The paper describes a new accurate two-dimensional (2D) image reconstruction method consisting of two steps. In the first step, the backprojected image is formed after taking the derivative of the parallel projection data. In the second step, a Hilbert filtering is applied along certain lines in the differentiated backprojection (DBP) image. Formulae for performing the DBP step in fanbeam geometry are also presented. The advantage of this two-step Hilbert transform approach is that in certain situations, regions of interest (ROIs) can be reconstructed from truncated projection data. Simulation results are presented that illustrate very similar reconstructed image quality using the new method compared to standard filtered backprojection, and that show the capability to correctly handle truncated projections. In particular, a simulation is presented of a wide patient whose projections are truncated laterally yet for which highly accurate ROI reconstruction is obtained.

This paper describes a flexible new methodology for accurate cone beam reconstruction with source positions on a curve (or set of curves). The inversion formulas employed by this methodology are based on first backprojecting a simple derivative in the projection space and then applying a Hilbert transform inversion in the image space. The local nature of the projection space filtering distinguishes this approach from conventional filtered-backprojection methods. This characteristic together with a degree of flexibility in choosing the direction of the Hilbert transform used for inversion offers two important features for the design of data acquisition geometries and reconstruction algorithms. First, the size of the detector necessary to acquire sufficient data for accurate reconstruction of a given region is often smaller than that required by previously documented approaches. In other words, more data truncation is allowed. Second, redundant data can be incorporated for the purpose of noise reduction. The validity of the inversion formulas along with the application of these two properties are illustrated with reconstructions from computer simulated data. In particular, in the helical cone beam geometry, it is shown that 1) intermittent transaxial truncation has no effect on the reconstruction in a central region which means that wider patients can be accommodated on existing scanners, and more importantly that radiation exposure can be reduced for region of interest imaging and 2) at maximum pitch the data outside the Tam-Danielsson window can be used to reduce image noise and thereby improve dose utilization. Furthermore, the degree of axial truncation tolerated by our approach for saddle trajectories is shown to be larger than that of previous methods.

This paper is about helical cone-beam reconstruction using the exact filtered backprojection formula recently suggested by Katsevich (2002a Phys. Med. Biol. 47 2583-97). We investigate how to efficiently and accurately implement Katsevich's formula for direct reconstruction from helical cone-beam data measured in two native geometries. The first geometry is the curved detector geometry of third-generation multi-slice CT scanners, and the second geometry is the flat detector geometry of C-arms systems and of most industrial cone-beam CT scanners. For each of these two geometries, we determine processing steps to be applied to the measured data such that the final outcome is an implementation of the Katsevich formula. These steps are first described using continuous-form equations, disregarding the finite detector resolution and the source position sampling. Next, techniques are presented for implementation of these steps with finite data sampling. The performance of these techniques is illustrated for the curved detector geometry of third-generation CT scanners, with 32, 64 and 128 detector rows. In each case, resolution and noise measurements are given along with reconstructions of the FORBILD thorax phantom.

In this paper, three exact formulae are derived for cone-beam reconstruction with source positions on a curve or set of curves. For reconstruction at a single point, these formulae all operate by applying a filtration step followed by a backprojection step to cone-beam data. The filtering is performed along a 1D curve which is defined as the intersection of the detector surface with a filtering plane. Two of these formulae allow a flexibility in the choice of the filtering direction. In some cases, this flexibility allows the efficiency of volume reconstruction to be improved. Alternatively, the flexibility can be used to reduce the detector size necessary to avoid truncation artefacts in the reconstruction or to change the noise properties of the reconstruction.