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Tomographic imaging is in general an ill-posed inverse problem. Typically, asingle regularized image estimate of the sought-after object is obtained fromtomographic measurements. However, there may be multiple objects that are allconsistent with the same measurement data. The ability to generate suchalternate solutions is important because it may enable new assessments ofimaging systems. In principle, this can be achieved by means of posteriorsampling methods. In recent years, deep neural networks have been employed forposterior sampling with promising results. However, such methods are not yetfor use with large-scale tomographic imaging applications. On the other hand,empirical sampling methods may be computationally feasible for large-scaleimaging systems and enable uncertainty quantification for practicalapplications. Empirical sampling involves solving a regularized inverse problemwithin a stochastic optimization framework to obtain alternate data-consistentsolutions. In this work, a new empirical sampling method is proposed thatcomputes multiple solutions of a tomographic inverse problem that areconsistent with the same acquired measurement data. The method operates byrepeatedly solving an optimization problem in the latent space of a style-basedgenerative adversarial network (StyleGAN), and was inspired by the PhotoUpsampling via Latent Space Exploration (PULSE) method that was developed forsuper-resolution tasks. The proposed method is demonstrated and analyzed vianumerical studies that involve two stylized tomographic imaging modalities.These studies establish the ability of the method to perform efficientempirical sampling and uncertainty quantification.

Mining the manifolds of deep generative models for multiple data-consistent solutions of ill-posed tomographic imaging problems