The Research On Image Reconstruction From Limited Angle Data In X-ray Imaging Technique

X-ray imaging technique has made a revolutionary impact on medical diagnosis and industrial non-destructive testing. It is not always possible to acquire projection data through a complete angular range in CT and tomosynthesis in real applications. Some examples would be X-ray dose limitations, or imaging system design constraints when imaging a moving object, or X-rays being obstructed when passing through high-density region of objects, any of which could result in loss of some projections. When projection data are only available in a limited angular range, as occurs in a number of applications in dental radiology, surgical imaging, thoracic imaging, mammography, etc. The conventional and most commonly used method for reconstruction from tomographic projections is the analytical reconstruction technique which is not so adaptable to incomplete projection data and results in poor reconstructions with severe artifacts in limited angle cases. One approach of overcoming the insufficient projections is to reconstruct the object by making use of iterative method. This dissertation is focused on image reconstructions when projection data is insufficient in limited angle range. Our results can be summarized into the following:(1) Considering the advantages of the total variation(TV) method, the paper introduced an iterative image reconstruction algorithm based on multiplicative regularization method.The method obtains the advantages of the TV method by introducing the TV as a multiplicative factor in the cost function, and it can also self-adaptively adjust the regularization parameter during the iterative process. Experimental results show that the proposed algorithm works effectively.(2) We propose the double constraint method to overcome data insufficiency based on non-quadratic penalties method. A classical method for solving limited angle tomogramphy is regularization with a quadratic penalty function in CT. However, this regularization method has a tendency of smoothing those sharp edges in solutions that often carry important information. The proposed method provides us a robust and efficient reconstruction by showing the convergence of the alternating minimization method. The results demonstrate that the reconstruction strategy has a comparable performance.(3) Considering the adavantages of the non-quadratic penalties method, a new TV objective function minimization is proposed for treatment of the limited angle tomography in this paper. The objective function minimization provided us a robust and efficient reconstruction without artificial parameters in iterative processes, by includeing the advantage of the non-quadratic penalties method. The results demonstrate that the reconstruction strategy can give good edge-preserving reconstructions.(4) Some research groups have been studing tomosynthesis reconstruction algorithm as well as its applications in recent years. The long calculation requirements of tomosynthesis reconstruction algorithm, however, limit its commercialization. In this paper, an adaptive wavelet galerkin method is introduced to reconstruct images in tomosynthesis. The method combined the numerical simplicity of Galerkin method with the inherent scale multiplicity characteristic of wavelet which is more adaptable to the resolution of the reconstructed image. Compared to the ART reconstruction, the results demonstrate that the reconstruction strategy has comparable performance with the improvement of the convergence speed and the reduction of computational time.