Practical statistical models for region-of-interest tomographic reconstruction and long object problem

This paper deals with reconstructing a small region- of-interest (ROI) of an object from non-truncated or truncated projection data by using statistical (iterative) methods. The imaging situations which we consider here can be classified into the following two scenarios. The first scenario is the case where non-truncated projection data is measured but only a small ROI needs to be reconstructed. The second scenario is the case where only truncated projection data passing through a ROI is measured and only the ROI needs to be reconstructed. When we blindly apply statistical methods to such cases, as described in the literature, the image matrix during the iteration must be large enough to contain the whole object (not only the ROI) even if the ROI to be reconstructed is small. This significantly increases the computational cost (approximately by a factor of the area of the whole object divided by the area of the ROI). Solutions to this problem have been investigated only very recently. We develop practical statistical models for the ROI reconstruction problem under the assumption that an initial estimate of the ROI image by an analytical method such as FBP or DBP is available. Thanks to a more rigorous treatment compared to the previous work, the proposed models are more accurate leading to significantly better noise properties as we demonstrate in the simulation study. Also, extending the proposed models to the 3D long object problem is discussed.