BRDF Model Inversion of Multiangular Remote Sensing: Ill-posedness and the Interior Point Solution Method

摘要

Evaluation of the land surface albedos by employing the bidirectional reflectance distribution function (BRDF) models is one of the important problems in remote sensing. As is known, the retrieval process is an inverse problem. In Proposition 3 of [Verstraete et al., 1996], the authors consider that the number of independent observations should be greater than the number of the unknown parameters to describe the physical model as an overdetermined system, then the inverse process can be solved. However as Li et al (1998) pointed out that such a requirement can be hardly satisfied even in the coming EOS era, the inversion procedure is always un-derdetermined in some sense. Therefore, in order to solve the BRDF inversion problem, some new technique must be developed. Generally speaking, the inverse problems are ill-posed. Therefore, some regularization technique should be applied to suppress the ill-posedness. One kind of way to alleviate the ill-posedness is incorporating with some apriori knowledge which has been developed in [Li et al., 2001], This is actually a constrained least squares error (LSE) method since the apriori knowledge can be considered as some kind of constraints to the solution. Another kind of way is by numerical truncated singular value decomposition by employing the hotspot remote sensing data [Wang et al., 2006). In this paper, we consider a new solution method, i.e., the l~1 norm solution method, which iteratively solves the kernel-driven bidirectional reflectance distribution function (BRDF) models for retrieval of land surface albedos. This method, is based on searching for an interior point solution for the problem in the feasible solution set. This method can always find a set of suitable BRDF coefficients for poor sampled data. Numerical performance is given for the widely used 18 data sets among the 73 data sets [Li et al., 2001].