  Many techniques have been proposed for image reconstruction in medical
imaging that aim to recover high-quality images especially from limited or
corrupted measurements. Model-based reconstruction methods have been
particularly popular (e.g., in magnetic resonance imaging and tomographic
modalities) and exploit models of the imaging system's physics together with
statistical models of measurements, noise and often relatively simple object
priors or regularizers. For example, sparsity or low-rankness based
regularizers have been widely used for image reconstruction from limited data
such as in compressed sensing. Learning-based approaches for image
reconstruction have garnered much attention in recent years and have shown
promise across biomedical imaging applications. These methods include synthesis
dictionary learning, sparsifying transform learning, and different forms of
deep learning involving complex neural networks. We briefly discuss classical
model-based reconstruction methods and then review reconstruction methods at
the intersection of model-based and learning-based paradigms in detail. This
review includes many recent methods based on unsupervised learning, and
supervised learning, as well as a framework to combine multiple types of
learned models together.
