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

Reduction of cone-beam CT artifacts in a robotic CBCT device using saddle trajectories with integrated infrared tracking

BACKGROUND

Cone beam computed tomography (CBCT) is widely used in many medical fields. However, conventional CBCT circular scans suffer from cone beam (CB) artifacts that limit the quality and reliability of the reconstructed images due to incomplete data.

PURPOSE

Saddle trajectories in theory might be able to improve the CBCT image quality by providing a larger region with complete data. Therefore, we investigated the feasibility and performance of saddle trajectory CBCT scans and compared them to circular trajectory scans.

METHODS

We performed circular and saddle trajectory scans using a novel robotic CBCT scanner (Mobile ImagingRing (IRm); medPhoton, Salzburg, Austria). For the saddle trajectory, the gantry executed yaw motion up to± 10 ∘ $\pm 10^{\circ }$ using motorized wheels driving on the floor. An infrared (IR) tracking device with reflective markers was used for online geometric calibration correction (mainly floor unevenness). All images were reconstructed using penalized least-squares minimization with the conjugate gradient algorithm from RTK with0.5 × 0.5 × 0.5 mm 3 $0.5 \times 0.5\times 0.5 \text{ mm}^3$ voxel size. A disk phantom and an Alderson phantom were scanned to assess the image quality. Results were correlated with the local incompleteness value represented bytan ( ψ ) $\tan (\psi)$ , which was calculated at each voxel as a function of the source trajectory and the voxel's 3D coordinates. We assessed the magnitude of CB artifacts using the full width half maximum (FWHM) of each disk profile in the axial center of the reconstructed images. Spatial resolution was also quantified by the modulation transfer function at 10% (MTF10).

RESULTS

When using the saddle trajectory, the region without CB artifacts was increased from 43 to 190 mm in the SI direction compared to the circular trajectory. This region coincided with low values fortan ( ψ ) $\tan (\psi)$ . Whentan ( ψ ) $\tan (\psi)$ was larger than 0.02, we found there was a linear relationship between the FWHM andtan ( ψ ) $\tan (\psi)$ . For the saddle, IR tracking allowed the increase of MTF10 from 0.37 to 0.98 lp/mm.

CONCLUSIONS

We achieved saddle trajectory CBCT scans with a novel CBCT system combined with IR tracking. The results show that the saddle trajectory provides a larger region with reliable reconstruction compared to the circular trajectory. The proposed method can be used to evaluate other non-circular trajectories.

Review of CT image reconstruction open source toolkits

Computed tomography (CT) has been widely applied in medical diagnosis, nondestructive evaluation, homeland security, and other science and engineering applications. Image reconstruction is one of the core CT imaging technologies. In this review paper, we systematically reviewed the currently publicly available CT image reconstruction open source toolkits in the aspects of their environments, object models, imaging geometries, and algorithms. In addition to analytic and iterative algorithms, deep learning reconstruction networks and open codes are also reviewed as the third category of reconstruction algorithms. This systematic summary of the publicly available software platforms will help facilitate CT research and development.

Prior-Free Respiratory Motion Estimation in Rotational Angiography

Rotational coronary angiography using C-arm angiography systems enables intra-procedural 3-D imaging that is considered beneficial for diagnostic assessment and interventional guidance. Despite previous efforts, rotational angiography was not yet successfully established in clinical practice for coronary artery procedures due to challenges associated with substantial intra-scan respiratory and cardiac motion. While gating handles cardiac motion during reconstruction, respiratory motion requires compensation. State-of-the-art algorithms rely on 3-D / 2-D registration that requires an uncompensated reconstruction of sufficient quality. To overcome this limitation, we investigate two prior-free respiratory motion estimation methods based on the optimization of: 1) epipolar consistency conditions (ECCs) and 2) a task-based auto-focus measure (AFM). The methods assess redundancies in projection images or impose favorable properties of 3-D space, respectively, and are used to estimate the respiratory motion of the coronary arteries within rotational angiograms. We evaluate our algorithms on the publicly available CAVAREV benchmark and on clinical data. We quantify reductions in error due to respiratory motion compensation using a dedicated reconstruction domain metric. Moreover, we study the improvements in image quality when using an analytic and a novel temporal total variation regularized algebraic reconstruction algorithm. We observed substantial improvement in all figures of merit compared with the uncompensated case. Improvements in image quality presented as a reduction of double edges, blurring, and noise. Benefits of the proposed corrections were notable even in cases suffering little corruption from respiratory motion, translating to an improvement in the vessel sharpness of (6.08 ± 4.46)% and (14.7 ± 8.80)% when the ECC-based and the AFM-based compensation were applied. On the CAVAREV data, our motion compensation approach exhibits an improvement of (27.6 ± 7.5)% and (97.0 ± 17.7)% when the ECC and AFM were used, respectively. At the time of writing, our method based on AFM is leading the CAVAREV scoreboard. Both motion estimation strategies are purely image-based and accurately estimate the displacements of the coronary arteries due to respiration. While current evidence suggests the superior performance of AFM, future work will further investigate the use of ECC in the context of angiography as they solely rely on geometric calibration and projection-domain images.

Three dimensional dose distribution comparison of simple and complex acquisition trajectories in dedicated breast CT

PURPOSE

A novel breast CT system capable of arbitrary 3D trajectories has been developed to address cone beam sampling insufficiency as well as to image further into the patient's chest wall. The purpose of this study was to characterize any trajectory-related differences in 3D x-ray dose distribution in a pendant target when imaged with different orbits.

METHODS

Two acquisition trajectories were evaluated: circular azimuthal (no-tilt) and sinusoidal (saddle) orbit with ±15° tilts around a pendant breast, using Monte Carlo simulations as well as physical measurements. Simulations were performed with tungsten (W) filtration of a W-anode source; the simulated source flux was normalized to the measured exposure of a W-anode source. A water-filled cylindrical phantom was divided into 1 cm(3) voxels, and the cumulative energy deposited was tracked in each voxel. Energy deposited per voxel was converted to dose, yielding the 3D distributed dose volumes. Additionally, three cylindrical phantoms of different diameters (10, 12.5, and 15 cm) and an anthropomorphic breast phantom, initially filled with water (mimicking pure fibroglandular tissue) and then with a 75% methanol-25% water mixture (mimicking 50-50 fibroglandular-adipose tissues), were used to simulate the pendant breast geometry and scanned on the physical system. Ionization chamber calibrated radiochromic film was used to determine the dose delivered in a 2D plane through the center of the volume for a fully 3D CT scan using the different orbits.

RESULTS

Measured experimental results for the same exposure indicated that the mean dose measured throughout the central slice for different diameters ranged from 3.93 to 5.28 mGy, with the lowest average dose measured on the largest cylinder with water mimicking a homogeneously fibroglandular breast. These results align well with the cylinder phantom Monte Carlo studies which also showed a marginal difference in dose delivered by a saddle trajectory in the central slice. Regardless of phantom material or filled fluid density, dose delivered by the saddle scan was negligibly different than the simple circular, no-tilt scans. The average dose measured in the breast phantom was marginally higher for saddle than the circular no tilt scan at 3.82 and 3.87 mGy, respectively.

CONCLUSIONS

Not only does nontraditional 3D-trajectory CT scanning yield more complete sampling of the breast volume but also has comparable dose deposition throughout the breast and anterior chest volume, as verified by Monte Carlo simulation and physical measurements.

Self-calibration of cone-beam CT geometry using 3D-2D image registration

Robotic C-arms are capable of complex orbits that can increase field of view, reduce artifacts, improve image quality, and/or reduce dose; however, it can be challenging to obtain accurate, reproducible geometric calibration required for image reconstruction for such complex orbits. This work presents a method for geometric calibration for an arbitrary source-detector orbit by registering 2D projection data to a previously acquired 3D image. It also yields a method by which calibration of simple circular orbits can be improved. The registration uses a normalized gradient information similarity metric and the covariance matrix adaptation-evolution strategy optimizer for robustness against local minima and changes in image content. The resulting transformation provides a 'self-calibration' of system geometry. The algorithm was tested in phantom studies using both a cone-beam CT (CBCT) test-bench and a robotic C-arm (Artis Zeego, Siemens Healthcare) for circular and non-circular orbits. Self-calibration performance was evaluated in terms of the full-width at half-maximum (FWHM) of the point spread function in CBCT reconstructions, the reprojection error (RPE) of steel ball bearings placed on each phantom, and the overall quality and presence of artifacts in CBCT images. In all cases, self-calibration improved the FWHM-e.g. on the CBCT bench, FWHM  =  0.86 mm for conventional calibration compared to 0.65 mm for self-calibration (p  <  0.001). Similar improvements were measured in RPE-e.g. on the robotic C-arm, RPE  =  0.73 mm for conventional calibration compared to 0.55 mm for self-calibration (p  <  0.001). Visible improvement was evident in CBCT reconstructions using self-calibration, particularly about high-contrast, high-frequency objects (e.g. temporal bone air cells and a surgical needle). The results indicate that self-calibration can improve even upon systems with presumably accurate geometric calibration and is applicable to situations where conventional calibration is not feasible, such as complex non-circular CBCT orbits and systems with irreproducible source-detector trajectory.

CT Scanning Imaging Method Based on a Spherical Trajectory

In industrial computed tomography (CT), the mismatch between the X-ray energy and the effective thickness makes it difficult to ensure the integrity of projection data using the traditional scanning model, because of the limitations of the object's complex structure. So, we have developed a CT imaging method that is based on a spherical trajectory. Considering an unrestrained trajectory for iterative reconstruction, an iterative algorithm can be used to realise the CT reconstruction of a spherical trajectory for complete projection data only. Also, an inclined circle trajectory is used as an example of a spherical trajectory to illustrate the accuracy and feasibility of this new scanning method. The simulation results indicate that the new method produces superior results for a larger cone-beam angle, a limited angle and tabular objects compared with traditional circle trajectory scanning.

The feasibility of an inverse geometry CT system with stationary source arrays

PURPOSE

Inverse geometry computed tomography (IGCT) has been proposed as a new system architecture that combines a small detector with a large, distributed source. This geometry can suppress cone-beam artifacts, reduce scatter, and increase dose efficiency. However, the temporal resolution of IGCT is still limited by the gantry rotation time. Large reductions in rotation time are in turn difficult due to the large source array and associated power electronics. We examine the feasibility of using stationary source arrays for IGCT in order to achieve better temporal resolution. We anticipate that multiple source arrays are necessary, with each source array physically separated from adjacent ones.

METHODS

Key feasibility issues include spatial resolution, artifacts, flux, noise, collimation, and system timing clashes. The separation between the different source arrays leads to missing views, complicating reconstruction. For the special case of three source arrays, a two-stage reconstruction algorithm is used to estimate the missing views. Collimation is achieved using a rotating collimator with a small number of holes. A set of equally spaced source spots are designated on the source arrays, and a source spot is energized when a collimator hole is aligned with it. System timing clashes occur when multiple source spots are scheduled to be energized simultaneously. We examine flux considerations to evaluate whether sufficient flux is available for clinical applications.

RESULTS

The two-stage reconstruction algorithm suppresses cone-beam artifacts while maintaining resolution and noise characteristics comparable to standard third generation systems. The residual artifacts are much smaller in magnitude than the cone-beam artifacts eliminated. A mathematical condition is given relating collimator hole locations and the number of virtual source spots for which system timing clashes are avoided. With optimization, sufficient flux may be achieved for many clinical applications.

CONCLUSIONS

IGCT with stationary source arrays could be an imaging platform potentially capable of imaging a complete 16-cm thick volume within a tenth of a second.

Modelling the physics in the iterative reconstruction for transmission computed tomography

There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.

Modelling the physics in the iterative reconstruction for transmission computed tomography

There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.

Completeness map evaluation demonstrated with candidate next-generation cardiac CT architectures

PURPOSE

In this report, the authors introduce the general concept of the completeness map, as a means to evaluate the completeness of data acquired by a given CT system design (architecture and scan mode). They illustrate the utility of completeness map by applying the completeness map concept to a number of candidate CT system designs, as part of a study to advance the state-of-the-art in cardiac CT.

METHODS

In order to optimally reconstruct a point within a volume of interest (VOI), the Radon transform on all possible planes through that point should be measured. The authors quantified the extent to which this ideal condition is satisfied for the entire image volume. They first determined a Radon completeness number for each point in the VOI, as the percentage of possible planes that is actually measured. A completeness map is then defined as a 3D matrix of the completeness numbers for the entire VOI. The authors proposed algorithms to analyze the projection datasets in Radon space and compute the completeness number for a fixed point and apply these algorithms to various architectures and scan modes that they are evaluating. In this report, the authors consider four selected candidate architectures, operating with different scan modes, for a total of five system design alternatives. Each of these alternatives is evaluated using completeness map.

RESULTS

If the detector size and cone angle are large enough to cover the entire cardiac VOI, a single-source circular scan can have ≥99% completeness over the entire VOI. However, only the central z-slice can be exactly reconstructed, which corresponds to 100% completeness. For a typical single-source architecture, if the detector is limited to an axial dimension of 40 mm, a helical scan needs about five rotations to form an exact reconstruction region covering the cardiac VOI, while a triple-source helical scan only requires two rotations, leading to a 2.5x improvement in temporal resolution. If the source and detector of an inverse-geometry (IGCT) system have the same axial extent, and the spacing of source points in the axial and transaxial directions is sufficiently small, the IGCT can also form an exact reconstruction region for the cardiac VOI. If the VOI can be covered by the x-ray beam in any view, a composite-circling scan can generate an exact reconstruction region covering the VOI.

CONCLUSIONS

The completeness map evaluation provides useful information for selecting the next-generation cardiac CT system design. The proposed completeness map method provides a practical tool for analyzing complex scanning trajectories, where the theoretical image quality for some complex system designs is impossible to predict, without yet-undeveloped reconstruction algorithms.

Cone-beam composite-circling scan and exact image reconstruction for a quasi-short object

Here we propose a cone-beam composite-circling mode to solve the quasi-short object problem, which is to reconstruct a short portion of a long object from longitudinally truncated cone-beam data involving the short object. In contrast to the saddle curve cone-beam scanning, the proposed scanning mode requires that the X-ray focal spot undergoes a circular motion in a plane facing the short object, while the X-ray source is rotated in the gantry main plane. Because of the symmetry of the proposed mechanical rotations and the compatibility with the physiological conditions, this new mode has significant advantages over the saddle curve from perspectives of both engineering implementation and clinical applications. As a feasibility study, a backprojection filtration (BPF) algorithm is developed to reconstruct images from data collected along a composite-circling trajectory. The initial simulation results demonstrate the correctness of the proposed exact reconstruction method and the merits of the proposed mode.

Accurate image reconstruction using real C-arm data from a Circle-plus-arc trajectory

OBJECTIVE

Developing an efficient tool for accurate three-dimensional imaging from projections measured with C-arm systems.

MATERIAL AND METHODS

A circle-plus-arc trajectory, which is complete and thus amenable to accurate reconstruction, is used. This trajectory is particularly attractive as its implementation does not require moving the patient. For reconstruction, we use the "M-line method", which allows processing the data in the efficient filtered backprojection mode. This method also offers the advantage of not requiring an ideal data acquisition geometry, i.e., the M-line algorithm can account for known deviations in the scanning geometry, which is important given that sizeable deviations are generally encountered in C-arm imaging.

RESULTS

A robust implementation scheme of the "M-line method" that applies straightforwardly to real C-arm data is presented. In particular, a numerically stable technique to compute the view-dependent derivative with respect to the source trajectory parameter is applied, and an efficient way to compute the π-line backprojection intervals via a polygonal weighting mask is presented. Projection data of an anthropomorphic thorax phantom were acquired on a medical C-arm scanner and used to demonstrate the benefit of using a complete data acquisition geometry with an accurate reconstruction algorithm versus using a state-of-the-art implementation of the conventional Feldkamp algorithm with a circular short scan of cone-beam data. A significant image quality improvement based on visual assessment is shown in terms of cone-beam artifacts.

A new method to combine 3D reconstruction volumes for multiple parallel circular cone beam orbits

PURPOSE

This article presents a new reconstruction method for 3D imaging using a multiple 360 degrees circular orbit cone beam CT system, specifically a way to combine 3D volumes reconstructed with each orbit. The main goal is to improve the noise performance in the combined image while avoiding cone beam artifacts.

METHODS

The cone beam projection data of each orbit are reconstructed using the FDK algorithm. When at least a portion of the total volume can be reconstructed by more than one source, the proposed combination method combines these overlap regions using weighted averaging in frequency space. The local exactness and the noise performance of the combination method were tested with computer simulations of a Defrise phantom, a FORBILD head phantom, and uniform noise in the raw data.

RESULTS

A noiseless simulation showed that the local exactness of the reconstructed volume from the source with the smallest tilt angle was preserved in the combined image. A noise simulation demonstrated that the combination method improved the noise performance compared to a single orbit reconstruction.

CONCLUSIONS

In CT systems which have overlap volumes that can be reconstructed with data from more than one orbit and in which the spatial frequency content of each reconstruction can be calculated, the proposed method offers improved noise performance while keeping the local exactness of data from the source with the smallest tilt angle.

Demonstration of dose and scatter reductions for interior computed tomography

With continuing developments in computed tomography (CT) technology and its increasing use of CT imaging, the ionizing radiation dose from CT is becoming a major public concern particularly for high-dose applications such as cardiac imaging. We recently proposed a novel interior tomography approach for x-ray dose reduction that is very different from all the previously proposed methods. Our method only uses the projection data for the rays passing through the desired region of interest. This method not only reduces x-ray dose but scatter as well. In this paper, we quantify the reduction in the amount of x-ray dose and scattered radiation that could be achieved using this method. Results indicate that interior tomography may reduce the x-ray dose by 18% to 58% and scatter to the detectors by 19% to 59% as the FOV is reduced from 50 to 8.6 cm.

Cardiac computed tomography radiation dose reduction using interior reconstruction algorithm with the aorta and vertebra as known information

High x-ray radiation dose is a major public concern with the increasing use of multidetector computed tomography (CT) for diagnosis of cardiovascular diseases. This issue must be effectively addressed by dose-reduction techniques. Recently, our group proved that an internal region of interest (ROI) can be exactly reconstructed solely from localized projections if a small subregion within the ROI is known. In this article, we propose to use attenuation values of the blood in aorta and vertebral bone to serve as the known information for localized cardiac CT. First, we describe a novel interior tomography approach that backprojects differential fan-beam or parallel-beam projections to obtain the Hilbert transform and then reconstructs the original image in an ROI using the iterative projection onto convex sets algorithm. Then, we develop a numerical phantom based on clinical cardiac CT images for simulations. Our results demonstrate that it is feasible to use practical prior information and exactly reconstruct cardiovascular structures only from projection data along x-ray paths through the ROI.

Knowledge-based dynamic volumetric cardiac computed tomography with saddle curve trajectory

Motion artifact is still a major issue in cardiac computed tomography because the current motion correction and electrocardiogram gating techniques have not fully addressed this problem. The image quality can be significantly improved by using information about the actual state of the heart and an exact reconstruction algorithm. We propose to extend a cardiac computed tomographic technique, using the knowledge of the volume and the relation between the state and the phase of the heart, to a saddle curve trajectory. This will optimize the image quality by reducing the artifacts resulting from approximate reconstruction and solve the long-object problem. Necessary background is provided, and the effectiveness of the algorithms is demonstrated in numerical simulations with the dynamic thorax phantom.

An outlook on x-ray CT research and development

Over the past decade, computed tomography (CT) theory, techniques and applications have undergone a rapid development. Since CT is so practical and useful, undoubtedly CT technology will continue advancing biomedical and non-biomedical applications. In this outlook article, we share our opinions on the research and development in this field, emphasizing 12 topics we expect to be critical in the next decade: analytic reconstruction, iterative reconstruction, local/interior reconstruction, flat-panel based CT, dual-source CT, multi-source CT, novel scanning modes, energy-sensitive CT, nano-CT, artifact reduction, modality fusion, and phase-contrast CT. We also sketch several representative biomedical applications.

Approximate and exact cone-beam reconstruction with standard and non-standard spiral scanning

The long object problem is practically important and theoretically challenging. To solve the long object problem, spiral cone-beam CT was first proposed in 1991, and has been extensively studied since then. As a main feature of the next generation medical CT, spiral cone-beam CT has been greatly improved over the past several years, especially in terms of exact image reconstruction methods. Now, it is well established that volumetric images can be exactly and efficiently reconstructed from longitudinally truncated data collected along a rather general scanning trajectory. Here we present an overview of some key results in this area.

Step-and-shoot data acquisition and reconstruction for cardiac x-ray computed tomography

Coronary artery imaging with x-ray computed tomography (CT) is one of the most recent advancements in CT clinical applications. Although existing "state-of-the-art" clinical protocols today utilize helical data acquisition, it suffers from the lack of ability to handle irregular heart rate and relatively high x-ray dose to patients. In this paper, we propose a step-and-shoot data acquisition protocol that significantly overcomes these shortcomings. The key to the proposed protocol is the large volume coverage (40 mm) enabled by the cone beam CT scanner, which allows the coverage of the entire heart in 3 to 4 steps. In addition, we propose a gated complementary reconstruction algorithm that overcomes the longitudinal truncation problem resulting from the cone beam geometry. Computer simulations, phantom experiments, and clinical studies were conducted to validate our approach.

Cone-beam mammo-computed tomography from data along two tilting arcs

Over the past several years there has been an increasing interest in cone-beam computed tomography (CT) for breast imaging. In this article, we propose a new scheme for theoretically exact cone-beam mammo-CT and develop a corresponding Katsevich-type reconstruction algorithm. In our scheme, cone-beam scans are performed along two tilting arcs to collect a sufficient amount of information for exact reconstruction. In our algorithm, cone-beam data are filtered in a shift-invariant fashion and then weighted backprojected into the three-dimensional space for the final reconstruction. Our approach has several desirable features, including tolerance of axial data truncation, efficiency in sequential/parallel implementation, and accuracy for quantitative analysis. We also demonstrate the system performance and clinical utility of the proposed technique in numerical simulations.

View-independent reconstruction algorithms for cone beam CT with general saddle trajectory

In Yang et al (2006 Phys. Med. Biol. 51 1157-72), an exact filtered backprojection (FBP) reconstruction algorithm was proposed for cone beam tomography with saddle trajectory based on the seminal works of Pack and Noo (2005a Inverse Problems 21 1105-20; 2005b 8th Int. Meeting on Fully 3D Reconstruction in Radiology and Nuclear Medicine (Salt Lake City) ed F Noo, H Kudo and L G Zeng pp 287-90). However, the artefacts due to discretization and/or sampling errors in the reconstructed images by this method were still visible, especially when the pitch is large. In this paper, two view-independent (VI) algorithms, which are similar to the FDK-type algorithms (Feldkamp et al 1984 J. Opt. Soc. Am. A 1 612-19), are proposed for planar detector geometry. The first VI algorithm involves two filtered projections and a small additional term (two-dimensional (2D) Radon transform term). One of the filtered projections is obtained by ramp filtering (as in the FDK algorithm for circular trajectory) and the other one is obtained by Hilbert transform. The 2D Radon transform term is just like the term which was first derived by Hu (1996 Scanning 18 572-81) for a circular trajectory. The second VI algorithm involves only one filtered projection term, which is obtained by differentiation followed by Hilbert transform and the 2D Radon transform term. Both algorithms involve only one backprojection step with a weighting factor as in the FDK algorithm. The simulation studies show that the pixel values of the reconstructed images by the VI algorithms are more accurate than those by the original view differencing (VD) algorithm, the streak artefacts are also reduced, and their computational times are comparable to that of the original VD algorithm. We also generalize the concept of saddle trajectory and the corresponding reconstruction algorithm. The generalized algorithm is also theoretically exact, has a shift-invariant FBP structure, and does not depend on the concept of pi-line.

A shift-invariant filtered backprojection (FBP) cone-beam reconstruction algorithm for the source trajectory of two concentric circles using an equal weighting scheme

In this paper, a shift-invariant filtered backprojection cone-beam image reconstruction algorithm is derived, based upon Katsevich's general inversion scheme, and validated for the source trajectory of two concentric circles. The source trajectory is complete according to Tuy's data sufficiency condition and is used as the basis for an exact image reconstruction algorithm. The algorithm proceeds according to the following steps. First, differentiate the cone-beam projection data with respect to the detector coordinates and with respect to the source trajectory parameter. The data are then separately filtered along three different orientations in the detector plane with a shift-invariant Hilbert kernel. Eight different filtration groups are obtained via linear combinations of weighted filtered data. Voxel-based backprojection is then carried out from eight sets of view angles, where separate filtered data are backprojected from each set according to the backprojection sets' associated filtration group. The algorithm is first derived for a scanning configuration consisting of two concentric and orthogonal circles. By performing an affine transformation on the image object, the developed image reconstruction algorithm has been generalized to the case where the two concentric circles are not orthogonal. Numerical simulations are presented to validate the reconstruction algorithm and demonstrate the dose advantage of the equal weighting scheme.

Exact cone beam reconstruction for a saddle trajectory

We propose an exact shift-invariant filtered backprojection (FBP) algorithm for inversion of cone beam (CB) data in the case where the source trajectory is a saddle. The algorithm allows for axial truncation of the cone beam data. The algorithm involves only one family of filtering lines on the detector plane, and it does not depend on the existence of pi-lines. The algorithm is derived from a general formula in Pack and Noo (2005 Inverse Problems 21 1105-20). We also give the steps to implement the algorithm for planar detector geometry and discuss how to select the parameter of the saddle and the size of the detector when the trajectory is a standard saddle. The algorithm is tested by simulation studies.

Exact BPF and FBP algorithms for nonstandard saddle curves

A hot topic in cone-beam CT research is exact cone-beam reconstruction from a general scanning trajectory. Particularly, a nonstandard saddle curve attracts attention, as this construct allows the continuous periodic scanning of a volume-of-interest (VOI). Here we evaluate two algorithms for reconstruction from data collected along a nonstandard saddle curve, which are in the filtered backprojection (FBP) and backprojection filtration (BPF) formats, respectively. Both the algorithms are implemented in a chord-based coordinate system. Then, a rebinning procedure is utilized to transform the reconstructed results into the natural coordinate system. The simulation results demonstrate that the FBP algorithm produces better image quality than the BPF algorithm, while both the algorithms exhibit similar noise characteristics.

Theory and algorithms for image reconstruction on chords and within regions of interest

We introduce a formula for image reconstruction on a chord of a general source trajectory. We subsequently develop three algorithms for exact image reconstruction on a chord from data acquired with the general trajectory. Interestingly, two of the developed algorithms can accommodate data containing transverse truncations. The widely used helical trajectory and other trajectories discussed in literature can be interpreted as special cases of the general trajectory, and the developed theory and algorithms are thus directly applicable to reconstructing images exactly from data acquired with these trajectories. For instance, chords on a helical trajectory are equivalent to the n-PI-line segments. In this situation, the proposed algorithms become the algorithms that we proposed previously for image reconstruction on PI-line segments. We have performed preliminary numerical studies, which include the study on image reconstruction on chords of two-circle trajectory, which is nonsmooth, and on n-PI lines of a helical trajectory, which is smooth. Quantitative results of these studies verify and demonstrate the proposed theory and algorithms.

A general exact reconstruction for cone-beam CT via backprojection-filtration

In this paper, we prove a generalized backprojection-filtration formula for exact cone-beam image reconstruction with an arbitrary scanning locus. Our proof is independent of the shape of the scanning locus, as long as the object is contained in a region where there is a chord through any interior point. As special cases, this generalized formula can be applied with cone-beam scanning along nonstandard spiral and saddle curves, as well as in an n-PI window setting. The algorithmic implementation and numerical results are described to support the correctness of our general claim.

Filtered backprojection formula for exact image reconstruction from cone-beam data along a general scanning curve

Recently, Katsevich proved a filtered backprojection formula for exact image reconstruction from cone-beam data along a helical scanning locus, which is an important breakthrough since 1991 when the spiral cone-beam scanning mode was proposed. In this paper, we prove a generalized Katsevich's formula for exact image reconstruction from cone-beam data collected along a rather flexible curve. We will also give a general condition on filtering directions. Based on this condition, we suggest a natural choice of filtering directions, which is more convenient than Katsevich's choice and can be applied to general scanning curves. In the derivation, we use analytical techniques instead of geometric arguments. As a result, we do not need the uniqueness of the PI lines. In fact, our formula can be used to reconstruct images on any chord as long as a scanning curve runs from one endpoint of the chord to the other endpoint. This can be considered as a generalization of Orlov's classical theorem. Specifically, our formula can be applied to (i) nonstandard spirals of variable radii and pitches (with PI- or n-PI-windows), and (ii) saddlelike curves.

Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data

In this paper, a new image reconstruction scheme is presented based on Tuy's cone-beam inversion scheme and its fan-beam counterpart. It is demonstrated that Tuy's inversion scheme may be used to derive a new framework for fanbeam and cone-beam image reconstruction. In this new framework, images are reconstructed via filtering the backprojection image of differentiated projection data. The new framework is mathematically exact and is applicable to a general source trajectory provided the Tuy data sufficiency condition is satisfied. By choosing a piece-wise constant function for one of the components in the factorized weighting function, the filtering kernel is one dimensional, viz. the filtering process is along a straight line. Thus, the derived image reconstruction algorithm is mathematically exact and efficient. In the cone-beam case, the derived reconstruction algorithm is applicable to a large class of source trajectories where the pi-lines or the generalized pi-lines exist. In addition, the new reconstruction scheme survives the super-short scan mode in both the fan-beam and cone-beam cases provided the data are not transversely truncated. Numerical simulations were conducted to validate the new reconstruction scheme for the fan-beam case.

Image reconstruction for the circle-and-arc trajectory

Proposed is an exact shift-invariant filtered backprojection algorithm for the circle-and-arc trajectory. The algorithm has several important features. First, it allows for the circle to be incomplete. Second, axial truncation of the cone beam data is allowed. Third, the length of the arc is determined only by the region of interest and is independent of the size of the entire object. The algorithm is quite flexible and can be used for even more general trajectories that consist of several circular segments and arcs. The algorithm applies also in the case when the circle (or, circles) is complete. A numerical experiment with the clock phantom demonstrated good image quality.

Exact and approximate algorithms for helical cone-beam CT

This paper concerns image reconstruction for helical x-ray transmission tomography (CT) with multi-row detectors. We introduce two approximate cone-beam (CB) filtered-backprojection (FBP) algorithms of the Feldkamp type, obtained by extending to three dimensions (3D) two recently proposed exact FBP algorithms for 2D fan-beam reconstruction. The new algorithms are similar to the standard Feldkamp-type FBP for helical CT. In particular, they can reconstruct each transaxial slice from data acquired along an arbitrary segment of helix, thereby efficiently exploiting the available data. In contrast to the standard Feldkamp-type algorithm, however, the redundancy weight is applied after filtering, allowing a more efficient numerical implementation. To partially alleviate the CB artefacts, which increase with increasing values of the helical pitch, a frequency-mixing method is proposed. This method reconstructs the high frequency components of the image using the longest possible segment of helix, whereas the low frequencies are reconstructed using a minimal, short-scan, segment of helix to minimize CB artefacts. The performance of the algorithms is illustrated using simulated data.

Volume CT with a flat-panel detector on a mobile, isocentric C-arm: Pre-clinical investigation in guidance of minimally invasive surgery

A mobile isocentric C-arm (Siemens PowerMobil) has been modified in our laboratory to include a large area flat-panel detector (in place of the x-ray image intensifier), providing multi-mode fluoroscopy and cone-beam computed tomography (CT) imaging capability. This platform represents a promising technology for minimally invasive, image-guided surgical procedures where precision in the placement of interventional tools with respect to bony and soft-tissue structures is critical. The image quality and performance in surgical guidance was investigated in pre-clinical evaluation in image-guided spinal surgery. The control, acquisition, and reconstruction system are described. The reproducibility of geometric calibration, essential to achieving high three-dimensional (3D) image quality, is tested over extended time scales (7 months) and across a broad range in C-arm angulation (up to 45 degrees), quantifying the effect of improper calibration on spatial resolution, soft-tissue visibility, and image artifacts. Phantom studies were performed to investigate the precision of 3D localization (viz., fiber optic probes within a vertebral body) and effect of lateral projection truncation (limited field of view) on soft-tissue detectability in image reconstructions. Pre-clinical investigation was undertaken in a specific spinal procedure (photodynamic therapy of spinal metastases) in five animal subjects (pigs). In each procedure, placement of fiber optic catheters in two vertebrae (L1 and L2) was guided by fluoroscopy and cone-beam CT. Experience across five procedures is reported, focusing on 3D image quality, the effects of respiratory motion, limited field of view, reconstruction filter, and imaging dose. Overall, the intraoperative cone-beam CT images were sufficient for guidance of needles and catheters with respect to bony anatomy and improved surgical performance and confidence through 3D visualization and verification of transpedicular trajectories and tool placement. Future investigation includes improvement in image quality, particularly regarding x-ray scatter, motion artifacts and field of view, and integration with optical tracking and navigation systems.