McSART: an iterative model-based, motion-compensated SART algorithm for CBCT reconstruction

4D cone beam computed tomography (CBCT) images of the thorax and abdomen can have reduced quality due to the limited number of projections per respiratory bin used in gated image reconstruction. In this work, we present a new algorithm to reconstruct high quality CBCT images by simultaneously reconstructing images and generating an associated respiratory motion model. This is done by updating model parameters to compensate for motion during the iterative image reconstruction process. CBCT image acquisition was simulated using the digital eXternal CArdiac Torso (XCAT) phantom, simulating breathing motion using four patient breathing traces. 4DCBCT images were reconstructed using the simultaneous algebraic reconstruction technique (SART), and compared to the proposed motion-compensated SART (McSART) algorithm. McSART used a motion model that describes tissue position as a function of diaphragm amplitude and velocity. The McSART algorithm alternately updated the motion model and image reconstruction, increasing the number of projections used for image reconstruction with every iteration. The model was able to interpolate and extrapolate deformations according to the magnitude of the surrogate signal. Without noise, the final iteration McSART images had HU errors at 31%, 34%, and 44% of their SART-reconstructed counterparts compared to ground truth XCAT images, with corresponding root-mean-square (RMS) motion model errors of 0.75 mm, 1.08 mm, and 1.17 mm respectively. With added image noise, McSART's HU error was 31% of the SART-reconstructed 4DCBCT error, with a 1.43 mm RMS motion model error. Qualitatively, blurring and streaking artifacts were reduced in all the reconstructed images compared to 3D or SART-reconstructed 4DCBCT. The output of the algorithm was a high quality reference image and a corresponding motion model, that could be used to deform the reference image to any other point in a breathing cycle.