## 1 Introduction  
Natural hazards, such as floods, disasters, forest fires, and landslides, occur frequently around the world and cause serious damage, and monitoring the environment consistently can reduce these adverse effects [1, 2, 3]. Vegetation mapping, especially crop mapping, is an important issue for land cover mapping, which is related to carbon storage and production forecast [4, 5, 6]. With the help of high-temporal-resolution remote sensing images, an effective way can be provided for these land surface dynamic applications extensively [7, 8, 9, 10]. Unfortunately, the temporal resolution of a satellite imaging system is roughly inversely proportional to the spatial resolution, leading to the dilemma that high-temporal resolution remote sensing images have degrading spatial resolution characteristics [11, 12, 13]. That means it is difficult to provide high-spatial and -temporal remote sensing images in large areas simultaneously. The AVHRR (Advanced Very-High-Resolution Radiometer) has a broad swath width, a short imaging period of less than a day, and about 1000 m of spatial resolution. The MODIS (Moderate Resolution Imaging Spectroradiometer) sensor in Terraand Aqua repeats daily global observation, but its highest image spatial resolution is only 250 m. The images from these high-temporal remote sensors are not suitable for monitoring land surface processes concerning to high-spatial variants [14; 15]. Biotic communities and residential buildings usually have a small size in large proportion, resulting in the difficulty of monitoring the damage and assessing the effects caused by natural hazards [16]. The cultivated land field size is often smaller than 250 m in some agricultural regions [17]. Therefore, these high-temporal images seem to lack the ability to map detailed land cover [18]. The Landsat series sensors have a 30 m spatial resolution and 16-day temporal resolution for multispectral bands, which have proven useful for land surface applications [19; 20]. However, about 35% of these Landsat images are cloud-cover-contaminated and cloud-free images can be as low as 10% in a given year [21]. According to a statistic, all Landsat images that can be used in the land cover mapping of the year 2010 on a global scale account for 41%. This shows even one available Landsat image can hardly be obtained for about 59% of the land surface in 2010. The current effective coverage and relatively low temporal resolution of Landsat images are limitations for the demands of high-frequency detailed land surface applications in large areas [14; 22]. The generation of high-temporal-resolution image series with high-spatial-resolution is one popular solution to bridge the gap [23; 24]. It utilizes the spatial detail information in high-spatial resolution images and the phonological information in high-temporal resolution images to create corresponding high-spatial-resolution image series, known as spatial and temporal data fusion [12; 25; 26; 27]. As one of the most widely adopted spatial and temporal data fusion technologies, linear spectral unmixing-based approaches are downscaling the coarse pixel value (e.g., radiance, reflectance, or derived indices) of a low-spatial-resolution image to the inner parts (e.g., endmembers, components, or land cover types) value of the pixel to improve spatial resolution [28; 29; 30; 31; 32]. The coarse pixel is regarded as the mixed pixel. Based on the linear spectral mixing model, one mixed pixel is translated into a linear equation, in which the pixel value is denoted as a known parameter and the value of several inner parts is denoted as an unknown parameter. For obvious reasons, several unknown values cannot be solved within only one equation. More pixels must be involved to make up a linear system with equation numbers that are no less than unknown value numbers.