# Augmented NETT Regularization of Inverse Problems

## TL;DR

aNETT introduces a novel data-driven regularization framework for inverse problems, combining encoder-decoder networks with Tikhonov regularization, offering stability, convergence guarantees, and efficient reconstruction especially for complex models.

## Contribution

It presents a new regularization method using neural networks that does not require repeated forward model evaluations and can adapt to different sampling rates without retraining.

## Key findings

- Achieves state-of-the-art results in sparse-view and low-dose CT reconstruction.
- Provides rigorous convergence analysis including stability and rates.
- Enables efficient inverse problem solving with expensive forward models.

## Abstract

We propose aNETT (augmented NETwork Tikhonov) regularization as a novel data-driven reconstruction framework for solving inverse problems. An encoder-decoder type network defines a regularizer consisting of a penalty term that enforces regularity in the encoder domain, augmented by a penalty that penalizes the distance to the data manifold. We present a rigorous convergence analysis including stability estimates and convergence rates. For that purpose, we prove the coercivity of the regularizer used without requiring explicit coercivity assumptions for the networks involved. We propose a possible realization together with a network architecture and a modular training strategy. Applications to sparse-view and low-dose CT show that aNETT achieves results comparable to state-of-the-art deep-learning-based reconstruction methods. Unlike learned iterative methods, aNETT does not require repeated application of the forward and adjoint models, which enables the use of aNETT for inverse problems with numerically expensive forward models. Furthermore, we show that aNETT trained on coarsely sampled data can leverage an increased sampling rate without the need for retraining.