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The 3D visualization of astronomical nebulae is a challenging problem since only a single 2D projection is observable from our fixed vantage point on Earth. We attempt to generate plausible and realistic looking volumetric visualizations via a tomographic approach that exploits the spherical or axial symmetry prevalent in some relevant types of nebulae. Different types of symmetry can be implemented by using different randomized distributions of virtual cameras. Our approach is based on an iterative compressed sensing reconstruction algorithm that we extend with support for position-dependent volumetric regularization and linear equality constraints. We present a distributed multi-GPU implementation that is capable of reconstructing high-resolution datasets from arbitrary projections. Its robustness and scalability are demonstrated for astronomical imagery from the Hubble Space Telescope. The resulting volumetric data is visualized using direct volume rendering. Compared to previous approaches, our method preserves a much higher amount of detail and visual variety in the 3D visualization, especially for objects with only approximate symmetry.