Simultaneous motion estimation and image reconstruction (SMEIR) for 4D cone‐beam CT

Purpose: Image reconstruction and motion model estimation in four‐dimensional cone‐beam CT (4D‐CBCT) are conventionally handled as two sequential steps. Due to the limited number of projections at each phase, the image quality of 4D‐CBCT is degraded by view aliasing artifacts, and the accuracy of subsequent motion modeling is decreased by the inferior 4D‐CBCT. The objective of this work is to enhance both the image quality of 4D‐CBCT and the accuracy of motion model estimation with a novel strategy enabling simultaneous motion estimation and image reconstruction (SMEIR). Methods: The proposed SMEIR algorithm consists of two alternating steps: (1) model‐based iterative image reconstruction to obtain a motion‐compensated primary CBCT (m‐pCBCT) and (2) motion model estimation to obtain an optimal set of deformation vector fields (DVFs) between the m‐pCBCT and other 4D‐CBCT phases. The motion‐compensated image reconstruction is based on the simultaneous algebraic reconstruction technique (SART) coupled with total variation minimization. During the forward‐ and backprojection of SART, measured projections from an entire set of 4D‐CBCT are used for reconstruction of the m‐pCBCT by utilizing the updated DVF. The DVF is estimated by matching the forward projection of the deformed m‐pCBCT and measured projections of other phases of 4D‐CBCT. The performance of the SMEIR algorithm is quantitatively evaluated on a 4D NCAT phantom. The quality of reconstructed 4D images and the accuracy of tumor motion trajectory are assessed by comparing with those resulting from conventional sequential 4D‐CBCT reconstructions (FDK and total variation minimization) and motion estimation (demons algorithm). The performance of the SMEIR algorithm is further evaluated by reconstructing a lung cancer patient 4D‐CBCT. Results: Image quality of 4D‐CBCT is greatly improved by the SMEIR algorithm in both phantom and patient studies. When all projections are used to reconstruct a 3D‐CBCT by FDK, motion‐blurring artifacts are present, leading to a 24.4% relative reconstruction error in the NACT phantom. View aliasing artifacts are present in 4D‐CBCT reconstructed by FDK from 20 projections, with a relative error of 32.1%. When total variation minimization is used to reconstruct 4D‐CBCT, the relative error is 18.9%. Image quality of 4D‐CBCT is substantially improved by using the SMEIR algorithm and relative error is reduced to 7.6%. The maximum error (MaxE) of tumor motion determined from the DVF obtained by demons registration on a FDK‐reconstructed 4D‐CBCT is 3.0, 2.3, and 7.1 mm along left–right (L‐R), anterior–posterior (A‐P), and superior–inferior (S‐I) directions, respectively. From the DVF obtained by demons registration on 4D‐CBCT reconstructed by total variation minimization, the MaxE of tumor motion is reduced to 1.5, 0.5, and 5.5 mm along L‐R, A‐P, and S‐I directions. From the DVF estimated by SMEIR algorithm, the MaxE of tumor motion is further reduced to 0.8, 0.4, and 1.5 mm along L‐R, A‐P, and S‐I directions, respectively. Conclusions: The proposed SMEIR algorithm is able to estimate a motion model and reconstruct motion‐compensated 4D‐CBCT. The SMEIR algorithm improves image reconstruction accuracy of 4D‐CBCT and tumor motion trajectory estimation accuracy as compared to conventional sequential 4D‐CBCT reconstruction and motion estimation.