The Role of Spatial Information in Disentangling the Irradiance–Reflectance–Transmittance Ambiguity

In the satellite hyperspectral measures, the contributions of light, surface, and atmosphere are mixed. Applications need separate access to the sources. Conventional inversion techniques usually take a pixelwise spectral-only approach. However, recent improvements in retrieving surface and atmosphere characteristics use heuristic spatial smoothness constraints. In this paper, we theoretically justify such heuristics by analyzing the impact of spatial information on the uncertainty of the solution. The proposed analysis allows to assess in advance the uniqueness (or robustness) of the solution depending on the curvature of a likelihood surface. In situations where pixel-based approaches become unreliable, it turns out that the consideration of spatial information always makes the problem to be better conditioned. With the proposed analysis, this is easily understood since the curvature is consistent with the complexity of the sources measured in terms of the number of significant eigenvalues (or free parameters in the problem). In agreement with recent results in hyperspectral image coding, spatial correlations in the sources imply that the intrinsic complexity of the spatio-spectral representation of the signal is always lower than its spectral-only counterpart. According to this, the number of free parameters in the spatio-spectral inverse problem is smaller, so the spatio-spectral approaches are always better than spectral-only approaches. Experiments using ensembles of actual reflectance values and realistic MODTRAN irradiance and atmosphere radiance and transmittance values show that the proposed analysis successfully predicts the practical difficulty of the problem and the improved quality of spatio-spectral retrieval.