Data-Efficient Limited-Angle CT Using Deep Priors and Regularization

TL;DR

The paper addresses the challenge of reconstructing images from limited-angle CT data, where angular coverage is insufficient to uniquely determine the interior. It introduces a gradient-based reconstruction framework that fuses multiple regularization strategies—Deep Image Prior, Total Variation, sinogram filtering, and Patch Similarity Regularization—via a differentiable Radon transform, and it includes a disk-mask with offset optimization to constrain the region. Demonstrating on the HTC'22 dataset, the approach achieves competitive results using only 12 data points for priors and hyperparameter selection, significantly less than typical data-driven methods. The findings highlight the potential of data-efficient, optimization-based CT reconstruction with well-chosen priors for practical, low-data scenarios, and the implementation is provided openly for reproducibility.

Abstract

Reconstructing an image from its Radon transform is a fundamental computed tomography (CT) task arising in applications such as X-ray scans. In many practical scenarios, a full 180-degree scan is not feasible, or there is a desire to reduce radiation exposure. In these limited-angle settings, the problem becomes ill-posed, and methods designed for full-view data often leave significant artifacts. We propose a very low-data approach to reconstruct the original image from its Radon transform under severe angle limitations. Because the inverse problem is ill-posed, we combine multiple regularization methods, including Total Variation, a sinogram filter, Deep Image Prior, and a patch-level autoencoder. We use a differentiable implementation of the Radon transform, which allows us to use gradient-based techniques to solve the inverse problem. Our method is evaluated on a dataset from the Helsinki Tomography Challenge 2022, where the goal is to reconstruct a binary disk from its limited-angle sinogram. We only use a total of 12 data points--eight for learning a prior and four for hyperparameter selection--and achieve results comparable to the best synthetic data-driven approaches.

Figures (5)

• Figure 1: The image shows the true image (left), the sinogram (middle), and the filtered sinogram ($\alpha=5.0$) (right). The filtering reduces high-frequency content which makes the holes more prominent in the sinogram, and mitigates overfitting to noise.
• Figure 2: Examples of patches encoded and decoded by the autoencoder. MAE is the mean absolute error between the true and reconstructed patches. Top row: Input patches. Bottom row: Reconstructed patches. The autoencoder learns to encode and decode patches that are similar to its training data. If the autoencoder is restrictive enough, it cannot encode noise or artifacts, thus providing a strong prior for the reconstruction.
• Figure 3: All 21 phantoms used in the HTC'22 challenge. From left to right: Level 1-7. From top to bottom: Phantom a, b, c.
• Figure 4: Accounting for the amount of data used, our method compares favorably to HTC'22 submissions. The x-axis shows the number of data points used in training, and the y-axis shows the MCC score on the level 7 test set.
• Figure 5: Reconstruction images of the binary disk from the HTC'22 challenge. From left to right: True image, FBP + Otsu + Mask, our method with no regularization, and our full method.