A Bayesian Network-Based Method to Alleviate the Ill-Posed Inverse Problem: A Case Study on Leaf Area Index and Canopy Water Content Retrieval

Retrieval of vegetation parameters from remotely sensed data using a radiative transfer model is generally hampered by the ill-posed inverse problem, which dramatically decreases the precision level of retrieved parameters. The purpose of this study was to use a Bayesian network-based method to allow the alleviation of the ill-posed inverse problem. This was achieved by introducing the correlations between the model free parameters into their prior joint probability distribution (PJPD), allowing the reduction of the probabilities of unrealistic combinations. Three sampling strategies intended to design three types of PJPDs that considered different correlations (represented by a correlation matrix) were presented. They were multivariate uniform distribution composed by independent free parameters, multivariate uniform distribution based on a simple correlation matrix, and multivariate Gaussian distribution based on a complicated correlation matrix, respectively. A case study of the presented method to retrieve leaf area index (LAI) and canopy water content (CWC) using the PROSAIL_5B (PROSPECT-5 + 4SAIL) model from Landsat 8 products was implemented. Results indicate that the presented method greatly improves the precision level of target parameters, with the coefficient of determination R ² of 0.69, 0.77, and 0.82 and root-mean-square error (RMSE) of 0.55, 0.51, and 0.44 m ² · m ^-2 for LAI and R ² = 0.68, 0.78, and 0.84 and RMSE = 230, 198, and 166 g · m ^-2 for CWC, respectively. Hence, the ill-posed inverse problem can be alleviated by the presented method, which can be widely applied for vegetation parameters retrieval.