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Statistical Distances and Their Applications to Biophysical Parameter Estimation: Information Measures, M-Estimates, and Minimum Contrast Methods

机译:统计距离及其在生物物理参数估计中的应用:信息量度,M估计和最小对比度方法

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Radiative transfer models predicting the bidirectional reflectance factor (BRF) of leaf canopies are powerful tools that relate biophysical parameters such as leaf area index (LAI), fractional vegetation cover fV and the fraction of photosynthetically active radiation absorbed by the green parts of the vegetation canopy (fAPAR) to remotely sensed reflectance data. One of the most successful approaches to biophysical parameter estimation is the inversion of detailed radiative transfer models through the construction of Look-Up Tables (LUTs). The solution of the inverse problem requires additional information on canopy structure, soil background and leaf properties, and the relationships between these parameters and the measured reflectance data are often nonlinear. The commonly used approach for optimization of a solution is based on minimization of the least squares estimate between model and observations (referred to as cost function or distance; here we will also use the terms “statistical distance” or “divergence” or “metric”, which are common in the statistical literature). This paper investigates how least-squares minimization and alternative distances affect the solution to the inverse problem. The paper provides a comprehensive list of different cost functions from the statistical literature, which can be divided into three major classes: information measures, M-estimates and minimum contrast methods. We found that, for the conditions investigated, Least Square Estimation (LSE) is not an optimal statistical distance for the estimation of biophysical parameters. Our results indicate that other statistical distances, such as the two power measures, Hellinger, Pearson chi-squared measure, Arimoto and Koenker–Basset distances result in better estimates of biophysical parameters than LSE; in some cases the parameter estimation was improved by 15%.
机译:预测叶片冠层的双向反射因子(BRF)的辐射传递模型是与生物物理参数(如叶面积指数(LAI),植被覆盖率f V 和吸收的光合有效辐射比例)相关的强大工具通过植被冠层的绿色部分(f APAR )获取遥感反射率数据。生物物理参数估计最成功的方法之一是通过构造查找表(LUT)来反转详细的辐射传递模型。反问题的解决方案需要有关冠层结构,土壤背景和叶片特性的其他信息,并且这些参数与测得的反射率数据之间的关系通常是非线性的。优化解决方案的常用方法是基于最小化模型和观测值之间的最小二乘估计值(称为成本函数或距离;这里我们还将使用术语“统计距离”或“差异”或“度量” ,这在统计资料中很常见)。本文研究最小二乘最小化和替代距离如何影响反问题的解决方案。本文提供了来自统计文献的各种成本函数的综合列表,这些函数可以分为三大类:信息度量,M估计和最小对比方法。我们发现,对于所研究的条件,最小二乘估计(LSE)并不是估计生物物理参数的最佳统计距离。我们的结果表明,其他统计距离,例如两个幂度量,Hellinger,Pearson卡方度量,Arimoto和Koenker-Basset距离,比LSE更好地估计了生物物理参数;在某些情况下,参数估计提高了15%。

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