## 1 Introduction  
CT (computed tomography) images are widely used in clinical diagnosis [1]. However, radiation exposure and the associated risk of cancer for patients in CT scans have already been one of the focusing concerns for medical and scientific research. To reduce radiation dose in CT scans, the iterative reconstruction methods were concerned in CT reconstruction because the iterative reconstruction methods can reconstruct CT images with few numbers of measured projection. Furthermore, the fewer numbers of measured projection can be acquired by fast scanning, and thus, the radiation dose delivered to the patients can be decreased [2]. SART (simultaneous algebraic reconstruction technique) is an iterative image reconstruction method [3] and plays a significant role in the quality of CT image reconstruction. However, the SART reconstruction method is limited by Nyquist sampling theorem [4], and CT images cannot be reconstructed by the measured projection data that does not satisfy sampling conditions. To further reduce radiation dose and perform CT image reconstruction with fewer measured projection data, the compressed sensing (CS) theory has been used recently. Compressive sensing (CS) converts the images, embedded in a high dimensional space, into a sparse representation that lie in the space of significantly smaller dimensions [5]. Sparse representations can be obtained with fewer data. Then, the reconstructed image is obtained by sparse representation. Compressive sensing theory guarantees that CT image reconstruction can be implemented by fewer measured projection that does not satisfy the sampling theorem [6; 7; 8; 9; 10]. On the other hand, it is apparent that the measured projection data has been degraded not only by noise but also by a point spread function [11]. The degradation of the measured projection data will propagate unhampered artifact in reconstructed images. Nevertheless, in the case of fewer projection data or serious degradation, SART reconstruction will be ineffective or seriously affect the result of the diagnosis. Image restoration method, a mechanism for eliminating the influence of the point spread function, was inserted into the iterative CT image reconstruction technique to form an optimization problem [12]. This method is appropriate in certain settings when the point spread function is known, and the measured noisy projection data satisfies the Nyquist sampling theorem. As a rapidly developing iterative algorithm, the CS reconstruction algorithm can complete CT reconstruction with fewer data. TV (total variation) transform [13], and wavelet transform [14] are the two most commonly used sparse representation methods. However, these CS algorithms have not considered for the point spread function, and the degradation caused by the point spread function can seriously affect the quality of the reconstruction image. Blind image restoration [15; 16] is a method that estimates images and eliminates the influence of the point spread function when the point spread function is unknown. To solve the CT reconstruction problem based on CS when the point spread function is unknown, a blind image restoration technique was embedded into the iterative process of compressive sensing CT image reconstruction. At each iteration, the iterative output image is improved because blind image restoration is introduced into the algorithm. Correspondingly, the input of the next iteration will be improved, and the convergence of the whole algorithm will be accelerated. CT reconstruction problem based on CS with blind image restoration is an ill-posed problem [17]. Bayesian methods were used to solve the ill-posed problem. Bayesian methods can provide a variety of probability distribution prediction to estimate the parameters, which can achieve the estimation of uncertainties in the CT blind restoration reconstruction with good anti-noise performance. The probability distributions are adopted as regularization terms to constrain the solution space.