# A Rigid Motion Artifact Reduction Method for CT Based on Blind Deconvolution
## 1 Introduction  
As one of the important technologies in medical diagnosis, a CT image can achieve a high performance in detecting and measuring small lesions [1; 2]. However, CT has a problem that the reconstructed image will suffer from motion artifacts if a moving object is reconstructed without motion correction, in severe cases resulting in false diagnosis [3]. To reduce motion artifacts, the main approaches are shortening the scan time [4; 5], external motion monitoring techniques [6; 7; 8], and motion estimation and compensation methods [9]. Since the third category of methods has the advantages of neither increasing hardware cost or design difficulty nor requiring additional devices, it has been widely studied. Among these methods, some were intended for 2D parallel-beam or fan-beam geometries and needed to assume a motion model that is an approximation of the real motion [9; 10; 11]. In [9], a novel method based on the Helgason-Ludwig consistency condition (HLCC) for estimation of rigid motion in fan-beam geometry was presented. Once the motion has been estimated, a compensation for the motion can be performed. This method has the disadvantages of large computational complexity and poor estimation accuracy. To solve this problem, a new method based on frequency domain analysis was proposed [10]. Motion parameters can be determined by the magnitude correlation of projections in frequency domain. This method was more accurate and faster on the performance ofmotion estimation than the method based on the HLCC. Using this method, a new method based on extended difference function was proposed, which further reduced the complexity of computation [11]. However, these three methods can only achieve in-plane motion estimation, which has limitations in clinical application. Some addressed the problem for cone beam CT (CBCT), but only for CBCT [12; 13]. Other methods iteratively estimated and compensated the motion during the reconstruction for head CT when head motion occurs in all six degrees of freedom (d.o.f.). [PERSON] et al. devised an iterative motion estimation and compensation scheme for helical CT [14]. [PERSON] et al. proposed a motion estimation and compensation method based on filtered back projection for CBCT [15]. [PERSON] et al. presented a motion artifact correction method based on local linear embedding for CBCT [16]. However, these methods cannot always estimate the motion parameters accurately, since the pose of the reconstructed object is arbitrary and slow components of the motions may not be fully estimated. Therefore, the goal of this paper is to develop a motion artifact reduction method that does not need to estimate the motion and can be suitable for any scanning mode. The aim of blind deconvolution (BD) is to recover an image without complete knowledge of the associated system function, which has been widely applied in medical images to improve the quality of images [17]. However, the deconvolution does not converge to the solution because the noise is amplified after iterations [18; 19; 20]. With the purpose of avoiding degradation of the image quality, recent works use the spatially adaptive total variation (SATV) as a regularization term [21]. A motion-blurred CT image can be considered as a convolution of a degraded system and original image. Therefore, the true image can be estimated from the blurred image using iterative blind deconvolution. The reason for selecting the image domain over the sinogram domain is because motion effects are better understood and motion trajectories are more tractable to model in the image space. In fact, motion artifacts are mainly manifested in strip artifacts, blurred tissue images, displacement of image contours and objects with similar attachments in the cavity. Thus, this paper develops a motion artifact reduction approach based on iterative blind deconvolution for CT image. The rigid motion is characterized by six d.o.f. (three rotations and three translations) [7].