In this paper, we propose a nonlocal total variation (NLTV)-based variational model for polarimetric synthetic aperture radar (PolSAR) data speckle reduction. This model, named WisNLTV, is obtained based on the Wishart fidelity term and the NLTV regularization defined for the complex-valued fourth-order tensor data. Since the proposed model is non-convex, an equivalent bi-convex model is obtained using the property of conjugate functions. Then, an efficient iteration algorithm is developed to solve the equivalent bi-convex model, based on the alternating minimization and the forward-backward operator splitting technique. The proposed iteration algorithm is proved to be convergent under certain conditions theoretically and numerically. Experimental results on both synthetic and real PolSAR data demonstrate that the proposed method can effectively reduce speckle noise and, meanwhile, better preserve the details and the repetitive structures such as textures and edges, and the polarimetric scattering characteristics, compared with the other methods.

Feature extraction is a very important step for polarimetric synthetic aperture radar (PolSAR) image classification. Many dimensionality reduction (DR) methods have been employed to extract features for supervised PolSAR image classification. However, these DR-based feature extraction methods only consider each single pixel independently and thus fail to take into account the spatial relationship of the neighboring pixels, so their performance may not be satisfactory. To address this issue, we introduce a novel tensor local discriminant embedding (TLDE) method for feature extraction for supervised PolSAR image classification. The proposed method combines the spatial and polarimetric information of each pixel by characterizing the pixel with the patch centered at this pixel. Then each pixel is represented as a third-order tensor, of which the first two modes indicate the spatial information of the patch (i.e. the row and the column of the patch) and the third mode denotes the polarimetric information of the patch. Based on the label information of samples and the redundance of the spatial and polarimetric information, a supervised tensor-based dimensionality reduction technique, called TLDE, is introduced to find three projections which project each pixel, that is, the third-order tensor into the low-dimensional feature. Finally, classification is completed based on the extracted features using the nearest neighbor (NN) classifier and the support vector machine (SVM) classifier. The proposed method is evaluated on two real PolSAR data sets and the simulated PolSAR data sets with various number of looks. The experimental results demonstrate that the proposed method not only improves the classification accuracy greatly, but also alleviates the influence of speckle noise on classification.

Reducing samples through convex hull vertices selection (CHVS) within each class is an important and effective method for online classification problems, since the classifier can be trained rapidly with the selected samples. However, the process of CHVS is NP-hard. In this paper, we propose a fast algorithm to select the convex hull vertices, based on the convex hull decomposition and the property of projection. In the proposed algorithm, the quadratic minimization problem of computing the distance between a point and a convex hull is converted into a linear equation problem with a low computational complexity. When the data dimension is high, an approximate, instead of exact, convex hull is allowed to be selected by setting an appropriate termination condition in order to delete more nonimportant samples. In addition, the impact of outliers is also considered, and the proposed algorithm is improved by deleting the outliers in the initial procedure. Furthermore, a dimension convention technique via the kernel trick is used to deal with nonlinearly separable problems. An upper bound is theoretically proved for the difference between the support vector machines based on the approximate convex hull vertices selected and all the training samples. Experimental results on both synthetic and real data sets show the effectiveness and validity of the proposed algorithm.