On the Influence of Smoothness Constraints in Computed Tomography Motion Compensation

TL;DR

The problem is CT motion artifacts due to patient motion; the aim is to understand how smoothness constraints via spline-based parameterization of the six rigid motions ($t_x$, $t_y$, $t_z$, $r_x$, $r_y$, $r_z$) influence recoverable motion frequencies. The approach extends a prior rigid motion compensation method for cone-beam CT with Akima spline parameterization using $N_n$ nodes, leveraging a differentiable Jacobian and a neural-network quality metric within an autofocus-like optimization. Frequency analysis: conduct band-limitation experiments with cutoff $f_c$ and compare to the Nyquist limit $f_{max}=0.5\omega$ to map recoverable frequencies under different $N_n$. Findings: higher $N_n$ broadens the recoverable frequency range, while low-frequency performance is robust at smaller node counts; optimal choice depends on anatomy, clinical use, and scan protocol, guiding tailored smoothness constraints for accurate motion compensation in cone-beam CT. Significance: results guide tailoring the smoothness prior to the expected motion spectrum for accurate motion compensation in clinical cone-beam CT protocols.

Abstract

Computed tomography (CT) relies on precise patient immobilization during image acquisition. Nevertheless, motion artifacts in the reconstructed images can persist. Motion compensation methods aim to correct such artifacts post-acquisition, often incorporating temporal smoothness constraints on the estimated motion patterns. This study analyzes the influence of a spline-based motion model within an existing rigid motion compensation algorithm for cone-beam CT on the recoverable motion frequencies. Results demonstrate that the choice of motion model crucially influences recoverable frequencies. The optimization-based motion compensation algorithm is able to accurately fit the spline nodes for frequencies almost up to the node-dependent theoretical limit according to the Nyquist-Shannon theorem. Notably, a higher node count does not compromise reconstruction performance for slow motion patterns, but can extend the range of recoverable high frequencies for the investigated algorithm. Eventually, the optimal motion model is dependent on the imaged anatomy, clinical use case, and scanning protocol and should be tailored carefully to the expected motion frequency spectrum to ensure accurate motion compensation.

Figures (4)

• Figure 1: High level overview of the motion compensation algorithm studied in this paper.
• Figure 2: Exemplary motion patterns obtained after limiting a random signal to the cutoff frequency $f_c$. Motion patterns with a low cutoff frequency oscillate slower than those with high cutoff frequencies.
• Figure 3: Plot of the change in reprojection error (RPE) (left) and structural similarity index measure (SSIM) (right). Both are displayed as their ratio of after/before motion compensation. While smaller values for RPE and higher values for SSIM are better, respectively, a ratio close to 1 reflects no improvement after motion compensation for either metric. The ratio is drawn as a function of the cutoff frequency $f_c$ in the perturbing motion pattern. Note that the x-axis is scaled logarithmically from small to high frequencies. The maximum measurable frequencies according to the Nyquist-Shannon theorem are indicated by gray dashed lines for both spline types and the unconstrained setting. The two curves show the results obtained with splines with 30 nodes and 100 nodes for the estimated motion signal. 95% confidence intervals are computed over ten different scans.
• Figure 4: Reconstruction results for an axial slice of one example scan from three different cutoff frequencies for the perturbing motion pattern and a spline with 100 nodes for the estimated signal. The ground truth is identical for all three cases. Motion-compensated results appear best for the lowest frequency and worst for the highest frequency.