# Solving ill-posed inverse problems using iterative deep neural networks

## TL;DR

This paper introduces a partially learned iterative method combining classical regularization with deep learning to solve ill-posed inverse problems, demonstrating improved accuracy and speed in tomographic image reconstruction.

## Contribution

The paper presents a novel gradient-like iterative scheme that incorporates learned components for solving nonlinear inverse problems more efficiently.

## Key findings

- Achieves 5.4 dB PSNR improvement over TV reconstruction.
- Reconstructs 512x512 images in about 0.4 seconds on a single GPU.
- Outperforms traditional FBP and TV methods in accuracy and speed.

## Abstract

We propose a partially learned approach for the solution of ill posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularization theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularizing functional. The method results in a gradient-like iterative scheme, where the "gradient" component is learned using a convolutional network that includes the gradients of the data discrepancy and regularizer as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against FBP and TV reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the TV reconstruction while being significantly faster, giving reconstructions of 512 x 512 volumes in about 0.4 seconds using a single GPU.