  Pulmonary respiratory motion artifacts are common in four-dimensional
computed tomography (4DCT) of lungs and are caused by missing, duplicated, and
misaligned image data. This paper presents a geodesic density regression (GDR)
algorithm to correct motion artifacts in 4DCT by correcting artifacts in one
breathing phase with artifact-free data from corresponding regions of other
breathing phases. The GDR algorithm estimates an artifact-free lung template
image and a smooth, dense, 4D (space plus time) vector field that deforms the
template image to each breathing phase to produce an artifact-free 4DCT scan.
Correspondences are estimated by accounting for the local tissue density change
associated with air entering and leaving the lungs, and using binary artifact
masks to exclude regions with artifacts from image regression. The
artifact-free lung template image is generated by mapping the artifact-free
regions of each phase volume to a common reference coordinate system using the
estimated correspondences and then averaging. This procedure generates a fixed
view of the lung with an improved signal-to-noise ratio. The GDR algorithm was
evaluated and compared to a state-of-the-art geodesic intensity regression
(GIR) algorithm using simulated CT time-series and 4DCT scans with clinically
observed motion artifacts. The simulation shows that the GDR algorithm has
achieved significantly more accurate Jacobian images and sharper template
images, and is less sensitive to data dropout than the GIR algorithm. We also
demonstrate that the GDR algorithm is more effective than the GIR algorithm for
removing clinically observed motion artifacts in treatment planning 4DCT scans.
Our code is freely available at https://github.com/Wei-Shao-Reg/GDR.
