Deep Learning with Enforced Data Consistency

Current deep learning methods for MRI image reconstruction handle data consistency in one of two ways: (1) add a penalty term into the loss function, or (2) add a data consis-tency layer into the network architecture. Adding a penalty to the loss function does not enforce data consistency; data inconsistent results are still often generated, which can result in erroneous reconstructions. The data consistency layer improves reconstruction quality on out-of-distribution data and largely eliminates hallucinations. However, it is too compu-tationally expensive for training with parallel imaging data. In this manuscript we explore a computationally efficient approximation to hard data consistency. We present results when adding this data consistency layer into two existing networks designed for MRI reconstruction. After retraining with the additional consistency layer, the networks show improved out-of-distribution performance and suppression of hallucinations.