Cone-beam computed tomography (CBCT) is a technique for imaging cross-sections of an object using a series of X-ray
measurements taken from different angles around the object. It has been widely applied in diagnostic medicine and industrial non-destructive testing. Traditional CT reconstructions are limited by many kinds of artifacts, and they give dissatisfactory image. To reduce image noise and artifacts, we propose a statistical iterative approach for cone-beam CT reconstruction. First the theory of maximum likelihood estimation is extended to X-ray scan, and an expectation-maximization (EM) formula is deduced for direct reconstruction of circular orbit cone-beam CT. Then the EM formula is implemented in cone-beam geometry for artifact reduction. EM algorithm is a feasible iterative method, which is based on the statistical properties of Poisson distribution. It can provide good quality reconstructions after a few iterations for cone-beam CT. In the end, experimental results with computer simulated data and real CT data are presented to verify our method is effective.
Traditional computed tomography reconstructions are limited by many kinds of artifacts. In general, they give dissatisfactory image. To reduce image noise and artifacts, we propose an iterative approach processing these reconstructed images, which are acquired by analytical inversion methods. In this paper, we describe ordered subsets expectation maximization (OS-EM) algorithms. Our reconstruction algorithm is based on a maximum a posteriori (MAP) approach, which allows us to incorporate priori information to stabilize the EM algorithm. The OS-EM algorithm provides good quality reconstructions after only a few iterations, yet beyond a critical number of iterations, the artifact is magnified due to inherent instability problem of OS-EM. To overcome this problem, we estimate the number of iterations by using priori information, the priori information is the blank region in the projection data resulting from a part of X-ray's air scan. In ideal case these corresponding regions in reconstructed image should also be blank. But in practice, they are not blank any more due to containing noise and artifacts. Based on this prior information, we can obtain an optimum number of iterations in the small air scan region. We process the whole estimated image with the same number of iterations. The two processes are carried on at the same time. Then the resulting image is considered as the best restoration of the original image. Experiments show that by our method, the artifacts and noise can be greatly suppressed and the contrast can be significantly improved.