Manifold Reconstruction of Differences: A Model-Based Iterative Statistical Estimation Algorithm With a Data-Driven Prior.

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-close CT. A manifold is a low-dimensional space that captures most of the variation in a class of data (e.g. chest CT images). This nonlinear reduction in dimensionality is one way to build up a sophisticated model of the features and structures present in image data. This nonlinear dimensionality reduction tends to learn features associated with the signal rather than the noise when provided with a large training dataset. However, the internal workings operation are typically not easy to understand. The results can be highly nonlinear and object-dependent. After training the model is fixed and during reconstruction is typically no check for fitness between the image estimates and the measured data. 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.