Learned iterative networks: An operator learning perspective
This work provides a foundational theoretical framework for researchers in computational imaging and inverse problems, though it is incremental as it unifies existing methods rather than introducing new ones.
The paper tackles the lack of a unified theoretical framework for learned iterative networks in image reconstruction by presenting an operator learning perspective that separates the computation process from the learning objectives, showing that many existing approaches are closely related.
Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation algorithms for solving variational problems. While the underlying algorithm is usually formulated in the functional analytic setting, learned approaches are often viewed as purely discrete. In this chapter we present a unified operator view for learned iterative networks. Specifically, we formulate a learned reconstruction operator, defining how to compute, and separately the learning problem, which defines what to compute. In this setting we present common approaches and show that many approaches are closely related in their core. We review linear as well as nonlinear inverse problems in this framework and present a short numerical study to conclude.