# Outlier Reconstruction of NDVI for Vegetation-Cover Dynamic Analyses
## 1 Introduction  
Global climate change has led to sea-level rise, desertification, and biodiversity losses [1, 2]. Vegetation cover is a sensitive indicator of climate change that feeds back to it by influencing energy, water, and carbon cycles [1, 3, 4]. Variability in vegetation cover represents one of the main sources of systematic changes over Earth's surface at different spatial scales [5, 6]. Such changes are especially evident in areas of concentrated terrestrial, oceanic, and atmospheric interactions, such as in estuarine coastal zones. The identification of patterns in vegetation-cover dynamics is paramount for a greater understanding of ecological responses of natural ecosystems to global climate change [3, 7]. The normalized difference vegetation index (NDVI), a near real-time vegetation index that is derived from optical remote-sensing images is often used as a proxy for vegetation-cover variance. Fine NDVI relies on clear-sky pixels in high-resolution optical remote-sensing images [8, 9]. Remote-sensing techniques with temporal continuity and large spatial coverage provide effective and comprehensive means for the accurate estimation of vegetation-cover conditions [3, 9]. The number of remote sensors capable of acquiring appropriate temporal data has increased considerably within the last few years [9, 10, 11]. With routine time-series observations, satellite remote sensing provides an unprecedented capability for estimating vegetation cover and its spatiotemporal variability at different spatial scales [3, 11, 12]. However, clouds cover roughly half of Earth [13, 14]. Persistent cloud cover poses significantchallenges for the acquisition of clear terrestrial optical remotely sensed imagery [14; 15; 16]. This occlusion produces a large number of outliers that are a persistent barrier to the operational monitoring of vegetation for many regions of the world, especially in Southeast Asia during the summer months [14; 17; 18]. Reconstructing the values of cloud-covered pixels in optical remote-sensing imagery is crucial because outliers in images can produce misleading results in environmental analyses [19; 20; 21]. Numerous algorithms were developed to reconstruct NDVI outliers for vegetation estimation over the past few years. Spatial-information-based methods are typically proposed on the basis of the spatial correlation between target pixels and neighboring clear-sky pixels [22; 23]. Other approaches are multisatellite data-fusion algorithms that combine information from multiple sensors with different spatial, spectral, and temporal resolutions to generate merged products with high spatiotemporal resolution [16; 24; 25]. Lastly, state-of-the-art machine-learning algorithms are used to reconstruct NDVI [26; 27]. Tensor stream analysis is a fundamental model in machine learning, especially in the field of computer vision and image processing [21; 28]. In recent years, tensor decomposition was verified to be effective in capturing global low-rank correlation for tensor recovery tasks. A fast low-rank tensor completion method was proposed for reducing dimensions of color images, MRI, and videos [29]. The tensor decomposition model is being paid much attention in outlier reconstruction for remote-sensing images. Low-rank tensor completion methods based on tensor singular-value decomposition and core tensor minimization were proposed [30]. However, accurately reconstructing NDVI for cloud-covered pixels is an urgent issue in widening NDVI-based applications [31; 32; 33]. To improve the accuracy of vegetation cover analyses, we explored a novel reconstruction algorithm for outliers on the basis of the Tucker decomposition method and sliding-window-based tensor stream analysis. Landsat series remote-sensing images are used in experiments to demonstrate the applicability of the proposed approach. As a case study, we successfully reconstructed NDVI in an estuary of Salween River in Southeast Asia. The proposed method is reliable and suitable for reconstructing outliers in cloud-covered pixels.