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

Solar light harvest: modified d-block metals in photocatalysis

With solar light, modified d-block metal photocatalysts are useful in areas where electricity is insufficient, with its chemical stability during the photocatalytic process, and its low-cost and nontoxicity.

Oxygen vacancies of the TiO2nano-based composite photocatalysts in visible light responsive photocatalysis

The TiO₂nano-based composite photocatalyst is best known for application in solving the recent issues related to energy and environmental purification.

BPF-type region-of-interest reconstruction for parallel translational computed tomography

The objective of this study is to present and test a new ultra-low-cost linear scan based tomography architecture. Similar to linear tomosynthesis, the source and detector are translated in opposite directions and the data acquisition system targets on a region-of-interest (ROI) to acquire data for image reconstruction. This kind of tomographic architecture was named parallel translational computed tomography (PTCT). In previous studies, filtered backprojection (FBP)-type algorithms were developed to reconstruct images from PTCT. However, the reconstructed ROI images from truncated projections have severe truncation artefact. In order to overcome this limitation, we in this study proposed two backprojection filtering (BPF)-type algorithms named MP-BPF and MZ-BPF to reconstruct ROI images from truncated PTCT data. A weight function is constructed to deal with data redundancy for multi-linear translations modes. Extensive numerical simulations are performed to evaluate the proposed MP-BPF and MZ-BPF algorithms for PTCT in fan-beam geometry. Qualitative and quantitative results demonstrate that the proposed BPF-type algorithms cannot only more accurately reconstruct ROI images from truncated projections but also generate high-quality images for the entire image support in some circumstances.

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.

Backprojection-filtration reconstruction without invoking a spatially varying weighting factor

PURPOSE

To develop a backprojection-filtration (BPF) algorithm with improved noise properties over the existing BPF algorithm through utilizing (approximate) redundant information in circular cone-beam or fan-beam scans.

METHODS

The backprojection steps in the existing filtered-backprojection (FBP) and BPF algorithms for fan-beam and cone-beam projections invoke spatially varying weighting factors, which may not only increase the computational load in image reconstruction but also, more importantly, result in reconstruction artifacts. Redundant information in fan-beam projections has been exploited for eliminating the weighting factor in the existing FBP algorithm. However, the new FBP algorithm cannot be applied to image reconstruction in a region of interest from transversely truncated data. In this work, the authors identify approximate data redundancy in circular cone-beam projections and propose a new BPF algorithm in which the approximate data redundancy is exploited for eliminating the spatially varying weighting factor in the existing BPF algorithm.

RESULTS

The authors have implemented and evaluated the proposed BPF algorithm in numerical studies of reconstructing 3D images from both the nontruncated and truncated projection data in a circular cone-beam scan. The results of numerical studies demonstrate that the proposed BPF algorithm retains the resolution property of the existing BPF algorithm, and that it can also reconstruct accurately ROI images from truncated data. More importantly, the results also indicate that the proposed BPF algorithm not only is computationally more efficient but also yields generally lower image variances than the existing BPF algorithm.

CONCLUSIONS

A BPF algorithm was proposed that not only retains the desirable properties of the existing BPF algorithm but also possesses improved computational and noise properties over the latter.

Region of Interest Imaging for a General Trajectory with the Rebinned BPF Algorithm

The back-projection-filtration (BPF) algorithm has been applied to image reconstruction for cone-beam configurations with general source trajectories. The BPF algorithm can reconstruct 3-D region-of-interest (ROI) images from data containing truncations. However, like many other existing algorithms for cone-beam configurations, the BPF algorithm involves a back-projection with a spatially varying weighting factor, which can result in the non-uniform noise levels in reconstructed images and increased computation time. In this work, we propose a BPF algorithm to eliminate the spatially varying weighting factor by using a rebinned geometry for a general scanning trajectory. This proposed BPF algorithm has an improved noise property, while retaining the advantages of the original BPF algorithm such as minimum data requirement.

Adaptive Bolus-chasing Computed Tomography Angiography in the Cases of Symmetric and Asymmetric Arterial Flows in Peripheral Arteries

Synchronization of the contrast bolus peak and CT imaging aperture is a crucial issue for computed tomography angiography (CTA). It affects the CTA image quality and the amount of contrast dose. A whole-body CTA procedure means to scan from the abdominal aorta to pedal arteries. In this context, the synchronization is much more difficult with the asymmetric arterial flow in lower extremities than in the case of symmetric arterial flow. In this paper, we propose an adaptive optimal controller to chase the contrast bolus peak while it propagates in the aorta and lower extremities with symmetric flow. In the case of asymmetric flow after the contrast bolus splitting into two lower limbs, we propose a dynamic programming approach to cover the lower limbs optimally. Simulation and experimental results show that the proposed methods outperform the current constant-speed method substantially.

Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?

Despite major advances in x-ray sources, detector arrays, gantry mechanical design and especially computer performance, one component of computed tomography (CT) scanners has remained virtually constant for the past 25 years-the reconstruction algorithm. Fundamental advances have been made in the solution of inverse problems, especially tomographic reconstruction, but these works have not been translated into clinical and related practice. The reasons are not obvious and seldom discussed. This review seeks to examine the reasons for this discrepancy and provides recommendations on how it can be resolved. We take the example of field of compressive sensing (CS), summarizing this new area of research from the eyes of practical medical physicists and explaining the disconnection between theoretical and application-oriented research. Using a few issues specific to CT, which engineers have addressed in very specific ways, we try to distill the mathematical problem underlying each of these issues with the hope of demonstrating that there are interesting mathematical problems of general importance that can result from in depth analysis of specific issues. We then sketch some unconventional CT-imaging designs that have the potential to impact on CT applications, if the link between applied mathematicians and engineers/physicists were stronger. Finally, we close with some observations on how the link could be strengthened. There is, we believe, an important opportunity to rapidly improve the performance of CT and related tomographic imaging techniques by addressing these issues.

Adaptive Bolus Chasing Computed Tomography Angiography: Control Scheme and Experimental Results

In this paper, a new adaptive bolus-chasing control scheme is proposed to synchronize the bolus peak in a patient's vascular system and the imaging aperture of a computed tomography (CT) scanner. The proposed control scheme is theoretically evaluated and experimentally tested on a modified Siemens SOMATOM Volume Zoom CT scanner. The first set of experimental results are reported on bolus-chasing CT angiography using realistic bolus dynamics, real-time CT imaging and adaptive table control with physical vasculature phantoms. The data demonstrate that the proposed control approach tracks the bolus propagation well, and clearly outperforms the constant-speed scheme that is the current clinical standard.

A new scheme for view-dependent data differentiation in fan-beam and cone-beam computed tomography

In computed tomography, analytical fan-beam (FB) and cone-beam (CB) image reconstruction often involves a view-dependent data differentiation. The implementation of this differentiation step is critical in terms of resolution and image quality. In this work, we present a new differentiation scheme that is robust to changes in the data acquisition geometry and to coarse view sampling. Our scheme was compared to two previously suggested methods, which we call the direct scheme and the chain-rule scheme. Image reconstructions were performed from computer-simulated data of the Shepp-Logan phantom, the FORBILD thorax phantom and a modified FORBILD head phantom. For FB reconstruction, we investigated three acquisition geometries: a circular, an ellipse-shaped and a square-shaped trajectory. For CB reconstruction, the circle-plus-line trajectory was considered. Image comparison showed that the new scheme performs consistently well when varying the scenario, in both FB and CB geometry, unlike the other two schemes.

Lambda tomography with discontinuous scanning trajectories

Lambda tomography (LT) is a well-known local reconstruction technology to reduce the radiation dose or accommodate a limited imaging geometry. After a theoretical analysis of the so-called Calderon operator (CO), the necessary conditions for exact LT reconstruction are presented in terms of the 2D and 3D COs. Based on our previous results on LT, a general scheme is proposed to construct exact LT formulae in terms of the 2D CO with multiple segment trajectories. Every 2D formula has a corresponding 3D cone-beam formula in the Feldkamp framework in terms of the 2D CO which was illustrated in a triple-segment case. Our simulation results verify the correctness and demonstrate the merits of the proposed scheme.

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.

Data consistency based rigid motion artifact reduction in fan-beam CT

It is well known that a rigid in-plane motion can be decomposed into a translation and a rotation around an origin. Based on our previous work, we first extend the Helgason-Ludwig consistency condition (HLCC) to cover a general rigid motion in fan-beam geometry. Then, we model the general motion by several parameters, and develop an iterative scheme for estimation of the in-plane motion parameters. This scheme determines the motion parameters by numerically minimizing an objective function constructed based on the HLCC. After the motion parameters are estimated, image reconstruction can be performed to compensate for the motion effects. Finally, we implement the algorithm and evaluate its performance in numerical simulations.

Practical cone-beam lambda tomography

As a potentially important technology for medical x-ray computed tomography (CT), lambda tomography (LT) is to reconstruct a gradient-like image only from local projection data. Based on our recently derived exact fan-beam LT formula, [H. Y. Gu and G. Wang, Int. J. Biomed. Imaging 2006(1), 1-9 (2006)] here we propose a practical cone-beam LT algorithm for LT reconstruction from local data collected along an arbitrary smooth three-dimensional curve. A key step in our algorithm is to determine an appropriate vector perpendicular to the line connecting the x-ray source and an image point. The algorithm is implemented assuming an equispatial planar detector and a nonstandard spiral trajectory. The numerical simulation results demonstrate the merits of our method.

Chord-based image reconstruction in cone-beam CT with a curved detector

Modern computed tomography (CT) scanners use cone-beam configurations for increasing volume coverage, improving x-ray-tube utilization, and yielding isotropic spatial resolution. Recently, there have been significant developments in theory and algorithms for exact image reconstruction from cone-beam projections. In particular, algorithms have been proposed for image reconstruction on chords; and advantages over the existing algorithms offered by the chord-based algorithms include the high flexibility of exact image reconstruction for general scanning trajectories and the capability of exact reconstruction of images within a region of interest from truncated data. These chord-based algorithms have been developed only for flat-panel detectors. Many cone-beam CT scanners employ curved detectors for important practical considerations. Therefore, in this work, we have derived chord-based algorithms for a curved detector so that they can be applied to reconstructing images directly from data acquired by use of a CT scanner with a curved detector. We have also conducted preliminary numerical studies to demonstrate and evaluate the reconstruction properties of the derived chord-based algorithms for curved detectors.

Extending Three-Dimensional Weighted Cone Beam Filtered Backprojection (CB-FBP) Algorithm for Image Reconstruction in Volumetric CT at Low Helical Pitches

A three-dimensional (3D) weighted helical cone beam filtered backprojection (CB-FBP) algorithm (namely, original 3D weighted helical CB-FBP algorithm) has already been proposed to reconstruct images from the projection data acquired along a helical trajectory in angular ranges up to [0, 2 π]. However, an overscan is usually employed in the clinic to reconstruct tomographic images with superior noise characteristics at the most challenging anatomic structures, such as head and spine, extremity imaging, and CT angiography as well. To obtain the most achievable noise characteristics or dose efficiency in a helical overscan, we extended the 3D weighted helical CB-FBP algorithm to handle helical pitches that are smaller than 1: 1 (namely extended 3D weighted helical CB-FBP algorithm). By decomposing a helical over scan with an angular range of [0, 2π + Δβ] into a union of full scans corresponding to an angular range of [0, 2π], the extended 3D weighted function is a summation of all 3D weighting functions corresponding to each full scan. An experimental evaluation shows that the extended 3D weighted helical CB-FBP algorithm can improve noise characteristics or dose efficiency of the 3D weighted helical CB-FBP algorithm at a helical pitch smaller than 1: 1, while its reconstruction accuracy and computational efficiency are maintained. It is believed that, such an efficient CB reconstruction algorithm that can provide superior noise characteristics or dose efficiency at low helical pitches may find its extensive applications in CT medical imaging.

Data consistency based translational motion artifact reduction in fan-beam CT

A basic assumption in the classic computed tomography (CT) theory is that an object remains stationary in an entire scan. In biomedical CT/micro-CT, this assumption is often violated. To produce high-resolution images, such as for our recently proposed clinical micro-CT (CMCT) prototype, it is desirable to develop a precise motion estimation and image reconstruction scheme. In this paper, we first extend the Helgason-Ludwig consistency condition (HLCC) from parallel-beam to fan-beam geometry when an object is subject to a translation. Then, we propose a novel method to estimate the motion parameters only from sinograms based on the HLCC. To reconstruct the moving object, we formulate two generalized fan-beam reconstruction methods, which are in filtered backprojection and backprojection filtering formats, respectively. Furthermore, we present numerical simulation results to show that our approach is accurate and robust.

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.

A differentiable Shepp–Logan phantom and its applications in exact cone-beam CT

Recently, several exact cone-beam reconstruction algorithms, such as the generalized filtered-backprojection (FBP) and backprojection-filtration (BPF) methods, have been developed to solve the long object problem. Although the well-known 3D Shepp-Logan phantom (SLP) is often used to validate these algorithms, it is deficient due to the discontinuity of the SLP. In this paper, we first construct a differentiable polynomial function to approximate the unit rectangular function on [-1, 1]. Then, we use this function to obtain a differentiable ellipsoid phantom, whose x-ray transform is differentiable for any smooth scanning trajectory. Finally, we propose a differentiable Shepp-Logan phantom (DSLP) for numerical simulation of the exact cone-beam CT algorithms. Our numerical simulation shows that the reconstructed DSLP has a better image quality than the reconstructed SLP, and is complementary to the traditional SLP for evaluation of the exact cone-beam CT algorithms.