Georgia Institute of Technology College of Sciences

 We will discuss the recent developments of fast image reconstrcution with total variation (TV) regularization whose robustness has been justfied by the theory of compressed sensing. However, the solution of TV based reconstruction encounters two main difficulties on the computational aspect of many applications: the inversion matrix can be large, irregular, and severely ill-conditioned, and the objective is nonsmooth. We introduce two algorithms that tackle the problem using variable splitting and optimized step size selection. The algorithms also provide a general framework for solving large and ill-conditioned linear inversion problem with TV regularization. An important and successful application of TV based image reconstruction in magnetic resonance imaging (MRI) known as paratially parallel imaging (PPI) will be discussed. The numerical results demonstrate significantly improved  efficiency and accuracy over the state-of-the-arts.