Computer Tomography (CT) is one of the widely used methods for diagnosis in medical, exploration and surveying systems. In most applications of CT, a full set of line-integral projections over a total view of 180° is obtained and hence an artifact free image can be reconstructed. However, in some situations, due to physical constraints, only limited views of projections can be obtained. This is called the missing-cone problem. In this thesis, we propose a novel method to extrapolate data in the missing region by using the spectral information of a complete set of projections (sinogram) and the non-uniform sampling method. A sampling scheme for the missing-cone problem is presented. A general matrix formulation which incorporates the result of the sampling scheme, the spectral and the sp...[ Read more ]

Computer Tomography (CT) is one of the widely used methods for diagnosis in medical, exploration and surveying systems. In most applications of CT, a full set of line-integral projections over a total view of 180° is obtained and hence an artifact free image can be reconstructed. However, in some situations, due to physical constraints, only limited views of projections can be obtained. This is called the missing-cone problem. In this thesis, we propose a novel method to extrapolate data in the missing region by using the spectral information of a complete set of projections (sinogram) and the non-uniform sampling method. A sampling scheme for the missing-cone problem is presented. A general matrix formulation which incorporates the result of the sampling scheme, the spectral and the spatial constraints of a sinogram is derived. Then, this is posed as a least square minimization problem. An iterative algorithm is employed to solve this minimization problem. Besides, a linear extrapolator which is based on our sampling scheme is also proposed to generate the missing part of the sinogram. Computer simulation results show that the quality of sinograms restored by our methods is comparable to that of sinograms restored by other commonly used methods.