Learned iterative networks: An operator learning perspective

TL;DR

This paper presents a unified operator perspective on learned iterative networks for image reconstruction, bridging the gap between classical algorithms and learned approaches in inverse problems.

Contribution

It introduces a unified operator framework for learned iterative networks, clarifying their relation to classical algorithms and providing a comprehensive view of their application.

Findings

Many learned approaches are closely related in their core.

The framework applies to both linear and nonlinear inverse problems.

Numerical studies support the unified operator perspective.

Abstract

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.