Truncated Data Problems In Helical Cone-Beam Tomography

Abstract

This report delves into two of the major truncated data problems in helical cone-beam tomography: Axial truncation and Lateral truncation. The problem of axial truncation, also classically known as the Long Object problem, was a major challenge in the development of helical scan tomography. Generalization of the Feldkamp method (FDK) for circular scan to the helical scan trajectory was known to give reasonable solutions to the problem. The FDK methods are approximate in nature and hence provide only approximate solution to the long object problem. Recently, many methods which provide exact solution to this problem have been developed the major breakthrough being the Katsevich’s algorithm which is exact, efficient and also requires lesser detector area compared to Feldkamp methods. The first part of the report deals with the implementation strategies for methods capable of handling axial truncation. Here, we specifically look at the exact and efficient Katsevich’s solution to long object problem and the class of approximate solutions provided by the generalized FDK formulae. The later half of the report looks at the lateral truncation problem and suggests new methods to handle such truncation in helical scan CT. Simulation results for reconstruction with laterally truncated projection data, assuming it to be complete, gives severe artifacts which even penetrates into the field of view (FOV). A row-by-row data completion approach using Linear Prediction is introduced for helical scan truncated data. An extension/improvement of this technique known as Windowed Linear Prediction approach is introduced. Efficacy of both these techniques are shown using simulation with standard phantoms. Various image quality measures for the resulting reconstructed images are used to evaluate the performance of the proposed methods against an already existing technique. Motivated by a study of the autocorrelation and partial autocorrelation functions of the projection data the use of a non-stationary linear model, the ARIMA model, is proposed for data completion. The new model is first validated in the 2D truncated data situation. Also a method of incorporating the parallel beam data consistency condition into this new method is considered. Performance evaluation of the new method with consistency condition shows that it can outperform the existing techniques. Simulation experiments show the efficacy of the ARIMA model for data completion in 2D as well as 3D truncated data scenario. The model is shown to work well for the laterally truncated helical cone-beam case.