Exact local regions-of-interest reconstruction in spiral cone-beam filtered-backprojection CT: numerical implementation and first image results

Abstract

In the long object problem it is intended to reconstruct exactly a region-of-interest (ROI) of an object from spiral cone beam data which covers the ROI and its nearest vicinity only. In the first paper in a series of two the theory of the local ROI method is derived using the filtered-backprojection approach. In the present second paper the demanding numerical implementation is described. The straightforward 4-step algorithm is applied. It mainly consists of explicit calculations of the derivatives of partial plane integrals of the object from line segments in the projection images. In the local ROI method grouping of line segments to particular (phi) -planes in 3-D Radon space is important. A rigorous grouping causes artifacts which can be avoided by a fuzzy correspondence of line segments to (phi) -planes. In the ROI the same image quality is achieved for a partial scan as for a full scan. However, the method suffers from high computational requirements. The filtering step can be speeded up by replacing the 4-step algorithm by convolution with spatially variant 1-D Hilbert transforms. An in-depth analysis of the empirical PSF of detector pixels filtered by the 4-step algorithm confirmed the theoretical results. Modifications for practical implementation are outlined which are subject to further investigations.