极化合成孔径雷达（Polarimetric Synthetic Aperture Radar，PolSAR）可以同时采用水平极化和垂直极化两种极化方式交替发射与接收雷达信号，这种全极化模式令其搜集到的目标信息更为全面和深入，为深入研究地物目标的复杂散射特性提供了重要的数据支撑。近年来，随着越来越多星载和机载极化SAR系统的成功研制与应用，海量的极化SAR图像资源被获取，为分析和解译极化SAR图像提供了必要的数据支持。极化SAR图像地物分类是极化SAR技术实际应用的一个重要发展方向，也是极化SAR图像解译的重要研究内容，在土地监测、城市乡镇的规划与建设、交通保养、灾害管理等多个应用领域，都展露出巨大的潜力。

在极化SAR图像分类中，图像的结构特征信息、空间邻域信息和统计分布特性等均起着至关重要的作用。然而，传统的极化SAR图像分类方法往往会忽视其背景信息以及像素之间的相关性。因此，本文以联合稀疏表示模型为理论基础，以极化SAR图像为研究对象，针对极化SAR图像高维特征导致的特征冗余和过拟合问题，展开基于联合稀疏表示的极化SAR图像特征筛选和分类研究。本文的主要研究内容如下：

1）针对如何利用极化SAR图像的空间相似性信息问题和如何减少极化SAR图像的高维特征信息带来的“维数灾难”问题，提出基于加权联合稀疏表示模型（Weighted Joint Sparse Representation, WJSR）和皮尔逊相关系数（Pearson Correlation Coefficient, PCC）的极化SAR图像特征筛选与分类算法。该算法将每个目标测试像素与其邻域像素的特征信息相结合，融合的结果体现在求解WJSR的目标函数得到的稀疏系数中，并以PCC分析实现特征筛选。本部分的主要工作包括：验证了联合稀疏表示（Joint Sparse Representation, JSR）模型融合空间信息的有效性，探讨了JSR的缺点并据此引出WJSR模型，推导了邻域加权算法和加权稀疏表示模型的目标函数；利用K-SVD字典学习算法和SOMP算法获得WJSR系数向量，在稀疏系数的基础上引入PCC分析法，筛选其中富含特征信息的向量，实现特征筛选；对筛选的稀疏系数进行局部最优重构来表征之前的特征样本，以此作为训练样本完成分类。为验证该算法的有效性，最后还在实测极化SAR图像上进行仿真。

2）针对单一分类模型、单一特征对分类贡献的局限性，提出了基于加权联合稀疏表示和决策融合的极化SAR图像分类算法。该算法利用Dempster-Shafer（D-S）证据理论进行多分类器的决策级融合，旨在融合不同特征、不同分类器的分类结果，并不同角度分析测试样本。本部分的主要工作包括：将SVM的分类结果映射为后验概率输出形式，选出部分伪标记样本，通过迭代使用SVM分类器，获得其中可信的决策构成伪训练样本集，实现扩充训练样本和得到SVM分类结果；基于D-S证据理论，推导了D-S合成规则和SVM输出、WJSR分类器输出的BPA函数构造公式；在多分类器决策融合中引入了决策可靠性分析，选出可靠性高的决策；最后根据D-S证据理论融合SVM和WJSR分类的决策结果，获得最终的图像分类结果。实验结果验证了该算法的有效性。

Polarimetric Synthetic Aperture Radar (PolSAR) can alternately transmit and receive radar signals by horizontal polarization and vertical polarization at the same time, which makes the target information collected by PolSAR more comprehensive and in-depth. It provides important data support for further study of the complex scattering characteristics of ground objects. In recent years, with the successful development and application of more and more spaceborne and airborne PolSAR systems, a large number of PolSAR image resources have been obtained, which provide necessary data support for the analysis and interpretation of PolSAR images. PolSAR image object classification is an important development direction in the practical application of PolSAR technology, and it is also an important research topic in PolSAR image interpretation. It has shown great potential in land monitoring, urban and township planning and construction, traffic maintenance, disaster management, and other application fields..

In PolSAR image classification, structure feature information, spatial neighborhood information, and image statistical distribution characteristics are all significant considerations. However, background information and pixel correlation are often overlooked by conventional PolSAR picture categorization techniques. In order to address the issues of feature redundancy and overfitting brought on by the high-dimensional features of PolSAR images, this paper investigates the feature screening and classification of PolSAR images based on the joint sparse representation model, using the PolSAR image as the research object. This paper's primary research findings and contents are summed up as follows:

Aiming at the problem of how to make use of the spatial similarity information of PolSAR images and how to reduce the "dimensional disaster" caused by the high-dimensional feature information of PolSAR images, we propose a PolSAR image feature selection and classification algorithm based on the weighted joint Sparse representation model (WJSR) and Pearson correlation coefficient (PCC). The algorithm combines the feature information of each target test pixel with that of its neighborhood pixel. The result of fusion is reflected in the sparse coefficient obtained by solving the objective function of WJSR, and the feature screening is realized by PCC analysis. The main work of this part includes: verifying the effectiveness of the joint sparse representation (JSR) model to integrate spatial information; discussing the shortcomings of JSR and drawing the WJSR model accordingly; deducing the neighborhood weighting algorithm and the objective function of the weighted sparse representation model; The K-SVD dictionary learning algorithm and SOMP algorithm are used to obtain the WJSR coefficient vector, and PCC analysis is introduced on the basis of sparse coefficients to screen the vectors rich in feature information to achieve feature screening. Finally, the selected sparse coefficients are reconstructed locally to characterize the previous feature samples, which are used as training samples to realize PolSAR image classification. Additionally, the simulation results are performed on the real polarimetric SAR images to confirm the efficacy of the suggested algorithm.

2) Aiming at the limitation of the contribution of a single classification model and a single feature, we propose a weighted PolSAR image classification algorithm based on joint sparse representation and decision fusion. This algorithm uses Dempster-Shafer (D-S) evidence theory to carry out decision-level fusion of multiple classifiers, aiming at integrating classification results of different features and different classifiers and analyzing test samples from different perspectives. The main work of this part includes: mapping SVM classification results to a posterior probability output form; selecting some pseudo-labeled samples; iteratively using the SVM classifier; obtaining the trusted decision to constitute a pseudo-training sample set; achieving the expansion of training samples; and obtaining SVM classification results. Based on the D-S evidence theory, D-S synthesis rules and BPA function construction formulas for SVM output and WJSR classification output are deduced. The decision reliability analysis is introduced into the decision fusion of multiple classifiers, and the decision with high reliability is selected. Finally, the final picture classification result is obtained by integrating the decision outcomes of SVM and WJSR, in accordance with D-S evidence theory. The suggested algorithm's usefulness is confirmed by the results of the experiments.