# Sparse aNETT for Solving Inverse Problems with Deep Learning

arXiv: https://arxiv.org/abs/2004.09565 · HTML: https://mlsanity.com/paper/2004.09565/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2020.

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

- [Regularising Inverse Problems with Generative Machine Learning Models](https://mlsanity.com/paper/2107.11191/) (2021)
- [Deep Preconditioners and their application to seismic wavefield processing](https://mlsanity.com/paper/2207.09938/) (2022)

## Abstract (arXiv)

We propose a sparse reconstruction framework (aNETT) for solving inverse problems. Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transforms, we train an autoencoder network D circ E with E acting as a nonlinear sparsifying transform and minimize a Tikhonov functional with learned regularizer formed by the ℓq-norm of the encoder coefficients and a penalty for the distance to the data manifold. We propose a strategy for training an autoencoder based on a sample set of the underlying image class such that the autoencoder is independent of the forward operator and is subsequently adapted to the specific forward model. Numerical results are presented for sparse view CT, which clearly demonstrate the feasibility, robustness and the improved generalization capability and stability of aNETT over post-processing networks.