Pokrovsky, O, Roujean, JL (2003). Land surface albedo retrieval via kernel-based BRDF modeling: II. An optimal design scheme for the angular sampling. REMOTE SENSING OF ENVIRONMENT, 84(1), 120-142.
In this paper, we address some fundamental issues regarding the strategy of inversion of the class of the bi-directional reflectance distribution function (BRDF) models known as kernel-based. We examine two main causes of uncertainty affecting the predicted reflectance values. They are a contribution of the random noise term in the measurements and the model residual after adjustment. For this purpose, we formulate notions of both the experimental design for angular sampling and the kernel response function for an arbitrary set of angular measurements. The Fisher informative matrix is considered to circumscribe the optimal design problem to search for the best angular sampling. Two approaches are presented and discussed: one relates to the random noise term of the BRDF model and is independent on the land cover type (LCT); the other is impacted by the residual term of the BRDF model and is determined by the reflectance peculiarities of the different LCTs. Additionally, we explore the residual terms as a function of the LCT and we analyze the sensitivity of the reflectance predicted by the various BRDF models to the kernel response function. This is achieved by segregating regions of the angular domain that are most responsive to the measurement noise. We further determined the optimal angular sampling distribution for ground-based multi-angular data sets over different LCT and known residual terms. Then, we extend it to the more general case, ignoring the residual term. It is shown that the functions that are associated with the chosen criteria saturate after the selection of five or six observing geometries. These inversion experiments in BRDF modeling confirm the efficiency of certain angular data sets as a solution to the optimal design problem in relation to the negative influence of the redundancy effect of observations. This effect arises from having an excessive number of angular measurements in relation to the number of retrieved parameters. Another manner to prove the optimal design validity is by statistical diagnosis. We carried out a diagnosis study based on the residual standard deviation, the Fisher and R-square statistics. A fast convergence rate is observed with angular measurements determined by the optimal design. (C) 2002 Elsevier Science Inc. All rights reserved.