Satellite Image Time Series (SITS) record the continuous temporal behavior of land cover types and thus provide a new perspective for finer-grained land cover classification compared with the usual spectral and spatial information contained in a static image. In addition, SITS data is becoming more accessible in recent years due to newly launched satellites and accumulated historical data. However, the lack of labeled training samples limits the exploration of SITS data, especially with sophisticated methods. Even with a straightforward classifier, such as k-nearest neighbor, the accuracy and efficiency of the SITS similarity measure is also a pending problem. In this paper, we propose SKNN-LB-DTW, a seeded SITS classification method based on lower-bounded Dynamic Time Warping (DTW). The word “seeded” indicates that only a few labeled samples are required, and this is not only because of the lack of labeled samples but also because of our aim to explore the rich information contained in SITS, rather than letting training samples dominate the classification results. We use a combination of cascading lower bounds and early abandoning of DTW as an accurate yet efficient similarity measure for large scale tasks. The experimental results on two real SITS datasets demonstrate the utility of the proposed SKNN-LB-DTW, which could become an effective solution for SITS classification when the amount of unlabeled SITS data far exceeds the labeled data.

Satellite Image Time Series (SITS) have become more accessible in recent years and SITS analysis has attracted increasing research interest. Given that labeled SITS training samples are time and effort consuming to acquire, clustering or unsupervised analysis methods need to be developed. Similarity measure is critical for clustering, however, currently established methods represented by Dynamic Time Warping (DTW) still exhibit several issues when coping with SITS, such as pathological alignment, sensitivity to spike noise, and limitation on capacity. In this paper, we introduce a new time series similarity measure method named time adaptive optimal transport (TAOT) to the application of SITS clustering. TAOT inherits several promising properties of optimal transport for the comparing of time series. Statistical and visual results on two real SITS datasets with two different settings demonstrate that TAOT can effectively alleviate the issues of DTW and further improve the clustering accuracy. Thus, TAOT can serve as a usable tool to explore the potential of precious SITS data.

China and its local governments have made a variety of efforts in vegetation protection and restoration to ensure sustainability especially in the area threatened by severe desertification, such as Ningxia. Studying the vegetation trend and the underlying driving factors is integral to the assessment of the effect of those efforts. This paper applied Ensemble Empirical Mode Decomposition (EEMD) in combination with Mann-Kendall (M-K) significance test to detect the monotonic trend of vegetation in Ningxia based on the 16-day MODIS NDVI time series spanning the period from 2006 to 2015. The result showed that the vegetation in Ningxia exhibited an upward trend in general. The area with upward and downward trend accounted for 80.94% and 14.87%, respectively, and the area without significant change accounted for 4.46%. A rapid increase was found in the central part of the Loess Plateau, whereas a non-increase occurred in the urban expansion area. The possible major driving factors for the detected trend include the implementation of the “Grain for Green” program and urbanization.

This paper presents a Finite Element Method (FEM) framework for solving the screened Poisson equation with a Dirac delta function as the forcing term. The singularity introduced by the delta function poses challenges for standard numerical methods, particularly in higher dimensions. To address this, we employ integrated Legendre basis functions, which yield sparse and structured system matrices characterized by a Banded-Block-Banded-Arrowhead ($B^3$-Arrowhead) form. In one dimension, the resulting linear system can be solved directly. In two and three dimensions, the equation can be efficiently solved using a generalized Alternating Direction Implicit (ADI) method combined with reverse Cholesky factorization. Numerical results in 1D, 2D, and 3D confirm that the method accurately captures the localized impulse response and reproduces the expected Green’s function behavior. The proposed approach offers a robust and scalable solution framework for partial differential equations with singular source terms and has potential applications in physics, engineering, and computational science.