[Paper Review] Near-Exact Recovery for Tomographic Inverse Problems via Deep Learning

Martin Genzel, Ingo Gühring+2 more|arXiv (Cornell University)|Jun 14, 2022

Medical Imaging Techniques and Applications30 citations

TL;DR

The paper demonstrates that an iterative end-to-end neural network (ItNet) with a data-driven forward-model calibration can achieve near-exact recovery for sparse-view CT in noiseless data, outperforming strong baselines and matching TV-minimization precision.

ABSTRACT

This work is concerned with the following fundamental question in scientific machine learning: Can deep-learning-based methods solve noise-free inverse problems to near-perfect accuracy? Positive evidence is provided for the first time, focusing on a prototypical computed tomography (CT) setup. We demonstrate that an iterative end-to-end network scheme enables reconstructions close to numerical precision, comparable to classical compressed sensing strategies. Our results build on our winning submission to the recent AAPM DL-Sparse-View CT Challenge. Its goal was to identify the state-of-the-art in solving the sparse-view CT inverse problem with data-driven techniques. A specific difficulty of the challenge setup was that the precise forward model remained unknown to the participants. Therefore, a key feature of our approach was to initially estimate the unknown fanbeam geometry in a data-driven calibration step. Apart from an in-depth analysis of our methodology, we also demonstrate its state-of-the-art performance on the open-access real-world dataset LoDoPaB CT.

Motivation & Objective

• Motivate whether deep-learning solvers can achieve near-perfect recovery for noise-free inverse problems in CT.
• Develop a data-driven pipeline that includes forward-operator estimation, end-to-end pre-trained UNet backbones, and iterative data-consistency.
• Evaluate against challenge baselines and real-world data, and analyze data-consistency and forward-model impact.
• Provide insights on design choices that generalize beyond synthetic data.

Proposed method

• Step 1 – Data-driven geometry identification to estimate the unknown fanbeam forward operator using 4000 sinogram–image pairs by gradient-descent-like optimization with coordinate descent.
• Step 2 – Pre-training a UNet as a computational backbone to post-process sparse-view FBP reconstructions via empirical risk minimization.
• Step 3 – Constructing ItNet, an iterative scheme that alternates UNet-based enhancement with a data-consistency step that uses FBP (instead of the unfiltered backprojection) to enforce forward model consistency.
• Use of a small number of iterations (K) with weight-sharing experiments and pre-initialization from Step 2 to boost performance.
• Analysis of data-consistency and forward-model error to gauge how much accuracy rests on the learned forward operator.

Experimental results

Research questions

• RQ1 Can end-to-end networks achieve near-perfect accuracy on a noiseless tomographic inverse problem?
• RQ2 What role does incorporating an explicitly learned forward model play in achieving high-precision reconstructions?
• RQ3 Does pre-training and iterative coupling (ItNet) outperform simple post-processing or other learned-primal-dual approaches in sparse-view CT?
• RQ4 How does the learned forward operator influence data-consistency and overall reconstruction quality across data distributions (synthetic vs LoDoPaB CT dataset)?

Key findings

• ItNet-post ensemble achieves near-exact recovery on the AAPM test set, with RMSE as low as 6.37e-6 in final challenge evaluation.
• ItNet variants outperform baselines such as post-processed UNet∘FBP, Tiramisu, and learned primal-dual (LPD) on the challenge data.
• Data-consistency analysis shows remaining error largely stems from forward-model estimation error rather than the reconstruction network, suggesting improvements from a more accurate forward operator.
• Pre-training UNet blocks and initializing ItNet with Step 2 weights significantly improves convergence speed and final accuracy.
• Only a few forward-model evaluations are needed for near-exact recovery, and a sweet spot around K=5 iterations with non-shared weights yields strong performance.