3-D image reconstruction in radiology

In this course, we present highlights on fully 3-D image reconstruction algorithms used in 3-D X-ray Computed Tomography (3-D-CT) and 3-D Rotational Radiography (3-D-RR). We first consider the case of spiral CT with a one-row detector. Starting from the 2-D fan-beam inversion formula for a circular trajectory, we introduce spiral CT 3-D image reconstruction algorithm using axial interpolation for each transverse slice. In order to improve the X-ray detection efficiency and to speed the acquisition process, the future is to use multi-row detectors associated with small angle cone-beam geometry. The generalization of the 2-D fan-beam image reconstruction algorithm to cone beam defined direct inversion formula referred as Feldkamp's algorithm for a circular trajectory and Wang's algorithm for a spiral trajectory. However, large area detectors does exist such as Radiological Image Intensifiers or in a near future solid state detectors. To get a larger zoom effect, it defines a cone-beam geometry associated with a large aperture angle. For this case, we introduce indirect image reconstruction algorithm by plane re-binning in the Radon domain. We will present some results from a prototype MORPHOMETER device using the RADON reconstruction software. Lastly, we consider the special case of 3-D Rotational Digital Subtraction Angiography with a restricted number of views. We introduce constraint optimization algorithm using quadratic, entropic or half-quadratic constraints. Generalized ART (Algebraic Reconstruction Technique) iterative reconstruction algorithm can be derived from the Bregman algorithm. We present reconstructed vascular trees from a prototype MORPHOMETER device. (author)