Efficient Algorithms for Inversion of Cone Beam Data for General Trajectories

The University Of Central Florida Board Of Trustees, Orlando FL

Investigators

Abstract

Award abstract 0505494, Alexander Katsevich, University of Central Florida Title: Efficient algorithms for inversion of cone beam data for general trajectories ABSTRACT The Principal Investigator (PI) plans to develop practical image reconstruction algorithms for inverting the cone beam transform in the cases when the x-ray source moves along trajectories, such as circle-and-arc, saddle, etc. It is expected that the new algorithms will be theoretically exact and efficient (i.e., with the Filtered Backprojection structure). In addition to algorithm development, the PI plans to perform theoretical analysis of the algorithms. As opposed to the Radon transform, inversion of the cone beam transform in the three dimensional Euclidean space is a complicated problem. Not much is known about the properties of exact inversion algorithms. Do they generalize to distributions? What is the stability of reconstruction in the scale of Sobolev spaces? What are possible artifacts in the case of non-perfect data? These are some of the questions that the PI plans to address. The proposed research is of practical significance, because the cone beam transform is a theoretical foundation of computer tomography (CT). The main principle of CT is based on transmitting a cone beam of x-rays through the patient from various directions. This is achieved by moving the x-ray source along a predetermined trajectory. For each source position a detector measures the intensity of the beam as it exits the patient. Then the data are inverted according to a mathematical algorithm. CT scans can be performed using a gantry or a C-arm. The circle-and-arc trajectory may arise when the scanner is a portable C-arm. There is a significant need for volumetric visualization using portable C-arms. The prime application is for image-guided interventional procedures requiring intraoperative imaging, in which moving the patient is to be avoided. The advantage of portable C-arms is that they can be moved into the room where the patient is undergoing the procedure. Saddle trajectories may be of interest for cardiac imaging. The theoretical component of the proposed research will result in a deeper understanding of cone beam transform inversion for general trajectories.