A linearly convergent method for solving high-order proximal operator

Recently, various high-order methods have been developed to solve the convex optimization problem. The auxiliary problem of these methods shares the general form that is the same as the high-order proximal operator proposed by Nesterov. In this paper, we present a linearly convergent method to solve the high-order proximal operator based on the classical proximal operator. In addition, some experiments are performed to demonstrate the performance of the proposed method

high-order proximal point algorithm for the monotone variational inequality problem and its application

The proximal point algorithm (PPA) has been developed to solve the monotone variational inequality problem. It provides a theoretical foundation for some methods, such as the augmented Lagrangian method (ALM) and the alternating direction method of multipliers (ADMM). This paper generalizes the PPA to the $p$th-order ($p\geq 1$) and proves its convergence rate $O \left(1/k^{p/2}\right)$ . Additionally, the $p$th-order ALM is proposed based on the $p$th-order PPA. Some numerical experiments are presented to demonstrate the performance of the $p$th-order ALM

Pen Culture Detection Using Filter Tensor Analysis with Multi-Temporal Landsat Imagery

Aquaculture plays an important role in China’s total fisheries production nowadays, and it leads to a few problems, for example water quality degradation, which has damaging effect on the sustainable development of environment. Among the many forms of aquaculture that deteriorate the water quality, disorderly pen culture is especially severe. Pen culture began very early in Yangchenghu Lake and Taihu Lake in China and part of the pen culture still exists. Thus, it is of great significance to evaluate the distribution and area of the pen culture in the two lakes. However, the traditional method for pen culture detection is based on the factual measurement, which is labor and time consuming. At present, with the development of remote sensing technologies, some target detection algorithms for multi/hyper-spectral data have been used in the pen culture detection, but most of them are intended for the single-temporal remote sensing data. Recently, a target detection algorithm called filter tensor analysis (FTA), which is specially designed for multi-temporal remote sensing data, has been reported and has achieved better detection results compared to the traditional single-temporal methods in many cases. This paper mainly aims to investigate the pen culture in Yangchenghu Lake and Taihu Lake with FTA implemented on the multi-temporal Landsat imagery, by determining the optimal time phases combination of the Landsat data in advance. Furthermore, the suitability and superiority of FTA over Constrained Energy Minimization (CEM) in the process of pen culture detection were tested. It was observed in the experiments on the data of those two lakes that FTA can detect the pen culture much more accurately than CEM with Landsat data of selected bands and of limited number of time phases

Improving the Accuracy of the Water Surface Cover Type in the 30 m FROM-GLC Product

The finer resolution observation and monitoring of the global land cover (FROM-GLC) product makes it the first 30 m resolution global land cover product from which one can extract a global water mask. However, two major types of misclassification exist with this product due to spectral similarity and spectral mixing. Mountain and cloud shadows are often incorrectly classified as water since they both have very low reflectance, while more water pixels at the boundaries of water bodies tend to be misclassified as land. In this paper, we aim to improve the accuracy of the 30 m FROM-GLC water mask by addressing those two types of errors. For the first, we adopt an object-based method by computing the topographical feature, spectral feature, and geometrical relation with cloud for every water object in the FROM-GLC water mask, and set specific rules to determine whether a water object is misclassified. For the second, we perform a local spectral unmixing using a two-endmember linear mixing model for each pixel falling in the water-land boundary zone that is 8-neighborhood connected to water-land boundary pixels. Those pixels with big enough water fractions are determined as water. The procedure is automatic. Experimental results show that the total area of inland water has been decreased by 15.83% in the new global water mask compared with the FROM-GLC water mask. Specifically, more than 30% of the FROM-GLC water objects have been relabeled as shadows, and nearly 8% of land pixels in the water-land boundary zone have been relabeled as water, whereas, on the contrary, fewer than 2% of water pixels in the same zone have been relabeled as land. As a result, both the user’s accuracy and Kappa coefficient of the new water mask (UA = 88.39%, Kappa = 0.87) have been substantially increased compared with those of the FROM-GLC product (UA = 81.97%, Kappa = 0.81)

Target Detection Method for Water Mapping Using Landsat 8 OLI/TIRS Imagery

Extracting surface water distribution with satellite imagery has been an important subject in remote sensing. Spectral indices of water only use information from a limited number of bands, thus they may have poor performance from pixels contaminated by ice/snow, clouds, etc. The detection algorithms using information from all spectral bands, such as constrained energy minimization (CEM), could avoid this problem to some extent. However, these are mostly designed for hyperspectral imagery, and may fail when applied to multispectral data. It has been proved that adding linearly irrelevant data to original data could improve the performance of CEM. In this study, two kinds of linearly irrelevant data are added for water extraction: the spectral indices and the spectral similarity metric data. CEM is designed for targets with low-probability distribution in an image, but water bodies do not always satisfy this condition. We thereby impose a sensible coefficient for each pixel to form the weighted autocorrelation matrix. In this study, the weight is based on the orthogonal subspace projection, so this new method is named Orthogonal subspace projection Weighted CEM (OWCEM). The newly launched Landsat 8 images over two lakes, the Hala Lake in China with ice/snow distributed in the north, and the Huron Lake in North America, a lake with a very large surface area, are selected to test the accuracy and robustness of our algorithm. The Kappa coefficient and the receiver operating characteristic (ROC) curve are calculated as an accuracy evaluation standard. For both lakes, our method can greatly suppress the background (including ice/snow and clouds) and extract the complete water surface with a high accuracy (Kappa coefficient > 0.96)