Statistical image reconstruction

Abstract

This thesis presents a statistical method for image reconstruction, which consists of two parts. In the first part, a new statistical approach which minimizes the second-order moment of an object is presented. The second-order moment indicates the variance and randomness in a statistical structure. By minimizing the second-order moment, the resulting image reflects a statistical structure suitable to the available projection data and is biased toward a flat gray structure in the non-available projection data. In the second part, improved statistical method in the case of incomplete projection data are presented. Statistical methods such as maximum entropy and minimum second-order moment reconstruct a degraded image from incomplete projection data, which results from missing portions of projection data. A way to reconstruct an artifact-free image is the estimation of missing data before reconstruction process and then reconstructs an image from the full set of projections that combine the estimated data with the available data. The maximum entropy and the minimum second-order moment algorithms among statistical method are improved by including the estimation of projection data for missing portions. The maximum entropy and the minimum second-order moment algorithms include iterative procedures. Improved algorithms perform the estimation for missing portions at each iteration, based on the fact that the missing informations for one view are included in the projections from different views.