Deep Mesh Projectors for Inverse Problems
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We develop a new learning-based approach to ill-posed inverse problems. Instead of directly learning the complex mapping from the measured data to the reconstruction, we learn an ensemble of simpler mappings from data to projections of the unknown model into random low-dimensional subspaces. We form the reconstruction by combining the estimated subspace projections. Structured subspaces of piecewise-constant images on random Delaunay triangulations allow us to address inverse problems with extremely sparse data and still get good reconstructions of the unknown geometry. This choice also makes our method robust against arbitrary data corruptions not seen during training. Further, it marginalizes the role of the training dataset which is essential for applications in geophysics where ground-truth datasets are exceptionally scarce.
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