  This dissertation is devoted to provide advanced nonconvex nonsmooth
variational models of (Magnetic Resonance Image) MRI reconstruction, efficient
learnable image reconstruction algorithms and parameter training algorithms
that improve the accuracy and robustness of the optimization-based deep
learning methods for compressed sensing MRI reconstruction and synthesis. The
first part introduces a novel optimization based deep neural network whose
architecture is inspired by proximal gradient descent for solving a variational
model. The second part is a substantial extension of the preliminary work in
the first part by solving the calibration-free fast pMRI reconstruction problem
in a discrete-time optimal control framework. The third part aims at developing
a generalizable Magnetic Resonance Imaging (MRI) reconstruction method in the
meta-learning framework. The last part aims to synthesize target modality of
MRI by using partially scanned k-space data from source modalities instead of
fully scanned data that is used in the state-of-the-art multimodal synthesis.
