A Grangeat-type half-scan algorithm for cone-beam CT

Modern CT and micro-CT scanners are rapidly moving from fan-beam toward cone-beam geometry. Half-scan CT algorithms are advantageous in terms of temporal resolution, and widely used in fan-beam and cone-beam geometry. While existing half-scan algorithms for cone-beam CT are in the Feldkamp framework, in this paper we compensate missing data explicitly in the Grangeat framework, and formulate a half-scan algorithm in the circular scanning case. The half-scan spans 180 degrees plus two cone angles that guarantee sufficient data for reconstruction of the midplane defined by the source trajectory. The smooth half-scan weighting functions are designed for the suppression of data inconsistency. Numerical simulation results are reported for verification of our formulas and programs. This Grangeat-type half-scan algorithm produces excellent image quality, without off-mid-plane artifacts associated with Feldkamp-type half-scan algorithms. The Grangeat-type half-scan algorithm seems promising for quantitative and dynamic biomedical applications of CT and micro-CT.     

Investigation of saddle trajectories for cardiac CT imaging in cone-beam geometry

This paper investigates cone-beam tomography for a wide class of x-ray source trajectories called saddles. In particular, a mathematical analysis of the number of intersections between a saddle and an arbitrary plane is given. This analysis demonstrates that axially truncated cone-beam projections acquired along a saddle can be used for exact reconstruction at any point in a large volume. The reconstruction can be achieved either using a new algorithm presented herein or using a formula recently introduced by Katsevich (2003 Int. J. Math. Math. Sci. 21 1305-21). The shape of the reconstructed volume and the properties of saddles make saddles attractive for cardiac imaging. Three examples of saddles are presented with a discussion of implementation on devices similar to modern C-arm systems and multislice CT scanners. Reconstruction with one of these saddles has been tested using computer-simulated data, with and without truncation. The imaged phantom for the truncated data is a FORBILD head phantom (representing the heart) that has been modified and embedded inside the FORBILD thorax phantom. The non-truncated data were generated by excluding the thorax. The reconstructed images demonstrate the accuracy of the mathematical results.     

A combination-weighted Feldkamp-based reconstruction algorithm for cone-beam CT

The combination-weighted Feldkamp algorithm (CW-FDK) was developed and tested in a phantom in order to reduce cone-beam artefacts and enhance cranio-caudal reconstruction coverage in an attempt to improve image quality when utilizing cone-beam computed tomography (CBCT). Using a 256-slice cone-beam CT (256CBCT), image quality (CT-number uniformity and geometrical accuracy) was quantitatively evaluated in phantom and clinical studies, and the results were compared to those obtained with the original Feldkamp algorithm. A clinical study was done in lung cancer patients under breath holding and free breathing. Image quality for the original Feldkamp algorithm is degraded at the edge of the scan region due to the missing volume, commensurate with the cranio-caudal distance between the reconstruction and central planes. The CW-FDK extended the reconstruction coverage to equal the scan coverage and improved reconstruction accuracy, unaffected by the cranio-caudal distance. The extended reconstruction coverage with good image quality provided by the CW-FDK will be clinically investigated for improving diagnostic and radiotherapy applications. In addition, this algorithm can also be adapted for use in relatively wide cone-angle CBCT such as with a flat-panel detector CBCT.     

Aperture weighted cardiac reconstruction for cone-beam CT

Multi-row detectors together with fast rotating gantries made cardiac imaging possible for CT. Due to the cardiac motion, ECG gating has to be integrated into the reconstruction of the data measured on a low pitch helical trajectory. Since the first multi-row scanners were introduced, it has been shown that approximative true cone-beam reconstruction methods are most suitable for the task of retrospectively gated cardiac volume CT. In this paper, we present the aperture weighted cardiac reconstruction (AWCR), which is a three-dimensional reconstruction algorithm of the filtered back-projection type. It is capable of handling all illumination intervals of an object point, which occur as a consequence of a low pitch helical cone-beam acquisition. Therefore, this method is able to use as much redundant data as possible, resulting in an improvement of the image homogeneity, the signal to noise ratio and the temporal resolution. Different optimization techniques like the heart rate adaptive cardiac weighting or the automatic phase determination can be adopted to AWCR. The excellent image quality achieved by AWCR is presented for medical datasets acquired with both a 40-slice and a 64-slice cone-beam CT scanner.     

Half-scan cone-beam CT fluoroscopy with multiple x-ray sources

To develop volumetric micro-CT fluoroscopy for small animal imaging, we have proposed a cone-beam system with multiple x-ray sources. In this paper, we extend Parker's single-source half-scan weighting scheme to the case of an odd number of x-ray sources that are equiangularly distributed, and apply it for half-scan Feldkamp-type reconstruction in this unique geometry. In the numerical simulation with the Shepp-Logan phantom, representative images indicate that the proposed half-scan Feldkamp-type algorithm produces temporal resolution significantly superior to that with a single x-ray source cone-beam system.     

A motion-compensated scheme for helical cone-beam reconstruction in cardiac CT angiography

Since coronary heart disease is one of the main causes of death all over the world, cardiac computed tomography (CT) imaging is an application of very high interest in order to verify indications timely. Due to the cardiac motion, electrocardiogram (ECG) gating has to be implemented into the reconstruction of the measured projection data. However, the temporal and spatial resolution is limited due to the mechanical movement of the gantry and due to the fact that a finite angular span of projections has to be acquired for the reconstruction of each voxel. In this article, a motion-compensated reconstruction method for cardiac CT is described, which can be used to increase the signal-to-noise ratio or to suppress motion blurring. Alternatively, it can be translated into an improvement of the temporal and spatial resolution. It can be applied to the entire heart in common and to high contrast objects moving with the heart in particular, such as calcified plaques or devices like stents. The method is based on three subsequent steps: As a first step, the projection data acquired in low pitch helical acquisition mode together with the ECG are reconstructed at multiple phase points. As a second step, the motion-vector field is calculated from the reconstructed images in relation to the image in a reference phase. Finally, a motion-compensated reconstruction is carried out for the reference phase using those projections, which cover the cardiac phases for which the motion-vector field has been determined.     

A rebinned backprojection-filtration algorithm for image reconstruction in helical cone-beam CT

In the last few years, mathematically exact algorithms, including the backprojection-filtration (BPF) algorithm, have been developed for accurate image reconstruction in helical cone-beam CT. The BPF algorithm requires minimum data, and can reconstruct region-of-interest (ROI) images from data containing truncations. However, similar to other existing reconstruction algorithms for helical cone-beam CT, the BPF algorithm involves a backprojection with a spatially varying weighting factor, which is computationally demanding and, more importantly, can lead to undesirable numerical properties in reconstructed images. In this work, we develop a rebinned BPF algorithm in which the backprojection invokes no spatially varying weighting factor for accurate image reconstruction from helical cone-beam projections. This rebinned BPF algorithm is computationally more efficient and numerically more stable than the original BPF algorithm, while it also retains the nice properties of the original BPF algorithm such as minimum data requirement and ROI-image reconstruction from truncated data. We have also performed simulation studies to validate and evaluate the rebinned BPF algorithm.     

A backprojection-filtration algorithm for nonstandard spiral cone-beam CT with an n-PI-window

For applications in bolus-chasing computed tomography (CT) angiography and electron-beam micro-CT, the backprojection-filtration (BPF) formula developed by Zou and Pan was recently generalized by Ye et al to reconstruct images from cone-beam data collected along a rather flexible scanning locus, including a nonstandard spiral. A major implication of the generalized BPF formula is that it can be applied for n-PI-window-based reconstruction in the nonstandard spiral scanning case. In this paper, we design an n-PI-window-based BPF algorithm, and report the numerical simulation results with the 3D Shepp-Logan phantom and Defrise disk phantom. The proposed BPF algorithm consists of three steps: cone-beam data differentiation, weighted backprojection and inverse Hilbert filtration. Our simulated results demonstrate the feasibility and merits of the proposed algorithm.     

A three-dimensional reconstruction algorithm for an inverse-geometry volumetric CT system

An inverse-geometry volumetric computed tomography (IGCT) system has been proposed capable of rapidly acquiring sufficient data to reconstruct a thick volume in one circular scan. The system uses a large-area scanned source opposite a smaller detector. The source and detector have the same extent in the axial, or slice, direction, thus providing sufficient volumetric sampling and avoiding cone-beam artifacts. This paper describes a reconstruction algorithm for the IGCT system. The algorithm first rebins the acquired data into two-dimensional (2D) parallel-ray projections at multiple tilt and azimuthal angles, followed by a 3D filtered backprojection. The rebinning step is performed by gridding the data onto a Cartesian grid in a 4D projection space. We present a new method for correcting the gridding error caused by the finite and asymmetric sampling in the neighborhood of each output grid point in the projection space. The reconstruction algorithm was implemented and tested on simulated IGCT data. Results show that the gridding correction reduces the gridding errors to below one Hounsfield unit. With this correction, the reconstruction algorithm does not introduce significant artifacts or blurring when compared to images reconstructed from simulated 2D parallel-ray projections. We also present an investigation of the noise behavior of the method which verifies that the proposed reconstruction algorithm utilizes cross-plane rays as efficiently as in-plane rays and can provide noise comparable to an in-plane parallel-ray geometry for the same number of photons. Simulations of a resolution test pattern and the modulation transfer function demonstrate that the IGCT system, using the proposed algorithm, is capable of 0.4 mm isotropic resolution. The successful implementation of the reconstruction algorithm is an important step in establishing feasibility of the IGCT system.     

A comparison of x-ray detectors for mouse CT imaging

There is significant interest in using computed tomography (CT) for in vivo imaging applications in mouse models of disease. Most commercially available mouse x-ray CT scanners utilize a charge-coupled device (CCD) detector coupled via fibre optic taper to a phosphor screen. However, there has been little research to determine if this is the optimum detector for the specific task of in vivo mouse imaging. To investigate this issue, we have evaluated four detectors, including an amorphous selenium (a-Se) detector, an amorphous silicon (a-Si) detector with a gadolinium oxysulphide (GOS) screen, a CCD with a 3:1 fibre taper and a GOS screen, and a CCD with a 2:1 fibre taper and both GOS and thallium-doped caesium iodide (CsI:Tl) screens. The detectors were evaluated by measuring the modulation transfer function (MTF), noise power spectrum (NPS), detective quantum efficiency (DQE), stability over multiple exposures, and noise in reconstructed CT images. The a-Se detector had the best MTF and the highest DQE (0.6 at 0 lp mm(-1)) but had the worst stability (45% reduction after 2000 exposure frames). The a-Si detector and the CCD with the 3:1 fibre, both of which used the GOS screen, had very similar performance with a DQE of approximately 0.30 at 0 lp mm(-1). For the CCD with the 2:1 fibre, the CsI:Tl screen resulted in a nearly two-fold improvement in DQE over the GOS screen (0.4 versus 0.24 at 0 lp mm(-1)). The CCDs both had the best stability, with less than a 1% change in pixel values over multiple exposures. The pixel values of the a-Si detector increased 5% over multiple exposures due to the effects of image lag. Despite the higher DQE of the a-Se detector, the reconstructed CT images acquired with the a-Si detector had lower noise levels, likely due to the blurring effects from the phosphor screen.     

Exact reconstruction of volumetric images in reverse helical cone-beam CT

Helical scanning configuration has been used widely in diagnostic cone-beam computed tomography (CBCT) for acquiring data sufficient for exact image reconstruction over an extended volume. In image-guided radiation therapy (IGRT) and other applications of CBCT, it can be difficult, if not impossible, to implement mechanically a multiple-turn helical trajectory on the imaging systems due to hardware constraints. However, imaging systems in these applications often allow for the implementation of a reverse helical trajectory in which the rotation direction changes between two consecutive turns. Because the reverse helical trajectory satisfies Tuy's condition, when projections of the imaged object are nontruncated, it yields data sufficient for exact image reconstruction within the reverse helix volume. The recently developed chord-based algorithms such as the backprojection filtration (BPF) algorithm can readily be applied to reconstructing images on chords of a reverse helical trajectory, and they can thus reconstruct an image within a volume covered by the chords. Conversely, the chord-based algorithms cannot reconstruct images within regions that are not intersected by chords. In a reverse helix volume, as shown below, chordless regions exist in which no images can thus be reconstructed by use of the chord-based algorithms. In this work, based upon Pack-Noo's formula, a shift-invariant filtered backprojection (FBP) algorithm is derived for exact image reconstruction within the reverse helix volume, including the chordless region. Numerical studies have also been conducted to demonstrate the chordless region in a reverse helix volume and to validate the FBP algorithm for image reconstruction within the chordless region. Results of the numerical studies confirm that the FBP algorithm can exactly reconstruct an image within the entire reverse helix volume, including the chordless region. It is relatively straightforward to extend the FBP algorithm to reconstruct images for general trajectories, including reverse helical trajectories with variable pitch, tilted axis, and/or additional segments between turns.     

Patient dose considerations for routine megavoltage cone-beam CT imaging

Megavoltage cone-beam CT (MVCBCT), the recent addition to the family of in-room CT imaging systems for image-guided radiation therapy (IGRT), uses a conventional treatment unit equipped with a flat panel detector to obtain a three-dimensional representation of the patient in treatment position. MVCBCT has been used for more than two years in our clinic for anatomy verification and to improve patient alignment prior to dose delivery. The objective of this research is to evaluate the image acquisition dose delivered to patients for MVCBCT and to develop a simple method to reduce the additional dose resulting from routine MVCBCT imaging. Conventional CT scans of phantoms and patients were imported into a commercial treatment planning system (TPS: Phillips, Pinnacle) and an arc treatment mimicking the MVCBCT acquisition process was generated to compute the delivered acquisition dose. To validate the dose obtained from the TPS, a simple water-equivalent cylindrical phantom with spaces for MOSFETs and an ion chamber was used to measure the MVCBCT image acquisition dose. Absolute dose distributions were obtained by simulating MVCBCTs of 9 and 5 monitor units (MU) on pelvis and head and neck patients, respectively. A compensation factor was introduced to generate composite plans of treatment and MVCBCT imaging dose. The article provides a simple equation to compute the compensation factor. The developed imaging compensation method was tested on routinely used clinical plans for prostate and head and neck patients. The quantitative comparison between the calculated dose by the TPS and measurement points on the cylindrical phantom were all within 3%. The dose percentage difference for the ion chamber placed in the center of the phantom was only 0.2%. For a typical MVCBCT, the dose delivered to patients forms a small anterior-posterior gradient ranging from 0.6 to 1.2 cGy per MVCBCT MU. MVCBCT acquisitions in the pelvis and head and neck areas deliver slightly more dose than current portal imaging but render soft tissue information for positioning. Overall, the additional dose from daily 9 MU MVCBCTs of prostate patients is small compared to the treatment dose (<4%). Dose-volume histograms of compensated plans for pelvis and head and neck patients imaged daily with MVCBCT showed no additional dose to the target and small increases at low doses. The results indicate that the dose delivered for MVCBCT imaging can be precisely calculated in the TPS and therefore included in the treatment plan. This allows simple plan compensations, such as slightly reducing the treatment dose, to minimize the total dose received by critical structures from daily positioning with MVCBCT. The proposed compensation factor reduces the number of MU per treatment beam per fraction. Both the number of fractions and the beam arrangement are kept unchanged. Reducing the imaging volume in the cranio-caudal direction can further reduce the dose delivered for MVCBCT. This is a useful feature to eliminate the imaging dose to the eyes or to focus on a specific region of interest for alignment.     

A constrained, total-variation minimization algorithm for low-intensity x-ray CT

Purpose: The authors developed an iterative image-reconstruction algorithm for application to low-intensity computed tomography projection data, which is based on constrained, total-variation (TV) minimization. The algorithm design focuses on recovering structure on length scales comparable to a detector bin width.Methods: Recovering the resolution on the scale of a detector bin requires that pixel size be much smaller than the bin width. The resulting image array contains many more pixels than data, and this undersampling is overcome with a combination of Fourier upsampling of each projection and the use of constrained, TV minimization, as suggested by compressive sensing. The presented pseudocode for solving constrained, TV minimization is designed to yield an accurate solution to this optimization problem within 100 iterations.Results: The proposed image-reconstruction algorithm is applied to a low-intensity scan of a rabbit with a thin wire to test the resolution. The proposed algorithm is compared to filtered backprojection (FBP).Conclusions: The algorithm may have some advantage over FBP in that the resulting noise level is lowered at equivalent contrast levels of the wire.     

A dynamic approach to identifying desired physiological phases for cardiac imaging using multislice spiral CT

In this investigation, we describe a quantitative technique to measure coronary motion, which can be correlated with cardiac image quality using multislice computed tomography (MSCT) scanners. MSCT scanners, with subsecond scanning, thin-slice imaging (sub-millimeter) and volume scanning capabilities have paved the way for new clinical applications like noninvasive cardiac imaging. ECG-gated spiral CT using MSCT scanners has made it possible to scan the entire heart in a single breath-hold. The continuous data acquisition makes it possible for multiple phases to be reconstructed from a cardiac cycle. We measure the position and three-dimensional velocities of well-known landmarks along the proximal, mid, and distal regions of the major coronary arteries [left main (LM), left anterior descending (LAD), right coronary artery (RCA), and left circumflex (LCX)] during the cardiac cycle. A dynamic model (called the "delay algorithm") is described which enables us to capture the same physiological phase or "state" of the anatomy during the cardiac cycle as the instantaneous heart rate varies during the spiral scan. The coronary arteries are reconstructed from data obtained during different physiological cardiac phases and we correlate image quality of different parts of the coronary anatomy with phases at which minimum velocities occur. The motion characteristics varied depending on the artery, with the highest motion being observed for RCA. The phases with the lowest mean velocities provided the best visualization. Though more than one phase of relative minimum velocity was observed for each artery, the most consistent image quality was observed during mid-diastole ("diastasis") of the cardiac cycle and was judged to be superior to other reconstructed phases in 92% of the cases. In the process, we also investigated correlation between cardiac arterial states and other measures of motion, such as the left ventricular volume during a cardiac cycle, which earlier has been demonstrated as an example of how anatomic-specific information can be used in a knowledge-based cardiac CT algorithm. Using these estimates in characterizing cardiac motion also provides realistic simulation models for higher heart rates and also in optimizing volume reconstructions for individual segments of the cardiac anatomy.     

A new method for x-ray scatter correction: first assessment on a cone-beam CT experimental setup

Cone-beam computed tomography (CBCT) enables three-dimensional imaging with isotropic resolution and a shorter acquisition time compared to a helical CT scanner. Because a larger object volume is exposed for each projection, scatter levels are much higher than in collimated fan-beam systems, resulting in cupping artifacts, streaks and quantification inaccuracies. In this paper, a general method to correct for scatter in CBCT, without supplementary on-line acquisition, is presented. This method is based on scatter calibration through off-line acquisition combined with on-line analytical transformation based on physical equations, to adapt calibration to the object observed. The method was tested on a PMMA phantom and on an anthropomorphic thorax phantom. The results were validated by comparison to simulation for the PMMA phantom and by comparison to scans obtained on a commercial multi-slice CT scanner for the thorax phantom. Finally, the improvements achieved with the new method were compared to those obtained using a standard beam-stop method. The new method provided results that closely agreed with the simulation and with the conventional CT scanner, eliminating cupping artifacts and significantly improving quantification. Compared to the beam-stop method, lower x-ray doses and shorter acquisition times were needed, both divided by a factor of 9 for the same scatter estimation accuracy.     

Analysis of an exact inversion algorithm for spiral cone-beam CT

In this paper we continue studying a theoretically exact filtered backprojection inversion formula for cone beam spiral CT proposed earlier by the author. Our results show that if the phantom f is constant along the axial direction, the formula is equivalent to the 2D Radon transform inversion. Also, the inversion formula remains exact as spiral pitch goes to zero and in the limit becomes again the 2D Radon transform inversion formula. Finally, we show that according to the formula the processed cone beam projections should be backprojected using both the inverse distance squared law and the inverse distance law.     

Evaluation of the ordered subset convex algorithm for cone-beam CT

Statistical methods for image reconstruction such as maximum likelihood expectation maximization (ML-EM) are more robust and flexible than analytical inversion methods and allow for accurate modelling of the photon transport and noise. Statistical reconstruction is prohibitively slow when applied to clinical x-ray cone-beam CT due to the large data sets and the high number of iterations required for reconstructing high resolution images. One way to reduce the reconstruction time is to use ordered subsets of projections during the iterations, which has been successfully applied to fan-beam x-ray CT. In this paper, we quantitatively analyse the use of ordered subsets in concert with the convex algorithm for cone-beam x-ray CT reconstruction, for the case of circular acquisition orbits. We focus on the reconstructed image accuracy of a 3D head phantom. Acceleration factors larger than 300 were obtained with errors smaller than 1%, with the preservation of signal-to-noise ratio. Pushing the acceleration factor towards 600 by using an increasing number of subsets increases the reconstruction error up to 5% and significantly increases noise. The results indicate that the use of ordered subsets can be extremely useful for cone-beam x-ray CT.     

Direct cone-beam cardiac reconstruction algorithm with cardiac banding artifact correction

Multislice helical computed tomography (CT) is a promising noninvasive technique for coronary artery imaging. Various factors can cause inconsistencies in cardiac CT data, which can result in degraded image quality. These inconsistencies may be the result of the patient physiology (e.g., heart rate variations), the nature of the data (e.g., cone-angle), or the reconstruction algorithm itself. An algorithm which provides the best temporal resolution for each slice, for example, often provides suboptimal image quality for the entire volume since the cardiac temporal resolution (TRc) changes from slice to slice. Such variations in TRc can generate strong banding artifacts in multiplanar reconstruction images or three-dimensional images. Discontinuous heart walls and coronary arteries may compromise the accuracy of the diagnosis. A beta-blocker is often used to reduce and stabilize patients' heart rate but cannot eliminate the variation. In order to obtain robust and optimal image quality, a software solution that increases the temporal resolution and decreases the effect of heart rate is highly desirable. This paper proposes an ECG-correlated direct cone-beam reconstruction algorithm (TCOT-EGR) with cardiac banding artifact correction (CBC) and disconnected projections redundancy compensation technique (DIRECT). First the theory and analytical model of the cardiac temporal resolution is outlined. Next, the performance of the proposed algorithms is evaluated by using computer simulations as well as patient data. It will be shown that the proposed algorithms enhance the robustness of the image quality against inconsistencies by guaranteeing smooth transition of heart cycles used in reconstruction.     

A computationally efficient method for automatic registration of orthogonal x-ray images with volumetric CT data

The paper presents a computationally efficient 3D-2D image registration algorithm for automatic pre-treatment validation in radiotherapy. The novel aspects of the algorithm include (a) a hybrid cost function based on partial digitally reconstructed radiographs (DRRs) generated along projected anatomical contours and a level set term for similarity measurement; and (b) a fast search method based on parabola fitting and sensitivity-based search order. Using CT and orthogonal x-ray images from a skull and a pelvis phantom, the proposed algorithm is compared with the conventional ray-casting full DRR based registration method. Not only is the algorithm shown to be computationally more efficient with registration time being reduced by a factor of 8, but also the algorithm is shown to offer 50% higher capture range allowing the initial patient displacement up to 15 mm (measured by mean target registration error). For the simulated data, high registration accuracy with average errors of 0.53 mm +/- 0.12 mm for translation and 0.61 +/- 0.29 degrees for rotation within the capture range has been achieved. For the tested phantom data, the algorithm has also shown to be robust without being affected by artificial markers in the image.