  An approach to incorporate deep learning within an iterative image
reconstruction framework to reconstruct images from severely incomplete
measurement data is presented. Specifically, we utilize a convolutional neural
network (CNN) as a quasi-projection operator within a least squares
minimization procedure. The CNN is trained to encode high level information
about the class of images being imaged; this information is utilized to
mitigate artifacts in intermediate images produced by use of an iterative
method. The structure of the method was inspired by the proximal gradient
descent method, where the proximal operator is replaced by a deep CNN and the
gradient descent step is generalized by use of a linear reconstruction
operator. It is demonstrated that this approach improves image quality for
several cases of limited-view image reconstruction and that using a CNN in an
iterative method increases performance compared to conventional image
reconstruction approaches. We test our method on several limited-view image
reconstruction problems. Qualitative and quantitative results demonstrate
state-of-the-art performance.
