# Learned iterative networks: An operator learning perspective

arXiv: https://arxiv.org/abs/2512.08444 · HTML: https://mlsanity.com/paper/2512.08444/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2025.

## Built on by (most cited first, 2 of 2)

- [Learning to Control: The iUzawa-Net for Nonsmooth Optimal Control of Linear PDEs](https://mlsanity.com/paper/2602.12273/) (2026)
- [Enabling self-supervised learned primal dual with Noise2Inverse](https://mlsanity.com/paper/2606.26991/) (2026)

## Abstract (arXiv)

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 survey 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 non-linear inverse problems in this framework and present a short numerical study to conclude.