## 1 Introduction  
The leaf area index (LAI) is defined as the one-sided green leaf area per unit of horizontal ground area [1]. LAI is a critical input parameter for models related to ecological and environmental monitoring, crop modeling, and climate change [2]. The precise estimation of LAI is critical for its subsequent application. At present, various fields have widely used long-term global LAI products,such as Moderate Resolution Imaging Spectroradiometer (MODIS), Satellite Pour l'Observation de la Terre (SPOT/VEGFATION) and Advanced Very High Resolution Radiometer (AVHRR). However, land surfaces tend to be highly heterogeneous at coarse resolutions, and existing remote sensing LAI products fail to satisfy the need for regional research. In response to this demand, many studies have been conducted to provide long time series LAI data with high temporal and spatial resolutions [3]. Due to technological and economic restrictions, sensors with a short revisit cycle usually have a coarse spatial resolution; however, sensors with high spatial resolutions are associated with a longer time interval between acquisitions of data in the same region. The revisit cycle of Landsat Thematic Mapper (TM) data (30 m spatial resolution) is 16 days in most cases. If the area is prone to cloud or haze cover, there may be only one available data point in a month or two. Therefore, LAI products with long time series have in the past been characterized by low or medium resolutions (no better than 500 m). However, in recent years, with the continuous progress of science and technology, sensors of various types have been developed. Many satellites with high spatial resolutions and revisit cycles of less than 3 days have been launched, such as the small environment and disaster monitoring and forecasting satellite constellation HJ-1A/B, FORMOSAT-2, the WorldView satellites and Sentinel-2 [3; 4; 5; 6]. The common algorithms used to estimate LAI based on remote sensing data are empirical regressions, nonparametric regressions, radiation transfer methods and hybrid methods [6; 7]. In detail, the empirical regression approach normally uses remotely sensed imagery and terrestrial survey data acquired simultaneously to carry out multilinear regression modeling [8] or statistical models [9] to estimate LAI; most of these methods use various vegetation indices [10; 11; 12; 13] as input parameters. Because these methods are subject to the availability of terrestrial survey data and to regional limitations, they are very difficult to generalize and use. LAI inversion using a radiative transfer model [14; 15; 16; 17] is an extremely effective method with superior generality. However, due to the complexity of the radiative transfer model and the relatively finite nature of remote sensing observational data, considerable prior data should be included when using these models. Moreover, the input parameters have difficulty accurately describing the spatial and temporal variation characteristics of vegetation; in most cases, this difficulty leads to an ill-posed inversion [18; 19]. The hybrid method combines elements of statistics and physically based methods [19; 20; 21]. This method has the advantages of high speed and flexibility and can produce uncertainty estimates. However, these methods may be difficult to use in practical applications. Nonparametric regression methods estimate LAI without a priori assumptions [22] and are optimized with a training process using reference data. In contrast to empirical regression methods, nonexplicit choices need to be made regarding the spectral band relationships, transformation or fitting function. Neural networks belong to nonparametric methods [23]. An artificial neural network can not only process nonlinear, nonnormal, and collinear data that cannot be dealt with in a statistical model [24], but also has been extensively used in remote sensing data classification [25; 26], biomass extraction [27; 28], and LAI estimation [29; 30; 31], among other applications.