Scalable Uncertainty Quantification for Data-Driven PET Image Reconstruction

This project is concerned with uncertainty quantification(UQ)for image reconstructions in positron emission tomography (PET). PETis a pillar of modern diagnostic imaging, allowing non-invasive, sensitive and specific detection of functional changes in a number of diseases. Hence, reliable PETimage reconstruction is of great practical importance and a large number of reconstruction algorithms have been developed duringthe last few decades. Mosttraditionalalgorithms rely on penalized maximum likelihood estimates, usingahand crafted prior(e.g., total variation and anatomical priors), or more recently learning based approaches, e.g., unrolled deep iterative networks, have been proposed. While these techniques have been very successful, theylack the capability to provide uncertainty estimates, even though such estimatesare highly desirable for downstream decision making.There are two notable challenges associated with uncertainty quantification (UQ)for PET imaging. First, the noise model is often of Poisson type, with nonnegativity constraint on the concentration, which precludes applying established statistical proceduresfor Poisson regression. Second, realistic PET imaging involves a large volume of data and a high-dimensional parameter space.In this project, we propose to exploit the versatile tools from machine learning, e.g., Gaussian processes and variational autoencoder (VAE), for scalable UQ for PET reconstruction.