  In this paper we investigate a variety of deep learning strategies for
solving inverse problems. We classify existing deep learning solutions for
inverse problems into three categories of Direct Mapping, Data Consistency
Optimizer, and Deep Regularizer. We choose a sample of each inverse problem
type, so as to compare the robustness of the three categories, and report a
statistical analysis of their differences. We perform extensive experiments on
the classic problem of linear regression and three well-known inverse problems
in computer vision, namely image denoising, 3D human face inverse rendering,
and object tracking, selected as representative prototypes for each class of
inverse problems. The overall results and the statistical analyses show that
the solution categories have a robustness behaviour dependent on the type of
inverse problem domain, and specifically dependent on whether or not the
problem includes measurement outliers. Based on our experimental results, we
conclude by proposing the most robust solution category for each inverse
problem class.
