Junfei Shi

Junfei Shi, Mengmeng Nie, Weisi Lin et al.

Deep learning is an effective end-to-end method for Polarimetric Synthetic Aperture Radar(PolSAR) image classification, but it lacks the guidance of related mathematical principle and is essentially a black-box model. In addition, existing deep models learn features in Euclidean space, where PolSAR complex matrix is commonly converted into a complex-valued vector as the network input, distorting matrix structure and channel relationship. However, the complex covariance matrix is Hermitian positive definite (HPD), and resides on a Riemannian manifold instead of a Euclidean one. Existing methods cannot measure the geometric distance of HPD matrices and easily cause some misclassifications due to inappropriate Euclidean measures. To address these issues, we propose a novel Riemannian Sparse Representation Learning Network (SRSR CNN) for PolSAR images. Firstly, a superpixel-based Riemannian Sparse Representation (SRSR) model is designed to learn the sparse features with Riemannian metric. Then, the optimization procedure of the SRSR model is inferred and further unfolded into an SRSRnet, which can automatically learn the sparse coefficients and dictionary atoms. Furthermore, to learn contextual high-level features, a CNN-enhanced module is added to improve classification performance. The proposed network is a Sparse Representation (SR) guided deep learning model, which can directly utilize the covariance matrix as the network input, and utilize Riemannian metric to learn geometric structure and sparse features of complex matrices in Riemannian space. Experiments on three real PolSAR datasets demonstrate that the proposed method surpasses state-of-the-art techniques in ensuring accurate edge details and correct region homogeneity for classification.

Junfei Shi, Wei Wang, Haiyan Jin et al.

Recently, deep learning methods have achieved superior performance for Polarimetric Synthetic Aperture Radar(PolSAR) image classification. Existing deep learning methods learn PolSAR data by converting the covariance matrix into a feature vector or complex-valued vector as the input. However, all these methods cannot learn the structure of complex matrix directly and destroy the channel correlation. To learn geometric structure of complex matrix, we propose a Riemannian complex matrix convolution network for PolSAR image classification in Riemannian space for the first time, which directly utilizes the complex matrix as the network input and defines the Riemannian operations to learn complex matrix's features. The proposed Riemannian complex matrix convolution network considers PolSAR complex matrix endowed in Riemannian manifold, and defines a series of new Riemannian convolution, ReLu and LogEig operations in Riemannian space, which breaks through the Euclidean constraint of conventional networks. Then, a CNN module is appended to enhance contextual Riemannian features. Besides, a fast kernel learning method is developed for the proposed method to learn class-specific features and reduce the computation time effectively. Experiments are conducted on three sets of real PolSAR data with different bands and sensors. Experiments results demonstrates the proposed method can obtain superior performance than the state-of-the-art methods.

Junfei Shi, Haojia Zhang, Haiyan Jin et al.

Polarimetric Synthetic Aperture Radar (PolSAR) covariance matrices and their extracted multi-features - such as scattering angle, entropy, texture, and boundary descriptors - provide complementary and physically interpretable information for image classification. Traditional fusion strategies typically concatenate these features or employ deep learning networks to combine them. However, the covariance matrices and multi-features, as two complementary views, lie on different manifolds with distinct geometric structures. Existing fusion methods also overlook the varying importance of different views and ignore uncertainty, often leading to unreliable predictions. To address these issues, we propose a Multiview Manifold Evidential Fusion (MMEFnet) method to effectively fuse these two views. It gives a new framework to integrate PolSAR manifold learning and evidence fusion into a unified architecture. Specifically, covariance matrices are represented on the Hermitian Positive Definite (HPD) manifold, while multi-features are modeled on the Grassmann manifold. Two different kernel metric learning networks are constructed to learn their manifold representations. Subsequently, a trusted multiview evidence fusion, replacing the conventional softmax classifier, estimates belief mass and quantifies the uncertainty of each view from the learned deep features. Finally, a Dempster-Shafer theory-based fusion strategy combines evidence, enabling a more reliable and interpretable classification. Extensive experiments on three real-world PolSAR datasets demonstrate that the proposed method consistently outperforms existing approaches in accuracy, robustness, and interpretability.

Junfei Shi, Yu Cheng, Haiyan Jin et al.

Diffusion models have demonstrated exceptional performance across various domains due to their ability to model and generate complicated data distributions. However, when applied to PolSAR data, traditional real-valued diffusion models face challenges in capturing complex-valued phase information.Moreover, these models often struggle to preserve fine structural details. To address these limitations, we leverage the Contourlet transform, which provides rich multiscale and multidirectional representations well-suited for PolSAR imagery. We propose a structural knowledge-guided complex diffusion model for PolSAR image classification in the Contourlet domain. Specifically, the complex Contourlet transform is first applied to decompose the data into low- and high-frequency subbands, enabling the extraction of statistical and boundary features. A knowledge-guided complex diffusion network is then designed to model the statistical properties of the low-frequency components. During the process, structural information from high-frequency coefficients is utilized to guide the diffusion process, improving edge preservation. Furthermore, multiscale and multidirectional high-frequency features are jointly learned to further boost classification accuracy. Experimental results on three real-world PolSAR datasets demonstrate that our approach surpasses state-of-the-art methods, particularly in preserving edge details and maintaining region homogeneity in complex terrain.

Junfei Shi, Yuke Li, Mengmeng Nie et al.

Deep learning has been extensively utilized for PolSAR image classification. However, most existing methods transform the polarimetric covariance matrix into a real- or complex-valued vector to comply with standard deep learning frameworks in Euclidean space. This approach overlooks the inherent structure of the covariance matrix, which is a complex Hermitian positive definite (HPD) matrix residing in the Riemannian manifold. Vectorization disrupts the matrix structure and misrepresents its geometric properties. To mitigate this drawback, we propose HPDNet, a novel framework that directly processes HPD matrices on the Riemannian manifold. The HPDnet fully considers the complex phase information by decomposing a complex HPD matrix into the real- and imaginarymatrices. The proposed HPDnet consists of several HPD mapping layers and rectifying layers, which can preserve the geometric structure of the data and transform them into a more separable manifold representation. Subsequently, a complex LogEig layer is developed to project the manifold data into a tangent space, ensuring that conventional Euclidean-based deep learning networks can be applied to further extract contextual features for classification. Furthermore, to optimize computational efficiency, we design a fast eigenvalue decomposition method for parallelized matrix processing. Experiments conducted on three real-world PolSAR datasets demonstrate that the proposed method outperforms state-of-the-art approaches, especially in heterogeneous regions.

Junfei Shi, Haiyan Jin

As a representation learning method, nearest regularized subspace(NRS) algorithm is an effective tool to obtain both accuracy and speed for PolSAR image classification. However, existing NRS methods use the polarimetric feature vector but the PolSAR original covariance matrix(known as Hermitian positive definite(HPD)matrix) as the input. Without considering the matrix structure, existing NRS-based methods cannot learn correlation among channels. How to utilize the original covariance matrix to NRS method is a key problem. To address this limit, a Riemannian NRS method is proposed, which consider the HPD matrices endow in the Riemannian space. Firstly, to utilize the PolSAR original data, a Riemannian NRS method(RNRS) is proposed by constructing HPD dictionary and HPD distance metric. Secondly, a new Tikhonov regularization term is designed to reduce the differences within the same class. Finally, the optimal method is developed and the first-order derivation is inferred. During the experimental test, only T matrix is used in the proposed method, while multiple of features are utilized for compared methods. Experimental results demonstrate the proposed method can outperform the state-of-art algorithms even using less features.

Fang Liu, Junfei Shi, Licheng Jiao et al.

For polarimetric SAR (PolSAR) image classification, it is a challenge to classify the aggregated terrain types, such as the urban area, into semantic homogenous regions due to sharp bright-dark variations in intensity. The aggregated terrain type is formulated by the similar ground objects aggregated together. In this paper, a polarimetric hierarchical semantic model (PHSM) is firstly proposed to overcome this disadvantage based on the constructions of a primal-level and a middle-level semantic. The primal-level semantic is a polarimetric sketch map which consists of sketch segments as the sparse representation of a PolSAR image. The middle-level semantic is a region map which can extract semantic homogenous regions from the sketch map by exploiting the topological structure of sketch segments. Mapping the region map to the PolSAR image, a complex PolSAR scene is partitioned into aggregated, structural and homogenous pixel-level subspaces with the characteristics of relatively coherent terrain types in each subspace. Then, according to the characteristics of three subspaces above, three specific methods are adopted, and furthermore polarimetric information is exploited to improve the segmentation result. Experimental results on PolSAR data sets with different bands and sensors demonstrate that the proposed method is superior to the state-of-the-art methods in region homogeneity and edge preservation for terrain classification.