Regularizing kernel-based BRDF model inversion method for ill-posed land surface parameter retrieval using smoothness constraint

[1] In this paper, we consider the problem how to solve the kernel-based bidirectional reflectance distribution function (BRDF) models for the retrieval of land surface albedos. The above problem is an ill-posed inverse problem. We will employ a new regularization technique to alleviate the ill-posedness. The Tikhonov regularization has been discussed for BRDF model inversion, however, much study has to be done before applying it in practice (Wang et al., 2007). In this paper, we thoroughly investigate this method, and propose a discrepancy method for a posteriori choice of the regularization parameter and several options for choosing the regularizing stabilizer. The proposed method can alleviate difficulties in numerical computation when the discrete kernel is badly conditioned and the number of observations is poor. Applying the proposed method can always find a set of suitable BRDF coefficients for poorly sampled data. The proposed method is an improvement of the traditional least squares error algorithm in AMBRALS (Algorithm for MODIS (Moderate Resolution Imaging Spectroradiometer) Bidirectional Reflectance Anisotropies of the Land Surface), see Strahler et al. (1999), and is comparable to the regularized singular value decomposition method developed by Wang et al. (2007). Hence the proposed method can be considered as a supplemental algorithm for the robust estimation of the land surface BRDF/albedos. Numerical performance is given in this paper for the widely used field-based 18 data sets among the 73 data sets (see Li et al., 2001) and for the satellite data.