Ray-driven Spectral CT Reconstruction Based on Neural Base-Material Fields

TL;DR

This work introduces neural base-material fields, a coordinate-based neural representation that parameterizes base-material attenuation as continuous 3D vectors, to address the ill-posed basis-material decomposition in spectral CT. By coupling a ray-driven forward model with an autodiff-based inverse problem and a discretized but continuous forward process, the method achieves high-resolution, artefact-resistant reconstructions without relying on traditional system matrices. The approach demonstrates robustness across noise, sparse-angle, and geometric-inconsistency scenarios, and extends to single-spectrum dual-material decomposition while delivering high-quality, resolution-independent material density images. Its self-supervised nature and compact network design offer practical advantages for spectral CT, with potential for fast, high-resolution material mapping in medical and industrial imaging.

Abstract

In spectral CT reconstruction, the basis materials decomposition involves solving a large-scale nonlinear system of integral equations, which is highly ill-posed mathematically. This paper proposes a model that parameterizes the attenuation coefficients of the object using a neural field representation, thereby avoiding the complex calculations of pixel-driven projection coefficient matrices during the discretization process of line integrals. It introduces a lightweight discretization method for line integrals based on a ray-driven neural field, enhancing the accuracy of the integral approximation during the discretization process. The basis materials are represented as continuous vector-valued implicit functions to establish a neural field parameterization model for the basis materials. The auto-differentiation framework of deep learning is then used to solve the implicit continuous function of the neural base-material fields. This method is not limited by the spatial resolution of reconstructed images, and the network has compact and regular properties. Experimental validation shows that our method performs exceptionally well in addressing the spectral CT reconstruction. Additionally, it fulfils the requirements for the generation of high-resolution reconstruction images.

Figures (16)

• Figure 1: Framework diagram of polychromatic projections for dual-material decomposition based on neural base-material fields. The network takes the coordinates $\mathbf{x}=(x,y,z)$ of sampling points along the ray $\mathbf{L}(l)$ as input and predicts the corresponding material densities $\mathbf{f}=(f_1,f_2)$. The network predicts the density that corresponds to this sampling point coordinates on the ray $\mathbf{L}(l)$ and calculates the polychromatic projection values $\hat{p}_{k,\mathbf{L}}$ along the path of $\mathbf{L}$ under the $k$-th spectrum using Eq.(\ref{['Eq6_']}). The loss between $\hat{p}_{k,\mathbf{L}}$ and the true projection $p_k$ is computed for backpropagation.
• Figure 2: Diagram illustrating the sampling points of X-rays. A right-handed coordinate system is established with the intersection point of the turntable axis and the perpendicular line from the X-ray source $S$ to the rotation axis as the origin. The $Z$ axis is parallel to the rotation axis, and the $Y$ axis points towards the X-ray source. $Ouv$ represents the detector coordinate system, where the u-axis and v-axis are parallel to the rows and columns of the detector, respectively, with the origin located at the centre of the detector. The line labelled $p'$ represents a ray at a certain angle. $SOD$ denotes the distance from the X-ray source to the rotation centre, $SDD$ denotes the distance from the X-ray source to the detector, and $H$ and $W$ represent the height and width of the detector. The radius $R$ of the Field of View is calculated as $R=\frac{SOD\cdot 0.5\cdot \min(H,W)}{\sqrt{SDD^2+(0.5\cdot \min(H,W))^2}}$.
• Figure 3: The architecture diagram illustrates the fan-beam neural base-material fields. Hidden layers, depicted in blue, indicate the vector dimensions within each block; blue arrows denote connections to ReLU activation functions, while black skip connections represent residual or shortcut connections.
• Figure 4: (a) Slice of the thorax phantom used in the numerical simulation; (b) X-ray spectra used in the numerical simulation.
• Figure 5: Reconstruction results of the noise-free data experiments