Artifacts reduction in 4D-CBCT via a joint free-form registration method of projection match and gradient constraint

4D-CBCT reconstruction technique could provide a sequence of phase-resolved images to alleviate motion blurring artifacts as a result of respiratory movement during CT scanning. However, 4D-CBCT images are degraded by streaking artifacts due to the under-sampled projection used for the reconstruction of each phase. Based on the high correlation of these 4D-CBCT images, estimating the deformation vector fields (DVF) among them via a deformable registration algorithm is one of the possible solutions to improve the image quality. Often, the intensity-based similarity metric is utilized in the optimization problem by minimizing the squared sum of intensity differences (SSD) of the reference image and the target image. However, this metric is not suitable for the 4D-CBCT registration case, because the quality of both the reference image and the target image are not always guaranteed. As a result, the registration accuracy of the conventional SSD metric still has room to improve. In our method, by considering the characteristic of the phase-depended images, we design a novel similarity metric: 1) A prior image reconstructed by the whole projection set is regarded as the reference image; 2) Instead of an intensity-based similarity metric alone, we proposed a free-form based optimization function associating the gradient information in spatial domain with the projection-based constraint. To validate the performance of the proposed method, we carried out a phantom data and a patient data to compare with the classical Demons algorithm. To be specific, the quality of the registered image was improved to a great extent, especially in regions of interest of moving tissues. Quantitative evaluations were shown in terms of the rooted mean square error (RMSE) by our method when compared with existing Demons method.