DeepGEM: Generalized Expectation-Maximization for Blind Inversion

Typically, inversion algorithms assume that a forward model, which relates a source to its resulting measurements, is known and fixed. Using collected indirect measurements and the forward model, the goal becomes to recover the source. When the forward model is unknown, or imperfect, artifacts due to model mismatch occur in the recovery of the source. In this paper, we study the problem of blind inversion: solving an inverse problem with unknown or imperfect knowledge of the forward model parameters. We propose DeepGEM, a variational Expectation-Maximization (EM) framework that can be used to solve for the unknown parameters of the forward model in an unsupervised manner.