Solving Energy-Independent Density for CT Metal Artifact Reduction via Neural Representation

TL;DR

This work addresses metal artifacts in CT by reframing MAR as an energy-independent density reconstruction problem. It introduces Density neural representation (Diner), which uses an MLP to learn a single density map $\sigma(\mathbf{x})$ and a differentiable forward path that maps densities to measurements through a physics-based LAC decomposition $μ(\mathbf{x},E)=σ(\mathbf{x})\big[(1-\mathcal{M}(\mathbf{x}))γ_{water}(E)+\mathcal{M}(\mathbf{x})γ_{metal}(E)\big]$. The approach is fully unsupervised and leverages a polychromatic forward model to produce a virtual monochromatic image while mitigating the nonlinear beam hardening effect. Empirical results on simulated and real CT datasets show that Diner achieves superior MAR performance and robustness, particularly under out-of-domain conditions, with strong qualitative and quantitative improvements over state-of-the-art baselines. The method reduces data requirements and offers practical utility across diverse scanning protocols, though it remains challenged by photon starvation in ultra-high-absorption metals.

Abstract

X-ray CT often suffers from shadowing and streaking artifacts in the presence of metallic materials, which severely degrade imaging quality. Physically, the linear attenuation coefficients (LACs) of metals vary significantly with X-ray energy, causing a nonlinear beam hardening effect (BHE) in CT measurements. Reconstructing CT images from metal-corrupted measurements consequently becomes a challenging nonlinear inverse problem. Existing state-of-the-art (SOTA) metal artifact reduction (MAR) algorithms rely on supervised learning with numerous paired CT samples. While promising, these supervised methods often assume that the unknown LACs are energy-independent, ignoring the energy-induced BHE, which results in limited generalization. Moreover, the requirement for large datasets also limits their applications in real-world scenarios. In this work, we propose Density neural representation (Diner), a novel unsupervised MAR method. Our key innovation lies in formulating MAR as an energy-independent density reconstruction problem that strictly adheres to the photon-tissue absorption physical model. This model is inherently nonlinear and complex, making it a rarely considered approach in inverse imaging problems. By introducing the water-equivalent tissues approximation and a new polychromatic model to characterize the nonlinear CT acquisition process, we directly learn the neural representation of the density map from raw measurements without using external training data. This energy-independent density reconstruction framework fundamentally resolves the nonlinear BHE, enabling superior MAR performance across a wide range of scanning scenarios. Extensive experiments on both simulated and real-world datasets demonstrate the superiority of our unsupervised Diner over popular supervised methods in terms of MAR performance and robustness.

Figures (14)

• Figure 1: MAC curves of different materials over the X-ray energy range $E$ of [20, 100] KeV. The data is from the XCOM database berger2009xcom.
• Figure 2: Overview of the proposed Diner model. For an X-ray $\mathbf{r}$, we first sample a set of coordinates $\mathbf{x}$ at a fixed interval $\Delta\mathbf{x}$. Then, we feed these coordinates $\mathbf{x}$ into an MLP network $g_\phi$ to predict the densities $\sigma(\mathbf{x})$ of the observed object at these positions. Furthermore, we use the proposed nonlinear forward model $\mathcal{T}$ (Eq. \ref{['eq: full-forward-model']}) to transform these MLP-predicted densities $\sigma(\mathbf{x}), \forall\mathbf{x}\in\mathbf{r}$ into measurement data $\hat{\rho}(\mathbf{r})$. Specifically, these densities $\sigma(\mathbf{x})$ are first converted into polychromatic LACs $\{\mu(\mathbf{x}, E_i)\}_{i=1}^N$ using our LAC decomposition model (Eq. \ref{['eq: lacs-density']}). Then, the measurement $\hat{p}(\mathbf{x})$ is generated from these LACs using the polychromatic model (Eq. \ref{['eq: dis-forward-model']}). Finally, we minimize the predicted errors $\mathcal{L}_\text{DC}$ between the estimated $\hat{\rho}(\mathbf{r})$ and raw $\rho(\mathbf{r})$ measurements to optimize the trainable weights of the MLP network $g_\phi$ for learning the density neural representation.
• Figure 3: a) A commercial Bruker SKYSCAN 1276 micro-CT scanner used in our mouse tight data acquisition and b) A commercial UIH uCT 768 scanner used in our body phantom data acquisition.
• Figure 4: Qualitative results of four compared methods and our Diner on two samples (#100 (top-two rows) and #50 (bottom-two rows)) of the DeepLesion deeplesion and LIDC LIDC datasets. The red regions denote metals.
• Figure 5: (Left) A sample among 2D projections for a mouse-thigh sample containing an intramedullary needle. (Right) Qualitative results of NRECON (i.e., a reconstruction toolkit developed by Bruker and equipped with Bruker SKYSCAN 1276 micro-CT scanner) and our Diner on the needle-corrupted measurement. The reference image is the clear version of the mouse thigh sample after removing the intramedullary needle. The white regions denote the intramedullary needle.

Theorems & Definitions (2)

• Remark 1
• Remark 2