Augmented NETT Regularization of Inverse Problems
This work addresses reconstruction challenges in medical imaging, offering a method that avoids computationally expensive forward models and adapts to increased sampling without retraining, though it is incremental in combining existing regularization ideas.
The authors tackled the problem of solving inverse problems in imaging by proposing aNETT, a data-driven reconstruction framework that achieves results comparable to state-of-the-art deep-learning methods in sparse-view and low-dose CT applications.
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.