  Medical imaging is crucial in modern clinics to guide the diagnosis and
treatment of diseases. Medical image reconstruction is one of the most
fundamental and important components of medical imaging, whose major objective
is to acquire high-quality medical images for clinical usage at minimal cost
and risk to the patients. Mathematical models in medical image reconstruction
or, more generally, image restoration in computer vision, have been playing a
prominent role. Earlier mathematical models are mostly designed by human
knowledge or hypothesis on the image to be reconstructed, and we shall call
these models handcrafted models. Later, handcrafted plus data-driven modeling
started to emerge which still mostly relies on human designs, while part of the
model is learned from the observed data. More recently, as more data and
computation resources are made available, deep learning based models (or deep
models) pushed data-driven modeling to the extreme where the models are mostly
based on learning with minimal human designs. Both handcrafted and data-driven
modeling have their own advantages and disadvantages. One of the major research
trends in medical imaging is to combine handcrafted modeling with deep modeling
so that we can enjoy benefits from both approaches. The major part of this
article is to provide a conceptual review of some recent works on deep modeling
from the unrolling dynamics viewpoint. This viewpoint stimulates new designs of
neural network architectures with inspiration from optimization algorithms and
numerical differential equations. Given the popularity of deep modeling, there
are still vast remaining challenges in the field, as well as opportunities
which we shall discuss at the end of this article.
