Ivan Dokmanic

I will present a new learning-based approach to ill-posed inverse problems. Instead of directly learning the ill-posed inverse mapping, we learn an ensemble of simpler mappings from the data to the projections of the unknown model into random low-dimensional subspaces. We choose structured subspaces of piecewise-constant images on random Delaunay triangulations. With this choice, the projected inverse maps are simpler to learn 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.