Solving Inverse Problems by Joint Posterior Maximization with a VAE Prior

Understand

In this paper we address the problem of solving ill-posed inverse problems in imaging where the prior is a neural generative model.

• Specifically we consider the decoupled case where the prior is trained once and can be reused for many different log-concave degradation models without retraining.
• Whereas previous MAP-based approaches to this problem lead to highly non-convex optimization algorithms, our approach computes the joint (space-latent) MAP that naturally leads to alternate optimization algorithms and to the use of a stochastic encoder to accelerate computations.
• The resulting technique is called JPMAP because it performs Joint Posterior Maximization using an Autoencoding Prior.