Determination of 3D PSFs from computed tomography reconstructed x-ray images of spherical objects and the effects of sphere radii.

Abstract

A method was developed to obtain three-dimensional (3D) point spread functions (PSFs) of reconstructed x-ray volumetric images using spheres of known diameters. The algorithm consists of a sphere localization step using template matching applied to the entire volume. Richardson Lucy (RL) deconvolution is used atypically to determine the PSF from the reconstructed x-ray image and a model of the sphere. The resulting PSF is arbitrary, that is, there are no assumptions of separability or symmetry. Oversampling is not used, and sample spacing matches the image. The effect of sphere radius on PSF estimate reproducibility is investigated. Phantoms were constructed by suspending five polytetrafluoroethylene (PTFE) spheres having known radii equal to 4.77, 7.95, 9.52, 12.68, and 19.53mm in an agar solution. The phantom included a 25μm steel wire to calculate a line spread function (LSF). The phantom was imaged and reconstructed with a Medtronic surgical O-Arm 23 times and a Toshiba Aquilion One computed tomography (CT) 20 times. A sharp reconstruction kernel exhibiting a nonmonotonic PSF was used with the Toshiba CT. PSFs and LSFs were computed for all of the images and repeated estimates were used to compute mean and standard deviation values for every point of the PSFs and LSFs. The PSFs from spheres were converted to LSFs and compared to the wire LSF. The standard deviations of the PSF estimates exhibit a decreasing trend as the sphere radius is increased. The PSF from the smallest 4.77mm sphere is the least reproducible. The normalized root mean square difference between the mean LSF derived from the 4.77mm radius sphere and the mean wire LSF is 2.0% for the O-arm and 1.2% for the CT. Richardson Lucy (RL) deconvolution provides a method to estimate generalized (no separability or other simplifying assumptions) 3D PSFs from spheres. X-ray noise in images acquired with typical clinical protocols cause noticeable variations in PSF estimates which can be mitigated by selecting larger spheres and combining PSF estimates from different images.