  Emerging neural reconstruction techniques based on tomography (e.g., NeRF,
NeAT, and NeRP) have started showing unique capabilities in medical imaging. In
this work, we present a novel Polychromatic neural representation (Polyner) to
tackle the challenging problem of CT imaging when metallic implants exist
within the human body. CT metal artifacts arise from the drastic variation of
metal's attenuation coefficients at various energy levels of the X-ray
spectrum, leading to a nonlinear metal effect in CT measurements. Recovering CT
images from metal-affected measurements hence poses a complicated nonlinear
inverse problem where empirical models adopted in previous metal artifact
reduction (MAR) approaches lead to signal loss and strongly aliased
reconstructions. Polyner instead models the MAR problem from a nonlinear
inverse problem perspective. Specifically, we first derive a polychromatic
forward model to accurately simulate the nonlinear CT acquisition process.
Then, we incorporate our forward model into the implicit neural representation
to accomplish reconstruction. Lastly, we adopt a regularizer to preserve the
physical properties of the CT images across different energy levels while
effectively constraining the solution space. Our Polyner is an unsupervised
method and does not require any external training data. Experimenting with
multiple datasets shows that our Polyner achieves comparable or better
performance than supervised methods on in-domain datasets while demonstrating
significant performance improvements on out-of-domain datasets. To the best of
our knowledge, our Polyner is the first unsupervised MAR method that
outperforms its supervised counterparts. The code for this work is available
at: https://github.com/iwuqing/Polyner.
