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Many PDE-based inpainting methods use sophisticated higher-order differential operators to bridge large gaps and to recover structures with low curvature. They require fairly advanced numerical methods, while the inpainting process is still fairly slow. We show that one can achieve results of competitive quality by the limiting case of a widely ignored anisotropic diffusion operator involving Gaussian convolution. It offers favourable shape reconstruction properties for sparse data, while allowing simple and efficient numerical algorithms.