Abstract
Sparse-view Computed Tomography (CT) reconstruction is a challenging ill-posed problem, often requiring extensive supervised training or resulting in artifacts with standard self-supervised methods. We present AC-IND, a novel reconstruction framework that incorporates a physical prior—the discrete number of materials—into an Implicit Neural Representation (INR). By mapping coordinates to a probability distribution over material categories and jointly estimating attenuation coefficients, AC-IND achieves superior reconstruction quality and provides unsupervised semantic segmentation. Experimental results on real-world walnut scans demonstrate significant improvements in PSNR and visual clarity over traditional and neural baselines.
Introduction
Computed Tomography (CT) is a cornerstone of modern medical and industrial imaging. However, standard "dense-view" CT involves high radiation doses and long acquisition times. Sparse-view CT offers a safer, faster alternative but introduces significant mathematical ambiguity. While deep learning has made strides, supervised models often struggle with domain shifts, and standard self-supervised Implicit Neural Representations (INRs) lack physical constraints, leading to blurry results and artifacts. AC-IND addresses these issues by leveraging the inherent physical property that most objects consist of a finite set of distinct materials.
Methodology: Attenuation Coefficient and Implicit Neural Distribution
The core innovation of AC-IND is the decoupling of spatial representation from physical density. Instead of a direct mapping from coordinates $(x, y)$ to a scalar density, the model employs two components:
- Implicit Neural Distribution ($f_\theta$): A Multi-Layer Perceptron (MLP) that outputs a probability distribution over $K$ material categories for any given coordinate. A "Modulated Softmax" function is used to encourage sharp, decisive material assignments.
- Attenuation Coefficient (AC) Estimator ($c_\phi$): A learnable vector representing the physical X-ray attenuation density for each of the $K$ materials.
The final reconstructed image is the expected value of the material densities at each point. This approach allows the model to perform unsupervised segmentation simultaneously with reconstruction.
Experimental Results
The performance of AC-IND was evaluated on synthetic phantoms and real-world datasets, such as the Walnut Slice Dataset, under highly sparse conditions (20, 40, and 60 views).
On the Walnut dataset with only 20 views, AC-IND significantly outperformed traditional and existing neural methods. It achieved a Peak Signal-to-Noise Ratio (PSNR) of 26.49 dB, compared to 23.80 dB for standard INRs and 19.78 dB for the iterative SIRT method. Qualitative analysis reveals that AC-IND produces much sharper boundaries and fewer streaking artifacts, as evidenced by the high PSNR and SSIM values achieved in comparative tests.
Discussion and Conclusion
AC-IND demonstrates that a simple physical prior—knowing the number of materials—can act as a powerful constraint for self-supervised CT reconstruction. This "weak prior" not only improves image quality but also yields interpretable latent spaces and "free" segmentation maps.
While the current method requires pre-specifying the number of materials, which may be challenging in some medical contexts with continuous density gradients, it represents a significant step toward more physically grounded and interpretable neural imaging. Future work will focus on extending the framework to 3D reconstruction and adaptive material estimation.