, given the reduced feature dimension as Construct a feature extraction objective function based on local nonnegative tensor decomposition:
[0033]
[0034] The above optimization function is based on the idea of CP decomposition and is aimed at... Factor matrices of all orders The optimization, among which These are the sparsity coefficients of the original feature space. It is a set of bases for the original feature space. express One line in the middle. It is the original feature set The model unfolds, Is it except Khatri-Rao product of all external factor matrices.
[0035] Step four: Iteratively solve the low-dimensional feature optimization objective function using the gradient descent method to extract the final low-dimensional interspectral feature set.
[0036] Optimize according to the following multiplicative iterative formula :
[0037]
[0038] in , .
[0039] Iterate until the maximum number of iterations is reached, and the final multi-band SAR inter-spectral feature set is: , .
[0040] Step 5: Based on the obtained multi-band SAR inter-spectral feature set, classify the ground features to be identified in the multi-band SAR image to obtain the classification results.
[0041] The advantages of this invention are:
[0042] (1) Practicality. The method proposed in this invention can realize the extraction of inter-spectral features of multi-band SAR. After extracting high-dimensional features containing multi-band characteristics in the spectral space, compact and discriminative inter-spectral features are obtained through a dimensionality reduction process.
[0043] (2) Targeted. This invention is the first to propose the direct mining of pixel distribution characteristics in the frequency dimension of multi-band SAR using inter-spectral co-occurrence tensors, overcoming the limitations of traditional methods that rely on single-band feature stitching.
[0044] (3) Robustness: The present invention uses a weighted strategy of significant pixel position of each band to accommodate multi-band registration error and improve the adaptability of features to spatial offset.
[0045] (4) Universality: The multi-band SAR feature extraction method proposed in this invention can not only be used for multi-band SAR land classification tasks in the embodiments, but can also be well transferred to other multi-band SAR target detection, identification and tracking tasks. Attached Figure Description
[0046] Figure 1 is an overall flowchart of a multi-band SAR inter-spectral feature extraction method according to the present invention;
[0047] Figure 2 is a three-band real airborne SAR image of the area to be identified in an embodiment of the present invention;
[0048] Figure 3 is a visualization representation of the interspectral co-occurrence tensor features extracted from different land cover categories in multi-band SAR images in an embodiment of the present invention; Figure 3(a) is a visualization representation of the features extracted by the gray-level co-occurrence matrix (GLCM) stitching method for comparison; Figure 3(b) is a visualization representation of the features extracted by the proposed method.
[0049] Figure 4 shows the classification results after feature extraction using the proposed method and the comparison method in the embodiments of the present invention; Figure 4(a) is the ground truth image of the ground category, Figure 4(b) is the classification result of direct pixel combination, Figure 4(c) is the classification result of direct GLCM stitching, and Figure 4(d) is the classification result of the proposed method. Detailed Implementation
[0050] The present invention will now be described in further detail with reference to the accompanying drawings and specific examples.
[0051] To address the problems of existing multi-band SAR feature extraction methods, such as neglecting inter-spectral information and high feature stitching redundancy, this invention proposes a multi-band SAR feature extraction method based on inter-spectral co-occurrence structures. This method selects significant pixels from each band in the neighborhood space of the pixels to be classified, constructs inter-spectral significant pixel vectors, and fuses position weights to generate an inter-spectral co-occurrence tensor (SCT), thereby extracting gray-level statistical features in the multi-band spectral space. Based on this, the idea of local preservation is introduced into non-negative tensor decomposition to perform feature filtering and dimensionality reduction on the inter-spectral co-occurrence tensor feature set of all samples. While preserving the local structure of the original data, redundant information in the originally sparse tensor features is removed, extracting final features with strong discriminative power and compactness. Using the proposed inter-spectral co-occurrence tensor feature extraction method, features are extracted from multi-band spaceborne SAR images and applied to ground cover classification tasks. The following details the implementation process of the proposed inter-spectral co-occurrence tensor-based feature extraction method in specific applications.
[0052] A method for extracting interspectral features of multi-band SAR for land cover classification, the implementation process of which is shown in Figure 1, specifically includes the following steps:
[0053] Step 1: For the given registered... For each pixel in a SAR image across all bands, a set of significant pixels is constructed in its neighborhood space using the Otsu threshold.
[0054] The specific process of constructing a set of significant pixels is as follows:
[0055] Step 101, use a size of Sliding windows in multi-band images Slide the slider on top to construct the pixels to be classified. Neighborhood image patch .in and Represents the horizontal and vertical coordinates of the image plane. This indicates the center frequency of the acquisition system corresponding to this image.
[0056] Step 102, for each band of image patch Calculate the probability distribution of the gray-level histogram. ,in This indicates the grayscale level.
[0057] Step 103: Iterate through the possible grayscale thresholds for each band of image patch. , will be greater than this threshold Pixels smaller than this threshold are classified as significant target pixels. Each pixel is assigned to the background pixel, and the proportion coefficient of pixels in the two categories is calculated separately.
[0058]
[0059] Calculate the pixel mean of the image patch in this band. And the average of target pixels and background pixels. , and variance , Further calculate the inter-class variance
[0060]
[0061] Step 103, select to Maximum threshold corresponding As the saliency scaling factor for this band, the overall saliency scaling factor of the image patch. The mean of the significance coefficients for each band:
[0062]
[0063] Step 104: Arrange the pixels of each band image block from largest to smallest, and select the first... The proportion of pixels as the salient pixel set:
[0064]
[0065] in ,and .
[0066] Step 2: Extract the spectral co-occurrence tensor features of the pixels to be detected using the salient pixel set, and form a feature sample set.
[0067] The specific steps are as follows:
[0068] Step 201: Initialize the interspectral co-occurrence tensor for each pixel to be classified. For pixels with... A multi-band SAR image of the nth band, if the nth band The gray levels of the image in each band are , No. The interspectral co-occurrence tensor of each pixel to be detected can be expressed as: Initialized to Zero-order tensors.
[0069] Step 202, from the first The salient pixel vector is composed of salient pixels from each band selected sequentially from the salient pixel set of the neighborhood image block of the pixel to be detected, as follows:
[0070]
[0071] in Indicates for the first The first pixel to be detected The first band of the salient pixel set One significant pixel, . The subscript indicates the significant pixel index combination for each band. Each band There are 1 significant pixels, totaling 100 pixels. A significant pixel vector.
[0072] Calculate the distance coefficient of the spectral salient pixel vector based on the position of the selected pixel in each band image:
[0073]
[0074] Add the distance coefficient to The corresponding position, which is composed of The grayscale values of pixels in each band determine the grayscale value.
[0075]
[0076] So
[0077]
[0078] Step 203: Traverse all By combining these elements and repeating step 202, the final interspectral co-occurrence tensor of the pixel to be detected is obtained. .
[0079] Step 204: For all For each pixel to be detected, steps 202 and 203 are performed to construct a spectral co-occurrence tensor feature sample set. ,in and , .
[0080] Step 3: Based on the locally preserving nonnegative tensor decomposition, analyze the spectral co-occurrence tensor feature sample set. Construct a low-dimensional feature optimization objective function.
[0081] The specific steps are as follows:
[0082] First, calculate the feature sample set in the original space. Similarity matrix
[0083]
[0084] in Indicates the first Inter-spectral co-occurrence tensor of each pixel to be detected express belong k-neighborhood, The Gaussian kernel bandwidth represents the control of similarity smoothness.
[0085] Then, given the reduced feature dimension as Construct a feature extraction objective function based on local nonnegative tensor decomposition:
[0086]
[0087] in Denotes the square of the Frobenius norm. This represents the weighting coefficient of the locally preserved term.
[0088] The above optimization function is based on the idea of CP decomposition (CANDECOMP / PARAFAC decomposition) and is aimed at... Factor matrices of all orders The optimization, among which These are the sparsity coefficients of the original feature space. It is a set of bases for the original feature space. express One line in the middle. It is the original feature set The model unfolds, Is it except The Khatri-Rao product of all external factor matrices, i.e.
[0089]
[0090] Step four: Iteratively solve the low-dimensional feature optimization objective function using the gradient descent method to extract the final low-dimensional interspectral feature set.
[0091] The specific steps are as follows:
[0092] Step 401: Initialize factor matrices of each order Given a random matrix and local preservation coefficients. .
[0093] Step 402: Factor the first-order matrix Optimize, will Performing a 1-mode expansion yields Except Taking the Khatri-Rao product of all factor matrices outside the matrix, we get... According to the following formula: Update:
[0094]
[0095] in , .
[0096] Step 403: Factor each of the other order matrices one by one Optimization, too conduct The module is expanded to obtain and except Taking the Khatri-Rao product of all factor matrices outside the matrix, we get... According to the following formula: Update:
[0097] (20)
[0098] Step 404: Repeat steps 402 and 403 until the maximum number of iterations is reached.
[0099] Step 405: The final multi-band SAR inter-spectral feature set is , .
[0100] Step 5: Based on the obtained multi-band SAR inter-spectral feature set, classify the ground features to be identified in the multi-band SAR image to obtain the classification results.
[0101] Experimental results
[0102] To demonstrate the effectiveness of this invention, this embodiment conducts experimental verification for a multi-band SAR ground feature classification task.
[0103] The S, C, and Ka bands of the Sheyang area from the high-resolution airborne multidimensional SAR land cover classification dataset were selected, and the HH polarization multiband SAR images were used as shown in Figure 2. The area contains five land cover categories: water, bare land, roads, residential areas, and planted areas.
[0104] The parameters used in the feature extraction process are shown in Table 1:
[0105] sheet Parameter settings of this invention
[0106] Parameter name numerical values Sliding window size 20*20 Gray levels in each band 10 Dimensionality after dimensionality reduction 100 150 100 Maximum number of iterations 1000
[0107] The multi-band SAR image features extracted using the method of this invention are visually compared with those extracted by the Gray-Level Co-occurrence Matrix (GLCM) feature concatenation method, the most commonly used texture feature extraction method in multi-band SAR. For a three-band SAR image, the constructed inter-spectral co-occurrence tensor feature is a third-order tensor, with the three dimensions representing the gray levels of the three bands. The GLCM features used for comparison also contain three dimensions: statistical feature dimensions (mean, variance, contrast, heterogeneity, homogeneity, energy, contrast, and entropy, a total of 8), offset vector dimensions (4 in total), and band dimensions (3 in total). The features extracted by these two methods for different land categories are visualized, as shown in Figure 3. For the sake of consistency in feature display, the features proposed by both methods are displayed in... The data is displayed in a three-dimensional space. As can be seen from Figure 3(a), the features based on GLCM always occupy the entirety of its constituent elements in different land categories. In the spatial representation, the differences between categories are only reflected in the feature values. However, Figure 3(b) shows that the third-order tensor features obtained by the method proposed in this invention, in addition to the numerical differences in the feature data, also exhibit different shapes and positions of the non-zero data in each category, which provides a basis for subsequent high-precision classification.
[0108] After extracting features using various methods, supervised classification was performed using the K-Nearest Neighbor (KNN) classifier. The classification results are shown in Figure 4, where Figure 4(a) is the ground truth image for the ground category. Figure 4(b) shows the worst visual effect when classification is performed by directly combining pixels, due to limited information utilization and the influence of registration errors, resulting in a large amount of salt-and-pepper noise. Figure 4(c) shows the classification result using the GLCM feature concatenation method. Because it utilizes spatial neighborhood information and extracts spatial texture features for each band, the classification effect is better than Figure 4(b). However, this method uses direct feature concatenation in the band dimension and does not mine inter-spectral information between bands, thus still resulting in a large amount of noise and misclassified blocks. The classification result of the proposed method is shown in Figure 4(d). Most of the salt-and-pepper noise is eliminated, the road area is more continuous, the residential and planted areas are cleaner, and the boundaries are clearer, resulting in a better overall visual effect compared to Figure 4(b) and Figure 4(c).
[0109] To more intuitively verify the effectiveness of the proposed method, the classification results were quantitatively evaluated, as shown in Table 2. In terms of classification accuracy, the proposed method achieved the highest overall accuracy (OA=85.84%) and Kappa coefficient (74.78%), representing improvements of 30.54% and 7.40% respectively compared to pixel stitching and GLCM stitching methods, indicating stronger overall classification ability. Specifically, the proposed method performed particularly well for easily confused features. For example, the road classification accuracy reached 71.46% (an improvement of 14.41% compared to GLCM stitching), and the bare land classification accuracy reached 73.60% (an improvement of 8.59% compared to GLCM stitching). Furthermore, the classification accuracy for water areas (68.56%), residential areas (89.57%), and planted areas (91.90%) was also optimal, demonstrating that the method effectively extracts interspectral information from multi-band SAR images, improving the ability to distinguish different features, and is particularly suitable for fine-grained feature classification tasks in multi-band SAR images.
[0110] sheet Evaluation of classification results of each feature extraction method (%)
[0111] Pixel stitching GLCM splicing The proposed method waters 38.51 67.87 68.56 bare land 24.16 65.01 73.60 the way 32.39 57.05 71.46 Residential 48.59 76.15 89.57 Planting area 72.46 87.03 91.90 OA 55.30 78.44 85.84 AA 37.41 63.30 70.74 Kappa 32.96 67.36 74.78
Claims
1. A method for extracting interspectral features of multi-band SAR for land cover classification, characterized in that, Includes the following steps: Step 1, for the given registered For each pixel in a SAR image of each band, a set of significant pixels is constructed in its neighborhood space using the Otsu threshold. Step 2: Extract the interspectral co-occurrence tensor features of the pixels to be detected using the set of significant pixels, and form a feature sample set; The specific steps are as follows: Step 201, initialize the interspectral co-occurrence tensor to Zero-order tensors; For those with A multi-band SAR image of the nth band, if the nth band The gray levels of the image in each band are , No. The interspectral co-occurrence tensor of each pixel to be detected is represented as Initialized to Zero-order tensors; Step 202: Select salient pixels from each band sequentially from the salient pixel set to form the interspectral salient pixel vector as follows: （1） in, Indicates for the first The first pixel to be detected The first _th band significant pixel set One significant pixel, ; The subscript indicates the significant pixel index combination for each band. Each band There are 1 significant pixels, totaling 100 pixels. One significant pixel vector; Calculate the distance coefficient of the spectral salient pixel vector based on the position of the selected pixel in each band image: （2） This distance coefficient is superimposed onto the corresponding position of the interspectral co-occurrence tensor, which is composed of... The grayscale values of pixels in each band are determined by the grayscale values of the pixels. （3） So （4） Step 203, iterate through all By combining these elements and repeating step 202, the final interspectral co-occurrence tensor of the pixel to be detected is obtained. ; Step 204: Extract interspectral co-occurrence tensor features from all pixels to be detected and construct a feature sample set. ,in Let be the number of samples, and , ; Step 3: Apply local preserving nonnegative tensor decomposition to the feature sample set. Construct a low-dimensional feature optimization objective function; The specific steps are as follows: First, the feature sample set in the original space is calculated based on the idea of k-adjacency matrix. Similarity matrix ; Then, given the reduced feature dimension as Construct a feature extraction objective function based on local nonnegative tensor decomposition: （5） The above optimization function is based on the idea of CP decomposition and is aimed at... Factor matrices of all orders Optimization, among which These are the sparsity coefficients of the original feature space. It is a set of bases for the original feature space. express One line in the middle; It is the original feature set The model unfolds, Is it except Khatri-Rao product of all external factor matrices; Step 4: Iteratively solve the low-dimensional feature optimization objective function using the gradient descent method to extract the final low-dimensional interspectral feature set; Step 5: Based on the obtained multi-band SAR inter-spectral feature set, classify the ground features to be identified in the multi-band SAR image to obtain the classification results.
2. The method for extracting interspectral features of multi-band SAR for land cover classification according to claim 1, characterized in that, The process of constructing a set of significant pixels is as follows: First, use a size of Sliding windows in multi-band images Slide the slider on top to construct the pixels to be classified. Neighborhood image patch ;in and Represents the horizontal and vertical coordinates of the image plane. This indicates the center frequency of the acquisition system corresponding to this image; Then, the saliency threshold for each band is selected using the Ostu method. The proportion of target pixels corresponding to the saliency threshold for each band is defined as the saliency ratio coefficient. The saliency ratio coefficient of a multi-band image patch is the mean of the saliency ratio coefficients of each band, denoted as . ; Finally, the pixel values of the image blocks in each band are arranged from largest to smallest, and the first pixel of each band is selected. The proportion of pixels as the salient pixel set: （6） in ,and .
3. The method for extracting interspectral features of multi-band SAR for land cover classification according to claim 2, characterized in that, The specific process of selecting the significance threshold for each band using the Ostu method is as follows: For each image patch in a band, all possible grayscale thresholds are traversed within the image grayscale range. Pixels greater than the current threshold are classified as salient target pixels, and pixels less than the threshold are classified as background pixels. The mean and variance of the pixels in the two categories are calculated separately, and then the inter-class variance is calculated. The threshold that maximizes the inter-class variance is selected as the saliency threshold for that band.
4. The method for extracting interspectral features of multi-band SAR for land cover classification according to claim 1, characterized in that, The similarity matrix of the feature sample set is: （7） in Indicates the first Inter-spectral co-occurrence tensor of each pixel to be detected express belong k-neighborhood, The Gaussian kernel bandwidth represents the control of similarity smoothness.
5. The method for extracting interspectral features of multi-band SAR for land cover classification according to claim 1, characterized in that, The specific steps for iteratively solving the low-dimensional feature optimization objective function using the gradient descent method are as follows: Step 401: Initialize factor matrices of each order Given a random matrix and local preservation coefficients. ; Step 402: Factor the first-order matrix Optimize, will Performing a 1-mode expansion yields ; except Taking the Khatri-Rao product of all factor matrices outside the matrix, we get... ; Perform according to the following formula Update: （8） in , ; Step 403: Factor each of the other order matrices one by one Optimization, too conduct The module is expanded to obtain and except Taking the Khatri-Rao product of all factor matrices outside the matrix, we get... ; Perform according to the following formula Update: （9） Step 404: Repeat steps 402 and 403 until the maximum number of iterations is reached; Step 405: The final multi-band SAR inter-spectral feature set is , .