AC-IND: Sparse CT reconstruction based on attenuation coefficient estimation and implicit neural distribution

TL;DR

AC-IND tackles sparse-view CT reconstruction by encoding a priori material-count information into a distribution-valued INR and a compact AC estimator. The method maps coordinates to distributions over materials, computes voxel attenuation as $g_{\theta,\\varphi}(z)=\\sum_{m\\in M} D_z(m) c_{\\varphi}(m)$, and optimizes jointly with data-consistency loss $L_{\\theta,\\varphi}$, where $X_{\\theta,\\varphi}[i,j]=\\sum_{k=1}^{|M|} f_{\\theta}((i,j))(k) c_{\\varphi}(k)$. It demonstrates superior sparse-view reconstruction on Walnut Slice and Ellipse Material datasets, and uniquely yields unsupervised segmentation maps during training, with AC-IND+ further improving performance via better AC initialization. The work reduces reliance on external-domain data, provides interpretable AC estimates converging to ground truth, and has potential for industrial nondestructive testing and medical imaging with reduced radiation.

Abstract

Computed tomography (CT) reconstruction plays a crucial role in industrial nondestructive testing and medical diagnosis. Sparse view CT reconstruction aims to reconstruct high-quality CT images while only using a small number of projections, which helps to improve the detection speed of industrial assembly lines and is also meaningful for reducing radiation in medical scenarios. Sparse CT reconstruction methods based on implicit neural representations (INRs) have recently shown promising performance, but still produce artifacts because of the difficulty of obtaining useful prior information. In this work, we incorporate a powerful prior: the total number of material categories of objects. To utilize the prior, we design AC-IND, a self-supervised method based on Attenuation Coefficient Estimation and Implicit Neural Distribution. Specifically, our method first transforms the traditional INR from scalar mapping to probability distribution mapping. Then we design a compact attenuation coefficient estimator initialized with values from a rough reconstruction and fast segmentation. Finally, our algorithm finishes the CT reconstruction by jointly optimizing the estimator and the generated distribution. Through experiments, we find that our method not only outperforms the comparative methods in sparse CT reconstruction but also can automatically generate semantic segmentation maps.

Figures (13)

• Figure 1: Performance comparison on the reconstruction image and segmentation image automatically generated by our method.
• Figure 1: Comparison of different reconstruction under 20 views setting.
• Figure 2: Comparison between modulated softmax and classic softmax, where the modulation coefficient $T$ is equal to 0.06.
• Figure 2: Comparison of different reconstruction under 40 views setting.
• Figure 3: The first row: FBP reconstrcution, Mask, the Ground Truth of Barbapapa phantom and the reconstruction from 20 views by our method. The second row: Mask, segmentation output automatically produced by our method during the reconstruction process.