Tomographic reconstruction from low resolution samples or limited-angle data is required in many fields including medical imaging, sonar and radar. Although these two situations are apparently different in nature, they both suffer from the imperfection, in quality or in angular completeness, of the projection samples. In this thesis, we present a unified sinogram restoration technique to solve these two problems by restoring another complete sinogram from the observed sinogram. By using two-dimensional sampling theory and the result by Rattey and Lindgen which shows that the spectral support of CT projection data is bowtie-shaped, matrix formulation is developed for each problem. Generalizing the two situations, they are posed as a least square minimization problem. This optimization p...[ Read more ]

Tomographic reconstruction from low resolution samples or limited-angle data is required in many fields including medical imaging, sonar and radar. Although these two situations are apparently different in nature, they both suffer from the imperfection, in quality or in angular completeness, of the projection samples. In this thesis, we present a unified sinogram restoration technique to solve these two problems by restoring another complete sinogram from the observed sinogram. By using two-dimensional sampling theory and the result by Rattey and Lindgen which shows that the spectral support of CT projection data is bowtie-shaped, matrix formulation is developed for each problem. Generalizing the two situations, they are posed as a least square minimization problem. This optimization problem is then implemented by a nonstandard neural network. A novel training algorithm is proposed to minimize a modified error criterion. Our technique does not require any a priori knowledge of the scanning object and can be applied to any set of projections data. Computer simulation results are presented to demonstrate the validity of the proposed technique.