Photoacoustic Imaging with Conditional Priors from Normalizing Flows

Abstract

For many ill-posed inverse problems, such as photoacoustic imaging, the uncertainty of the solution is highly affected by measurement noise and data incompleteness (due, for example, to limited aperture). For these problems, the choice of prior information is a crucial aspect of a computationally effective solution scheme. We propose a regularization scheme for photoacoustic imaging that leverages prior information learned by a generative network. We train conditional normalizing flows on pairs of photoacoustic sources (the unknowns of the problem) and the associated data in order to exploit the posterior distribution of the solution. The learned prior is combined with physics-based optimization (enforced by partial differential equations), according to the deep prior framework, in order to achieve robustness with respect to out-of-distribution data. Numerical evidence suggests the superiority of this approach with respect to non-conditional deep priors, and the ability to retrieve features of the unknowns that are typically challenging for limited-view photoacoustics.