Light field reconstruction from scattered light using plenoptic data

We investigate the utility of plenoptic data for extracting information from a scene where the light from objects in the scene is viewable only after scattering from a surface such as a wall. We derive the rigorous relationship between the object and the scattered light, which is cast in terms of a system of Fredholm integral equations of the first kind with the bidirectional reflectance distribution function (BRDF) of the scattering surface; further, the object information is reconstructed by solving the equations. Based on the Fourier transformation, we propose a simple BRDF model and analyze the reconstruction errors by introducing newly defined parameters reflecting the BRDF's characteristics, i.e., the degree of specularity and the effective SNR, and obtain optimal regularized solutions under a variety of surface BRDFs. Moreover, we provide a fundamental limit of retrievable information content from the scattered light. A comparison with experimental results is reported.