Elliptical Extrapolation of Truncated 2D CT Projections Using Helgason-Ludwig Consistency Conditions

Image reconstruction from truncated tomographic data is an important practical problem in CT in order to reduce the X-ray dose and to improve the resolution. The main problem with the Radon Transform is that in 2D the inversion formula globally depends upon line integrals of the object function. The standard Filtered Backprojection algorithm (FBP) does not allow any type of truncation. A typical strategy is to extrapolate the truncated projections with a smooth 1D function in order to reduce the discontinuity artefacts. The lowfrequency artifact reduction however, severely depends upon the width of the extrapolation, which is unknown in practice. In this paper we develop a modified ConTraSPECT-type method for specific use on truncated 2D CT-data, when only a local area (ROI) is to be imaged. The algorithm describes the shape and structure of the region surrounding the ROI by a specific object with only few parameters, in this paper a uniform ellipse. The parameters of this ellipse are optimized by minimizing the Helgason-Ludwig consistency conditions for the sinogram completed with Radon data of the ellipse. Simulations show that the MSE of the reconstructions is reduced significantly, depending on the type of truncation.