Fast Bayesian inversion for high dimensional inverse problems

We investigate the use of learning approaches to handle Bayesian inverse problems in a computationally efficient way when the signals to be inverted present a moderately high number of dimensions and are in large number. We propose a tractable inverse regression approach which has the advantage to produce full probability distributions as approximations of the target posterior distributions. In addition to provide confidence indices on the predictions, these distributions allow a better exploration of inverse problems when multiple equivalent solutions exist. We then show how these distributions can be used for further refined predictions using importance sampling, while also providing a way to carry out uncertainty level estimation if necessary. The relevance of the proposed approach is illustrated both on simulated and real data in the context of a physical model inversion in planetary remote sensing. The approach shows interesting capabilities both in terms of computational efficiency and multimodal inference.