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The use of an x-ray flat panel detector is increasingly becoming popular in 3D cone beam volume CT machines. Due to the deficient semiconductor array manufacturing process, the cone beam projection data are often corrupted by different types of abnormalities, which cause severe ring and radiant artifacts in a cone beam reconstruction image, and as a result, the diagnostic image quality is degraded. In this paper, a novel technique is presented for the correction of error in the 2D cone beam projections due to abnormalities often observed in 2D x-ray flat panel detectors. Template images are derived from the responses of the detector pixels using their statistical properties and then an effective non-causal derivative-based detection algorithm in 2D space is presented for the detection of defective and mis-calibrated detector elements separately. An image inpainting-based 3D correction scheme is proposed for the estimation of responses of defective detector elements, and the responses of the mis-calibrated detector elements are corrected using the normalization technique. For real-time implementation, a simplification of the proposed off-line method is also suggested. Finally, the proposed algorithms are tested using different real cone beam volume CT images and the experimental results demonstrate that the proposed methods can effectively remove ring and radiant artifacts from cone beam volume CT images compared to other reported techniques in the literature.

The ongoing development of easily accessible, fast optical readout tools promises to remove one of the barriers to acceptance of gel dosimetry as a viable tool in cancer clinics. This paper describes the characterization of a number of basic properties of the Vista cone beam CCD-based optical scanner, which can obtain high resolution reconstructed data in less than 20 min total imaging and reconstruction time. The suitability of a filtered back projection cone beam reconstruction algorithm is established for optically absorbing dosimeters using this scanner configuration. The system was then shown to be capable of imaging an optically absorbing media-filled 1 L polyethylene terephthalate (PETE) jar dosimeter to a reconstructed voxel resolution of 0.5 x 0.5 x 0.5 mm(3). At this resolution, more than 60% of the imaged volume in the dosimeter exhibits minimal spatial distortion, a measurement accuracy of 3-4% and the mean to standard deviation signal-to-noise ratio greater than 100 over an optical absorption range of 0.06-0.18 cm(-1). An inter-day scan precision of 1% was demonstrated near the upper end of this range. Absorption measurements show evidence of stray light perturbation causing artifacts in the data, which if better managed would improve the accuracy of optical readout. Cone beam optical attenuation measurements of scattering dosimeters, on the other hand, are nonlinearly affected by angled scatter stray light. Scatter perturbation leads to significant cupping artifacts and other inaccuracies that greatly limit the readout of scattering polymer gel dosimeters with cone beam optical CT.

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.

Retrospectively gated cardiac volume CT imaging has become feasible with the introduction of heart rate adaptive cardiac CT reconstruction algorithms. The development in detector technology and the rapid introduction of multi-row detectors has demanded reconstruction schemes which account for the cone geometry. With the extended cardiac reconstruction (ECR) framework, the idea of approximate helical cone beam CT has been extended to be used with retrospective gating, enabling heart rate adaptive cardiac cone beam reconstruction. In this contribution, the ECR technique is evaluated for systems with an increased number of detector rows, which leads to larger cone angles. A simulation study has been carried out based on a 4D cardiac phantom consisting of a thorax model and a dynamic heart insert. Images have been reconstructed for different detector set-ups. Reconstruction assessment functions have been calculated for the detector set-ups employing different rotation times, relative pitches and heart rates. With the increased volume coverage of large area detector systems, low-pitch scans become feasible without resulting in extensive scan times, inhibiting single breath hold acquisitions. ECR delivers promising image results when being applied to systems with larger cone angles.

This paper is about helical cone-beam reconstruction and the use of redundant data in the framework of two reconstruction methods. The first method is the approximate wedge reconstruction formula introduced by Tuy at the 3D meeting in 1999. The second method is a (exact) hybrid implementation of the exact filtered backprojection formula of Katsevich (2004 Adv. Appl. Math. at press) that combines filtering in the native cone-beam geometry with backprojection in the wedge geometry. The similarity of the two methods is explored and their image quality performance is compared for geometries with up to 112 detector rows. Furthermore, the concept of aperture weighting is introduced to allow the handling of variable amounts of redundant data. A reduction of motion artefacts using redundant data is demonstrated for geometries with 16, 32 and 112 detector rows using a pitch factor of 1.25. For scans with up to 100 rows, utilizing 50% of the redundant data provided excellent results without any introduction of cone-beam artefacts. For larger cone angles, an alternative approach that utilizes all available redundant data, even at reduced pitch factors, is suggested.

In modern computer tomography (CT) systems, the fast rotating gantry and the increased detector width enable 3D imaging of the heart. Cardiac volume CT has a high potential for non-invasive coronary angiography with high spatial resolution and short scan time. Due to the increased detector width, true cone beam reconstruction methods are needed instead of adapted 2D reconstruction schemes. In this paper, the extended cardiac reconstruction method is introduced. It integrates the idea of retrospectively gated cardiac reconstruction for helical data acquisition into a cone beam reconstruction framework. It leads to an efficient and flexible algorithmic scheme for the reconstruction of single- and multi-phase cardiac volume datasets. The method automatically adapts the number of cardiac cycles used for the reconstruction. The cone beam geometry is fully taken into account during the reconstruction process. Within this paper, results are presented on patient datasets which have been acquired using a 16-slice cone beam CT system.

We derive unified inversion formulae for the cone beam transform similar to the Radon transform. Reinterpreting Grangeat's formula we find a relation between the Radon transform of the gradient of the searched-for function and a quantity computable from cone beam data. This gives a uniqueness result for the cone beam transform of compactly supported functions under much weaker assumptions than the Tuy–Kirillov condition. Furthermore this relation leads to an exact formula for the direct calculation of derivatives of the density distribution; but here, similar to the classical Radon transform, complete Radon data are needed, hence the Tuy–Kirillov condition has to be imposed. Numerical experiments reported in Hahn B N et al (2013 Meas. Sci. Technol. 24 125601) indicate that these calculations are less corrupted by beam-hardening noise. Finally, we present flat detector versions for these results, which are mathematically less attractive but important for applications.

The mechanical motion of the gantry in conventional cone beam CT scanners restricts the speed of data acquisition in applications with near real time requirements. A possible resolution of this problem is to replace the moving source detector assembly with static parts that are electronically activated. An example of such a system is the Rapiscan Systems RTT80 real time tomography scanner, with a static ring of sources and axially offset static cylinder of detectors. A consequence of such a design is asymmetrical axial truncation of the cone beam projections resulting, in the sense of integral geometry, in severely incomplete data. In particular we collect data only in a fraction of the Tam–Danielsson window, hence the standard cone beam reconstruction techniques do not apply. In this work we propose a family of multi-sheet surface rebinning methods for reconstruction from such truncated projections. The proposed methods combine analytical and numerical ideas utilizing linearity of the ray transform to reconstruct data on multi-sheet surfaces, from which the volumetric image is obtained through deconvolution. In this first paper in the series, we discuss the rebinning to multi-sheet surfaces. In particular we concentrate on the underlying transforms on multi-sheet surfaces and their approximation with data collected by offset multi-source scanning geometries like the RTT. The optimal multi-sheet surface and the corresponding rebinning function are found as a solution of a variational problem. In the case of the quadratic objective, the variational problem for the optimal rebinning pair can be solved by a globally convergent iteration. Examples of optimal rebinning pairs are computed for different trajectories. We formulate the axial deconvolution problem for the recovery of the volumetric image from the reconstructions on multi-sheet surfaces. Efficient and stable solution of the deconvolution problem is the subject of the second paper in this series (Betcke and Lionheart 2013 Inverse Problems 29 115004).