Unsupervised Multi-Parameter Inverse Solving for Reducing Ring Artifacts in 3D X-Ray CBCT

TL;DR

This work reformulates RAR as a multi-parameter inverse problem, where the non-ideal responses of X-ray detectors are parameterized as solvable physical variables, and proposes Riner, a new unsupervised RAR method that outperforms existing SOTA supervised methods.

Abstract

Ring artifacts are prevalent in 3D cone-beam computed tomography (CBCT) due to non-ideal responses of X-ray detectors, substantially affecting image quality and diagnostic reliability. Existing state-of-the-art (SOTA) ring artifact reduction (RAR) methods rely on supervised learning with large-scale paired CT datasets. While effective in-domain, supervised methods tend to struggle to fully capture the physical characteristics of ring artifacts, leading to pronounced performance drops in complex real-world acquisitions. Moreover, their scalability to 3D CBCT is limited by high memory demands. In this work, we propose Riner, a new unsupervised RAR method. Based on a theoretical analysis of ring artifact formation, we reformulate RAR as a multi-parameter inverse problem, where the non-ideal responses of X-ray detectors are parameterized as solvable physical variables. Using a new differentiable forward model, Riner can jointly learn the implicit neural representation of artifact-free images and estimate the physical parameters directly from CT measurements, without external training data. Additionally, Riner is memory-friendly due to its ray-based optimization, enhancing its usability in large-scale 3D CBCT. Experiments on both simulated and real-world datasets show Riner outperforms existing SOTA supervised methods.

Figures (13)

• Figure 1: Illustration of 3D CBCT acquisition. An X-ray source emits cone-shaped beams that pass through objects and are received by a 2D detector array. Due to hardware limitations boas2012ct, the X-ray detectors can be ideal (accurate response), non-ideal (fluctuating response), or defective (no response).
• Figure 2: We propose Riner, an unsupervised method for reducing ring artifacts in 3D X-ray CBCT imaging. On a real-world Chicken foot sample (see Appendix) with image dimension of 512$\times$512$\times$80 and an ultra-high resolution of 60$\times$60$\times$60 $\mu$m3, acquired by a commercial Bruker SKYSCAN 1276 micro-CT scanner, our Riner effectively removes ring artifacts and reconstructs high-quality CT volumes, outperforming SOTA model-based algorithms (FDK fdk and Super vo2018Super) and SOTA supervised deep learning models (DeepRAR trapp2022deeprar and Restormer zamir2022restormer)
• Figure 3: Overview of the proposed Riner method. Given raw measurements $\widetilde{\rho}(\theta, s)$, an MLP network $f_\mathbf{\Phi}$ receives multiple spatial coordinates $\mathbf{x}$ along an X-ray path $L(\theta,s)$ as input and predicts the corresponding CT intensities $\mu(\mathbf{x})=f_{\mathbf{\Phi}}(\mathbf{x})$. These predicted intensities, $\mu(\mathbf{x}),\forall\mathbf{x}\in L(\theta,s)$, the response factor $\alpha_s$, and the mask $\beta_s$ are then used to generate estimated measurements $\widehat{\rho}(\theta, s)$ via a differentiable physical model $\boldsymbol{A}$ (Eq. \ref{['eq:physical_model']}). Finally, the MLP network $f_\mathbf{\Phi}$ and parameters $\alpha_s$, $\beta_s$ jointly are optimized by minimizing the loss function $\mathcal{L}$ (Eq. \ref{['eq:loss']}) without using any external data.
• Figure 4: Parameter estimations of our Riner on a sample ($\#$9) of DeepLesion dataset deeplesion.
• Figure 5: Qualitative results of our Riner and compared methods on two representative samples of three simulated datasets (2D FBCT DeepLesion deeplesion and 3D CBCT AAPM aapm).