Post-Stack Inversion with Uncertainty Estimation through Bayesian Deep Image Prior

We propose a Bayesian framework for post-stack inversion and uncertainty estimation based on deep priors. A Convolutional Neural Network acts like a nonlinear preconditioner to the inversion problem, capturing the priors from the data in its inner layers. At the same time, it also provides an estimate of the aleatoric uncertainty; this is achieved by minimizing a joint objective function in the CNN parameters space. Then, in a Bayesian framework, Montecarlo dropout is leveraged in order to sample the posterior and characterize the inherent uncertainty. Through synthetic examples we prove our methodology to be effective.