  Tomographic imaging is in general an ill-posed inverse problem. Typically, a
single regularized image estimate of the sought-after object is obtained from
tomographic measurements. However, there may be multiple objects that are all
consistent with the same measurement data. The ability to generate such
alternate solutions is important because it may enable new assessments of
imaging systems. In principle, this can be achieved by means of posterior
sampling methods. In recent years, deep neural networks have been employed for
posterior sampling with promising results. However, such methods are not yet
for use with large-scale tomographic imaging applications. On the other hand,
empirical sampling methods may be computationally feasible for large-scale
imaging systems and enable uncertainty quantification for practical
applications. Empirical sampling involves solving a regularized inverse problem
within a stochastic optimization framework to obtain alternate data-consistent
solutions. In this work, a new empirical sampling method is proposed that
computes multiple solutions of a tomographic inverse problem that are
consistent with the same acquired measurement data. The method operates by
repeatedly solving an optimization problem in the latent space of a style-based
generative adversarial network (StyleGAN), and was inspired by the Photo
Upsampling via Latent Space Exploration (PULSE) method that was developed for
super-resolution tasks. The proposed method is demonstrated and analyzed via
numerical studies that involve two stylized tomographic imaging modalities.
These studies establish the ability of the method to perform efficient
empirical sampling and uncertainty quantification.
