Region-of-interest reconstruction from truncated data by combined classical filtered-backprojection and virtual fanbeam reconstruction

Region-of-Interest (ROI) image reconstruction in two-dimensions is broadly based on the virtual fanbeam (VFB) method or on the more familiar method of differentiated backprojection (DBP) with Hilbert filtering. Although the VFB method is more complicated, it has the advantage of potentially handling some interior-type ROI problems that cannot be resolved by DBP-Hilbert methods. We have previously proposed combined filtered-backprojection (FBP) and VFB reconstruction for handling truncated projections, but with the constraint that the object support must lie within a known ellipse. However, this elliptical constraint is too restrictive for some truncation problems. In this work we have extended the FBP-VFB method to handle any convex support. The algorithm applies standard FBP filtering to all non-truncated parallel projections, and applies the VFB method to the truncated parallel projections which involves one-dimensional filtering that moves obliquely across the sinogram. We illustrate our method with a specific truncation problem for a thorax-like object support. Our example can not be resolved by other existing analytic methods.