Implementation of a cone-beam reconstruction algorithm for the single-circle source orbit with embedded misalignment correction using homogeneous coordinates.

We present an efficient implementation of an approximate cone-beam image reconstruction algorithm for application in tomography, which accounts for scanner mechanical misalignment. The implementation is based on the algorithm proposed by Feldkamp et al. and is directed at circular scan paths. The algorithm has been developed for the purpose of reconstructing volume data from projections acquired in an experimental x-ray micro-tomography (microCT) scanner. To mathematically model misalignment we use matrix notation with homogeneous coordinates to describe the scanner geometry, its misalignment, and the acquisition process. For convenience analysis is carried out for x-ray CT scanners, but it is applicable to any tomographic modality, where two-dimensional projection acquisition in cone beam geometry takes place, e.g., single photon emission computerized tomography. We derive an algorithm assuming misalignment errors to be small enough to weight and filter original projections and to embed compensation for misalignment in the backprojection. We verify the algorithm on simulations of virtual phantoms and scans of a physical multidisk (Defrise) phantom.

A high-resolution phantom for MRI.

Assessment of spatial resolution is an important step to test the performance of new sequence techniques-especially ultrafast techniques with dedicated k-space trajectories or interpolation algorithms. Measurement of the modulation transfer function (MTF) is a rather difficult procedure, but using suitable resolution phantoms allows a simple visual evaluation of spatial resolution. In contrast to commonly used test objects with a very restricted number of resolution patterns we developed a phantom containing resolution patterns from 0.1 to 1.5 mm in steps of 0.1 mm. One resolution pattern consists of five parallel Plexiglas strips with the distance of the strips being equal to their thickness. Together with a Plexiglas cuboid the resolution patterns are mounted on a Plexiglas plate on the bottom of the cylindrical phantom. An aqueous solution of manganese chloride is used to fill the phantom. High resolution cross sections (pixel size: 50 microm) through the resolution patterns were measured to confirm the correct dimensions of the phantom. To verify the appropriateness of the 0.1 and 0.2 mm stacks micro-CT images with a pixel size of 25 microm were acquired additionally for both patterns. Besides visual inspection evaluation of the profile function of signal intensity across the stacks demonstrates that the resolution patterns are sufficiently correct. T(1)-weighted SE sequences with slightly different pixel sizes as well as T(1)- and T(2*)- weighted gradient echo sequences were applied to demonstrate some possible applications of this phantom. In conclusion, the proposed phantom is well suited to assess the spatial resolution qualitatively (i.e., visually) and quantitatively over a wide range in steps of 0.1 mm.