I presented our work on deep mesh projections at the SIAM Conference on Imaging Sciences in Bologna.

Abstract

We propose a new learning-based approach to ill-posed inverse problems. Instead of directly learning the unstable inverse mapping, we learn an ensemble of simpler mappings from the data to the projections of the unknown model into random low-dimensional subspaces. With structured subspaces of piecewise-constant images on random Delaunay triangulations, the projected inverse maps are simpler to learn than the full inverse in terms of robustness and generalization error. We form the reconstruction by combining the estimated subspace projections. This allow us to address inverse problems with extremely sparse data and still get good reconstructions of the unknown geometry; it 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.