The role of spatial information in disentangling the
irradiancereflectancetransmitance ambiguity
Sandra Jiménez and Jesús Malo
Abstract 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, spectralonly 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 pixelbased 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 spatiospectral representation of the signal is always lower than its spectralonly counterpart. According to this, the number of free parameters in the spatiospectral inverse problem is smaller so the spatiospectral approaches are always better than spectralonly 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 spatiospectral retrieval. 

Related Papers The role of spatial information in disentangling the irradiancereflectancetransmitance ambiguity. Sandra Jiménez and Jesús Malo. Accepted to IEEE Trans. Geosci. Rem. Sens. Full text: manuscr_TGRS_2012_00431.pdf 

Supplementary Material: 1. Extends the results in the manuscript to different spatial structures 2. Extends the results in the manuscript to different wavelength range and spatiospectral resolution 3. Statistically justifies the initialization scheme of sources 4. Provides sample data and code The generality of the conclusion is not surprising since the imaging equation and the PCA decompositions do not depend on the specific spatiospectral resolution or wavelength range. The joint spatiospectral approach will simplify the problem whenever there are relations between the signal at different spatial positions, which is true in a wide range of situations given the spatial continuity of the physical sources (the reflecting objects and the atmospheric phenomena). 1. Effect of the spatial structure
