Generalized deep learning-based proximal gradient descent for MR reconstruction

Before employing deep learning in accelerated MRI reconstruction, conventional methods for parallel MR imaging are based on the numerical pseudo-inversion of ill-posed MRI encoding matrix, which could be prone to reconstruction error at poor conditioning. The encoding matrix comprises the k-space under-sampling scheme, coil sensitivities, Fourier transform. The traditional reconstruction involves some gradient descent methods for minimizing the cost function of the k-space fidelity and the regularization term

With the fast growth of machine learning, the supervised learning have been applied to MRI reconstruction. Those methods MRI encoding matrices were fully included in the neural network models. These models were trained with predetermined encoding matrices and corresponding under-sampling artifacts. After training, imaging configurations, including the k-space under-sampling schemes and coil sensitivities, associated encoding matrices, must also be unchanged or changed only within predetermined sampling patterns, during the validation and application, which could be cumbersome or to some extent impractical for the potential clinical use.

To tackle this design challenge, we unroll proximal gradient descent steps into a network and call it Proximator-Net. The proposed method was adapted from proximal gradient descent. This study’s objective was to develop a flexible and practical deep learning-based MRI reconstruction method and implement and validate the proposed method in an experimental setting regarding changeable k-space undersampling schemes.