THESIS
1994

v, 76 leaves : ill. ; 30 cm

**Abstract**
This thesis develops a new tomographic reconstruction method to reconstruct a sequence of good images of the cross section of a time-varying object. To obtain a good image of a time-varying object without motion artifacts one requires a large number of consistent projections equally spaced in angle. A set of projections are consistent if all the projections relate to the same x-ray absorptivity distribution. In practice, the scanning machine can only measure a few projections simultaneously. Since the distribution of the time-varying object is changing during the scanning procedure, a complete set of consistent projections for each distribution cannot be measured. To solve this problem, a new technique to extra.polate the missing consistent projections is developed in this study. To ove...[

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This thesis develops a new tomographic reconstruction method to reconstruct a sequence of good images of the cross section of a time-varying object. To obtain a good image of a time-varying object without motion artifacts one requires a large number of consistent projections equally spaced in angle. A set of projections are consistent if all the projections relate to the same x-ray absorptivity distribution. In practice, the scanning machine can only measure a few projections simultaneously. Since the distribution of the time-varying object is changing during the scanning procedure, a complete set of consistent projections for each distribution cannot be measured. To solve this problem, a new technique to extra.polate the missing consistent projections is developed in this study. To overcome the illposedness of this extrapolation problem, various a priori information of legitimate sinograms are explored and used as regularization constraints. The extrapolation is then posed as a least square optimization problem which has unique solution. An equivalent optimization problem is derived by introducing a dummy variable. By exploring the special structure of the problem and using the technique of alternating projection, a computationally efficient iterative algorithm is devised which independent of the initializations converges to the desired minimum. It is found that the least square problem can be mapped into an artificial neural network with special structure. Hence, the iterative algorithm can also be regarded as a training algorithm for this neural network. Finally, simulation results show that our method results in superior reconstruction as compared to the conventional method.

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