In this paper, we show that the recent theory of Compressive Sensing (CS) can successfully be applied to solve a model-based inverse lighting problem for single face images, even in harsh lighting with multiple light sources, including cast shadows and specularities. It has been shown that an illumination cone can be used to perform realistic inverse lighting. In this work, the cone images are synthetically generated using directional lights and a realistic reflectance of faces. Thereby, the face model is achieved by fitting a 3D Morphable Model to the input image. We apply CS to find the sparsest illumination setup from few random measurements of the RGB input and the cone images. The proposed method significantly reduces the dimensionality through stochastic sampling and a greedy algorithm for the sparse support estimation, yielding low runtimes. The greedy search is designed to handle non-negativity of the light sources and joint-support selection. We show that the proposed method reaches a quality of illumination estimation equal to previous work, while dramatically reducing the number of active light sources. Thorough experimental evaluation shows that stable recovery is achievable for compression rates up to 99%. The method exhibits outstanding robustness to additive noise in the input image.
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