  Emerging unsupervised reconstruction techniques based on implicit neural
representation (INR), such as NeRP, CoIL, and SCOPE, have shown unique
capabilities in CT linear inverse imaging. In this work, we propose a novel
unsupervised density neural representation (Diner) to tackle the challenging
problem of CT metal artifacts when scanned objects contain metals. The drastic
variation of linear attenuation coefficients (LACs) of metals over X-ray
spectra leads to a nonlinear beam hardening effect (BHE) in CT measurements.
Recovering CT images from metal-affected measurements therefore poses a
complicated nonlinear inverse problem. Existing metal artifact reduction (MAR)
techniques mostly formulate the MAR as an image inpainting task, which ignores
the energy-induced BHE and produces suboptimal performance. Instead, our Diner
introduces an energy-dependent polychromatic CT forward model to the INR
framework, addressing the nonlinear nature of the MAR problem. Specifically, we
decompose the energy-dependent LACs into energy-independent densities and
energy-dependent mass attenuation coefficients (MACs) by fully considering the
physical model of X-ray absorption. Using the densities as pivot variables and
the MACs as known prior knowledge, the LACs can be accurately reconstructed
from the raw measurements. Technically, we represent the unknown density map as
an implicit function of coordinates. Combined with a novel differentiable
forward model simulating the physical acquisition from the densities to the
measurements, our Diner optimizes a multi-layer perception network to
approximate the implicit function by minimizing predicted errors between the
estimated and real measurements. Experimental results on simulated and real
datasets confirm the superiority of our unsupervised Diner against popular
supervised techniques in MAR performance and robustness.
