  Manifold learning using deep neural networks been shown to be an effective
tool for building sophisticated prior image models that can be applied to noise
reduction in low-dose CT. We propose a new iterative CT reconstruction
algorithm, called Manifold Reconstruction of Differences (MRoD), which combines
physical and statistical models with a data-driven prior based on manifold
learning. The MRoD algorithm involves estimating a manifold component,
approximating common features among all patients, and the difference component
which has the freedom to fit the measured data. By applying a
sparsity-promoting penalty to the difference image rather than a hard
constraint to the manifold, the MRoD algorithm is able to reconstruct features
which are not present in the training data. The difference component itself may
be independently useful. While the manifold captures typical patient features
(e.g. healthy anatomy), the difference image highlights patient-specific
elements (e.g. pathology). In this work, we present a description of an
optimization framework which combines trained manifold-based modules with
physical modules. We present a simulation study using anthropomorphic lung data
showing that the MRoD algorithm can both isolate differences between a
particular patient and the typical distribution, but also provide significant
noise reduction with less bias than a typical penalized likelihood estimator in
composite manifold plus difference reconstructions.
