Region of interest reconstruction from truncated data in circular cone-beam CT

Dual Encoder-Based Dynamic-Channel Graph Convolutional Network With Edge Enhancement for Retinal Vessel Segmentation

Retinal vessel segmentation with deep learning technology is a crucial auxiliary method for clinicians to diagnose fundus diseases. However, the deep learning approaches inevitably lose the edge information, which contains spatial features of vessels while performing down-sampling, leading to the limited segmentation performance of fine blood vessels. Furthermore, the existing methods ignore the dynamic topological correlations among feature maps in the deep learning framework, resulting in the inefficient capture of the channel characterization. To address these limitations, we propose a novel dual encoder-based dynamic-channel graph convolutional network with edge enhancement (DE-DCGCN-EE) for retinal vessel segmentation. Specifically, we first design an edge detection-based dual encoder to preserve the edge of vessels in down-sampling. Secondly, we investigate a dynamic-channel graph convolutional network to map the image channels to the topological space and synthesize the features of each channel on the topological map, which solves the limitation of insufficient channel information utilization. Finally, we study an edge enhancement block, aiming to fuse the edge and spatial features in the dual encoder, which is beneficial to improve the accuracy of fine blood vessel segmentation. Competitive experimental results on five retinal image datasets validate the efficacy of the proposed DE-DCGCN-EE, which achieves more remarkable segmentation results against the other state-of-the-art methods, indicating its potential clinical application.

Enhancing Finite Element-Based Photoacoustic Tomography by Localized Reconstruction Method

Iterative reconstruction algorithm based on finite element (FE) modeling is a powerful approach in photoacoustic tomography (PAT). However, an iterative inverse algorithm using conventional FE meshing of the entire imaging zone is computationally demanding, which hinders this powerful tool in applications where quick image acquisition and/or a large image matrix is needed. To address this challenge, parallel computing techniques are proposed and implemented in the field. Here, we present an alternative approach for 2D PAT, which locoregionally reconstructs the region of interest (ROI) instead of the full imaging zone. Our simulated and phantom experimental results demonstrate that this ROI reconstruction algorithm can produce almost the same image quality as the conventional full zone-based reconstruction algorithm; however, the computation time can be significantly reduced without any additional hardware cost by more than two orders of magnitude (100-fold). This algorithm is further applied and validated in an in vivo study. The major vessel structures in a rat’s brain can be imaged clearly using our ROI-based approach, coupled with a mesh of 11,801 nodes. This novel algorithm can also be parallelized using MPI or GPU acceleration techniques to further enhance the reconstruction performance of FE-based PAT.

Projection-to-image transform frame: a lightweight block reconstruction network (LBRN) for computed tomography

To solve the problem of learning based computed tomography (CT) reconstruction, several reconstruction networks were invented. However, applying neural network to tomographic reconstruction still remains challenging due to unacceptable memory space requirement. In this study, we presents a novel lightweight block reconstruction network (LBRN), which transforms the reconstruction operator into a deep neural network by unrolling the filter back-projection (FBP) method. Specifically, the proposed network contains two main modules, which, respectively, correspond to the filter and back-projection of FBP method. The first module of LBRN decouples the relationship of Radon transform between the reconstructed image and the projection data. Therefore, the following module, block back-projection module, can use the block reconstruction strategy. Due to each image block is only connected with part filtered projection data, the network structure is greatly simplified and the parameters of the whole network is dramatically reduced. Moreover, this approach is trained end-to-end, working directly from raw projection data and does not depend on any initial images. Five reconstruction experiments are conducted to evaluate the performance of the proposed LBRN: full angle, low-dose CT, region of interest (ROI), metal artifacts reduction and real data experiment. The results of the experiments show that the LBRN can be effectively introduced into the reconstruction process and has outstanding advantages in terms of different reconstruction problems.

Data Extrapolation From Learned Prior Images for Truncation Correction in Computed Tomography

Data truncation is a common problem in computed tomography (CT). Truncation causes cupping artifacts inside the field-of-view (FOV) and anatomical structures missing outside the FOV. Deep learning has achieved impressive results in CT reconstruction from limited data. However, its robustness is still a concern for clinical applications. Although the image quality of learning-based compensation schemes may be inadequate for clinical diagnosis, they can provide prior information for more accurate extrapolation than conventional heuristic extrapolation methods. With extrapolated projection, a conventional image reconstruction algorithm can be applied to obtain a final reconstruction. In this work, a general plug-and-play (PnP) method for truncation correction is proposed based on this idea, where various deep learning methods and conventional reconstruction algorithms can be plugged in. Such a PnP method integrates data consistency for measured data and learned prior image information for truncated data. This shows to have better robustness and interpretability than deep learning only. To demonstrate the efficacy of the proposed PnP method, two state-of-the-art deep learning methods, FBPConvNet and Pix2pixGAN, are investigated for truncation correction in cone-beam CT in noise-free and noisy cases. Their robustness is evaluated by showing false negative and false positive lesion cases. With our proposed PnP method, false lesion structures are corrected for both deep learning methods. For FBPConvNet, the root-mean-square error (RMSE) inside the FOV can be improved from 92HU to around 30HU by PnP in the noisy case. Pix2pixGAN solely achieves better image quality than FBPConvNet solely for truncation correction in general. PnP further improves the RMSE inside the FOV from 42HU to around 27HU for Pix2pixGAN. The efficacy of PnP is also demonstrated on real clinical head data.

A motion correction approach for oral and maxillofacial cone-beam CT imaging

Patient movement affects image quality in oral and maxillofacial cone-beam computed tomography imaging. While many efforts are made to minimize the possibility of motion during a scan, relatively little attention has been given to motion correction after acquisition. We propose a novel method which can improve the image quality after an oral and maxillofacial scan. The proposed method is based on our previous work and is a retrospective motion estimation and motion compensation (ME/MC) approach that iteratively estimates and compensates for rigid pose change over time. During motion estimation, image update and motion update are performed alternately in a multi-resolution scheme to obtain the motion. We propose use of a feature-based motion update and patch-based image update in the iterative estimation process, to alleviate the effect of limited scan field of view on estimation. During motion compensation, a fine-resolution image reconstruction was performed with compensation for the estimated motion. The proposed ME/MC method was evaluated with simulations, phantom and patient studies. Two experts in dentomaxillofacial radiology assessed the diagnostic importance of the resulting motion artifact suppression. The quality of the reconstructed images was improved after motion compensation, and most of the image artifacts were eliminated. Quantitative analysis by comparison to a reference image and by calculation of a sharpness metric agreed with the qualitative observation. The results are promising, and further evaluation is required to assess the clinical value of the proposed method.

Global imaging with high resolution region of interest using fusion data based on dual-field of view detection system

X-ray micro-computed tomography (CT) is an important tool for high-resolution three-dimensional imaging. But one limitation of micro-CT is the compromise between resolution and fields of view (FOV). In this paper, we develop an x-rays dual-FOV optical coupling detection (DFOCD) system for global imaging with high-resolution region of interest (ROI). In DFOCD system, the beam splitter separates lights to form two sub-optical paths, two objectives with different FOV and magnification are used in the two sub-optical paths for dual-FOV imaging. Then a data fusion method is proposed to register and fuse dual-FOV data. Reconstructed images are obtained based on back projection filtering algorithm using fusion data. Dual-FOV data are collected simultaneously in DFOCD system, which precludes artifacts in fusion images from phantom movement or changes in two acquisitions on common micro-CT, and also saves scanning time. Simulation and experimental results show that details in ROI and global morphology of phantoms are correctly reconstructed. Bright ring artifacts of ROI caused by truncated data are corrected in reconstruction images. Therefore, global imaging with high-resolution ROI of samples can be obtained by single scan experiment using DFOCD system and data fusion method, which is expected to expand the application of micro-CT.

A TV-minimization image-reconstruction algorithm without system matrix

PURPOSE

Total Variation (TV) minimization algorithm is a classical compressed sensing (CS) based iterative image reconstruction algorithm that can accurately reconstruct images from sparse-view projections in computed tomography (CT). However, the system matrix used in the algorithm is often too large to be stored in computer memory. The purpose of this study is to investigate a new TV algorithm based on image rotation and without system matrix to avoid the memory requirement of system matrix.

METHODS

Without loss of generality, a rotation-based adaptive steepest descent-projection onto convex sets (R-ASD-POCS) algorithm is proposed and tested to solve the TV model in parallel beam CT. Specifically, simulation experiments are performed via the Shepp-Logan, FORBILD and real CT image phantoms are used to verify the inverse-crime capability of the algorithm and evaluate the sparse reconstruction capability and the noise suppression performance of the algorithm.

RESULTS

Experimental results show that the algorithm can achieve inverse-crime, accurate sparse reconstruction and thus accurately reconstruct images from noisy projections. Compared with the classical ASD-POCS algorithm, the new algorithm may yield the similar image reconstruction accuracy without use of the huge system matrix, which saves the computational memory space significantly. Additionally, the results also show that R-ASD-POCS algorithm is faster than ASD-POCS.

CONCLUSIONS

The proposed new algorithm can effectively solve the problem of using huge memory in large scale and iterative image reconstruction. Integrating with ASD-POCS frame, this no-system-matrix based scheme may be readily extended and applied to any iterative image reconstructions.

Differentiated Backprojection Domain Deep Learning for Conebeam Artifact Removal

Conebeam CT using a circular trajectory is quite often used for various applications due to its relative simple geometry. For conebeam geometry, Feldkamp, Davis and Kress algorithm is regarded as the standard reconstruction method, but this algorithm suffers from so-called conebeam artifacts as the cone angle increases. Various model-based iterative reconstruction methods have been developed to reduce the cone-beam artifacts, but these algorithms usually require multiple applications of computational expensive forward and backprojections. In this paper, we develop a novel deep learning approach for accurate conebeam artifact removal. In particular, our deep network, designed on the differentiated backprojection domain, performs a data-driven inversion of an ill-posed deconvolution problem associated with the Hilbert transform. The reconstruction results along the coronal and sagittal directions are then combined using a spectral blending technique to minimize the spectral leakage. Experimental results under various conditions confirmed that our method generalizes well and outperforms the existing iterative methods despite significantly reduced runtime complexity.

Volume-of-interest imaging with dynamic fluence modulation using multiple aperture devices

Volume-of-interest (VOI) imaging is a strategy in computed tomography (CT) that restricts x-ray fluence to particular anatomical targets via dynamic beam modulation. This permits dose reduction while retaining image quality within the VOI. VOI-CT implementation has been challenged, in part, by a lack of hardware solutions for tailoring the incident fluence to the patient and anatomical site, as well as difficulties involving interior tomography reconstruction of truncated projection data. We propose a general VOI-CT imaging framework using multiple aperture devices (MADs), an emerging beam filtration scheme based on two binary x-ray filters. Location of the VOI is prescribed using two scout views at anterior-posterior (AP) and lateral perspectives. Based on a calibration of achievable fluence field patterns, MAD motion trajectories were designed using an optimization objective that seeks to maximize the relative fluence in the VOI subject to minimum fluence constraints. A modified penalized-likelihood method is developed for reconstruction of heavily truncated data using the full-field scout views to help solve the interior tomography problem. Physical experiments were conducted to show the feasibility of noncentered and elliptical VOI in two applications-spine and lung imaging. Improved dose utilization and retained image quality are validated with respect to standard full-field protocols. We observe that the contrast-to-noise ratio (CNR) is 40% higher compared with low-dose full-field scans at the same dose. The total dose reduction is 50% for equivalent image quality (CNR) within the VOI.

Backprojection Filtration Image Reconstruction Approach for Reducing High-Density Object Artifacts in Digital Breast Tomosynthesis

While an accurate image reconstruction of digital breast tomosynthesis (DBT) is fundamentally impossible due to its limited data, the DBT is increasingly used in clinics for its rich image information at a relatively low dose. One of the dominant image artifacts in DBT that hinders a faithful diagnosis is high-density object artifact in conjunction with a limited angle problem. In this paper, we developed a very efficient method for reconstructing DBT images with much reduced high-density object artifacts. The method is based on backprojection filtration reconstruction algorithm, voting strategy, and image blending. Data derivatives were backprojected with appropriate weights to reduce ripple artifacts by use of the voting strategy. We generated another differentiated backprojection volume, where the edges of high-density objects are replaced by the background. After Hilbert transform, we blended the two images to reduce undershoot artifacts. Physical phantoms were scanned and we compared conventional filtered backprojection, filtered backprojection with weighted backprojection, and our proposed method. Ripple artifacts were dramatically suppressed and undershoot artifacts were also greatly suppressed in the proposed method.

A weighted rebinned backprojection-filtration algorithm from partially beam-blocked data for a single-scan cone-beam CT with hybrid type scatter correction

PURPOSE

Scatter contamination constitutes a dominant source of degradation of image quality in cone-beam computed tomography (CBCT). We have recently developed an analytic image reconstruction method with a scatter correction capability from the partially blocked cone-beam data out of a single scan. Despite its easy implementation and its computational efficiency, the developed method may result in additional image artifacts for a large cone angle geometry due to data inconsistency. To improve the image quality at a large cone angle, we propose a weighted rebinned backprojection-filtration (wrBPF) algorithm in conjunction with a hybrid type scatter correction approach.

METHODS

The proposed method uses a beam-blocker array that provides partial data for scatter correction and image reconstruction and that only blocks the beam within a limited cone angle. This design allows a chance to keep the image quality at larger cone angles by use of data redundancy since the projection data corresponding to larger cone angles are not blocked. However, the scatter correction would not be straightforward. In order to correct for the scatter in the projections at larger cone angles, we propose a novel scatter correction method combining a measurement-based and a convolution-based method. We first estimated the scatter signal using a measurement-based method in the partially beam-blocked regions, and then optimized the fitting parameters of a convolution-kernel that can be used for scatter correction in the projections at larger cone angles. For image reconstruction, we developed a wrBPF with butterfly filtering. We have conducted an experimental study to validate the proposed algorithm for image reconstruction and scatter correction.

RESULTS

The experimental results revealed that the developed reconstruction method makes full use of the benefits of partial beam-blocking for scatter correction and image reconstruction and at the same time enhances image quality at larger cone angles by use of an optimized convolution-based scatter correction.

CONCLUSIONS

The proposed method that enjoys the advantages of both measurement-based and convolution-based methods for scatter correction has successfully demonstrated its capability of reconstructing accurate images out of a single scan in circular CBCT.

On the data acquisition, image reconstruction, cone beam artifacts, and their suppression in axial MDCT and CBCT - A review

PURPOSE

In the clinic, computed tomography (CT) has evolved into an essential modality for diagnostic imaging by multidetector row CT (MDCT) and image guided intervention by cone beam CT (CBCT). Recognizing the increasing importance of axial MDCT/CBCT in clinical and preclinical applications, and the existence of CB artifacts in MDCT/CBCT images, we provide a review of CB artifacts' root causes, rendering mechanisms and morphology, and possible solutions for elimination and/or reduction of the artifacts.

METHODS

By examining the null space in Radon and Fourier domain, the root cause of CB artifacts (i.e., data insufficiency) in axial MDCT/CBCT is analytically investigated, followed by a review of the data sufficiency conditions and the "circle +" source trajectories. The rendering mechanisms and morphology of CB artifacts in axial MDCT/CBCT and their special cases (e.g., half/short scan and full scan with latitudinally displaced detector) are then analyzed, followed by a survey of the potential solutions to suppress the artifacts. The phenomenon of imaged zone indention and its variation over FBP, BPF/DBPF, two-pass and iterative CB reconstruction algorithms and/or schemes are discussed in detail.

RESULTS

An interdomain examination of the null space provides an insightful understanding of the root cause of CB artifacts in axial MDCT/CBCT. The decomposition of CB artifacts rendering mechanisms facilitates understanding of the artifacts' behavior under different conditions and the potential solutions to suppress them. An inspection of the imaged zone intention phenomenon provides guidance on the design and implementation of CB image reconstruction algorithms and schemes for CB artifacts suppression in axial MDCT/CBCT.

CONCLUSIONS

With increasing importance of axial MDCT/CBCT in clinical and preclinical applications, this review article can update the community with in-depth information and clarification on the latest progress in dealing with CB artifacts and thus increase clinical/preclinical confidence.

X-ray diffraction tomography with limited projection information

X-ray diffraction tomography (XDT) records the spatially-resolved X-ray diffraction profile of an extended object. Compared to conventional transmission-based tomography, XDT displays high intrinsic contrast among materials of similar electron density and improves the accuracy in material identification thanks to the molecular structural information carried by diffracted photons. However, due to the weak diffraction signal, a tomographic scan covering the entire object typically requires a synchrotron facility to make the acquisition time more manageable. Imaging applications in medical and industrial settings usually do not require the examination of the entire object. Therefore, a diffraction tomography modality covering only the region of interest (ROI) and subsequent image reconstruction techniques with truncated projections are highly desirable. Here we propose a table-top diffraction tomography system that can resolve the spatially-variant diffraction form factor from internal regions within extended samples. We demonstrate that the interior reconstruction maintains the material contrast while reducing the imaging time by 6 folds. The presented method could accelerate the acquisition of XDT and be applied in portable imaging applications with a reduced radiation dose.

Theoretically exact backprojection filtration algorithm for multi-segment linear trajectory

A theoretically exact backprojection filtration algorithm is proved and implemented for image reconstruction from a multi-segment linear trajectory assuming fan-beam geometry. The reconstruction formula is based on a concept of linear PI-line (L-PI) proposed in our previous work. The proof is completed in two consecutive steps. In the first step, it is proved that theoretically exact image reconstruction can be obtained on an arbitrary L-PI line from an infinite straight-line trajectory. In the second step, it is shown that accurate image reconstruction can be achieved from a multi-segment line trajectory by introducing a weight function to deal with the data redundancy. Numerical implementation and simulation results validate the correctness of our theoretical results.

An Investigation of Low-Dose 3D Scout Scans for Computed Tomography

PURPOSE

Commonly 2D scouts or topograms are used prior to CT scan acquisition. However, low-dose 3D scouts could potentially provide additional information for more effective patient positioning and selection of acquisition protocols. We propose using model-based iterative reconstruction to reconstruct low exposure tomographic data to maintain image quality in both low-dose 3D scouts and reprojected topograms based on those 3D scouts.

METHODS

We performed tomographic acquisitions on a CBCT test-bench using a range of exposure settings from 16.6 to 231.9 total mAs. Both an anthropomorphic phantom and a 32 cm CTDI phantom were scanned. The penalized-likelihood reconstructions were made using Matlab and CUDA libraries and reconstruction parameters were tuned to determine the best regularization strength and delta parameter. RMS error between reconstructions and the highest exposure reconstruction were computed, and CTDI_W values were reported for each exposure setting. RMS error for reprojected topograms were also computed.

RESULTS

We find that we are able to produce low-dose (0.417 mGy) 3D scouts that show high-contrast and large anatomical features while maintaining the ability to produce traditional topograms.

CONCLUSIONS

We demonstrated that iterative reconstruction can mitigate noise in very low exposure CT acquisitions to enable 3D CT scout. Such additional 3D information may lead to improved protocols for patient positioning and acquisition refinements as well as a number of advanced dose reduction strategies that require localization of anatomical features and quantities that are not provided by simple 2D topograms.

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.

A two-step filtering-based iterative image reconstruction method for interior tomography

The optimization-based method that utilizes the additional sparse prior of region-of-interest (ROI) image, such as total variation, has been the subject of considerable research in problems of interior tomography reconstruction. One challenge for optimization-based iterative ROI image reconstruction is to build the relationship between ROI image and truncated projection data. When the reconstruction support region is smaller than the original object, an unsuitable representation of data fidelity may lead to bright truncation artifacts in the boundary region of field of view. In this work, we aim to develop an iterative reconstruction method to suppress the truncation artifacts and improve the image quality for direct ROI image reconstruction. A novel reconstruction approach is proposed based on an optimization problem involving a two-step filtering-based data fidelity. Data filtering is achieved in two steps: the first takes the derivative of projection data; in the second step, Hilbert filtering is applied in the differentiated data. Numerical simulations and real data reconstructions have been conducted to validate the new reconstruction method. Both qualitative and quantitative results indicate that, as theoretically expected, the proposed method brings reasonable performance in suppressing truncation artifacts and preserving detailed features. The presented local reconstruction method based on the two-step filtering strategy provides a simple and efficient approach for the iterative reconstruction from truncated projections.

Analytic image reconstruction from partial data for a single-scan cone-beam CT with scatter correction

PURPOSE

A beam-blocker composed of multiple strips is a useful gadget for scatter correction and/or for dose reduction in cone-beam CT (CBCT). However, the use of such a beam-blocker would yield cone-beam data that can be challenging for accurate image reconstruction from a single scan in the filtered-backprojection framework. The focus of the work was to develop an analytic image reconstruction method for CBCT that can be directly applied to partially blocked cone-beam data in conjunction with the scatter correction.

METHODS

The authors developed a rebinned backprojection-filteration (BPF) algorithm for reconstructing images from the partially blocked cone-beam data in a circular scan. The authors also proposed a beam-blocking geometry considering data redundancy such that an efficient scatter estimate can be acquired and sufficient data for BPF image reconstruction can be secured at the same time from a single scan without using any blocker motion. Additionally, scatter correction method and noise reduction scheme have been developed. The authors have performed both simulation and experimental studies to validate the rebinned BPF algorithm for image reconstruction from partially blocked cone-beam data. Quantitative evaluations of the reconstructed image quality were performed in the experimental studies.

RESULTS

The simulation study revealed that the developed reconstruction algorithm successfully reconstructs the images from the partial cone-beam data. In the experimental study, the proposed method effectively corrected for the scatter in each projection and reconstructed scatter-corrected images from a single scan. Reduction of cupping artifacts and an enhancement of the image contrast have been demonstrated. The image contrast has increased by a factor of about 2, and the image accuracy in terms of root-mean-square-error with respect to the fan-beam CT image has increased by more than 30%.

CONCLUSIONS

The authors have successfully demonstrated that the proposed scanning method and image reconstruction algorithm can effectively estimate the scatter in cone-beam projections and produce tomographic images of nearly scatter-free quality. The authors believe that the proposed method would provide a fast and efficient CBCT scanning option to various applications particularly including head-and-neck scan.

Effect of Low-Dose MDCT and Iterative Reconstruction on Trabecular Bone Microstructure Assessment

We investigated the effects of low-dose multi detector computed tomography (MDCT) in combination with statistical iterative reconstruction algorithms on trabecular bone microstructure parameters. Twelve donated vertebrae were scanned with the routine radiation exposure used in our department (standard-dose) and a low-dose protocol. Reconstructions were performed with filtered backprojection (FBP) and maximum-likelihood based statistical iterative reconstruction (SIR). Trabecular bone microstructure parameters were assessed and statistically compared for each reconstruction. Moreover, fracture loads of the vertebrae were biomechanically determined and correlated to the assessed microstructure parameters. Trabecular bone microstructure parameters based on low-dose MDCT and SIR significantly correlated with vertebral bone strength. There was no significant difference between microstructure parameters calculated on low-dose SIR and standard-dose FBP images. However, the results revealed a strong dependency on the regularization strength applied during SIR. It was observed that stronger regularization might corrupt the microstructure analysis, because the trabecular structure is a very small detail that might get lost during the regularization process. As a consequence, the introduction of SIR for trabecular bone microstructure analysis requires a specific optimization of the regularization parameters. Moreover, in comparison to other approaches, superior noise-resolution trade-offs can be found with the proposed methods.

The Added Value of Volume-of-Interest C-Arm CT Imaging during Endovascular Treatment of Intracranial Aneurysms

BACKGROUND AND PURPOSE

Successful endovascular treatment of intracranial aneurysms requires understanding the exact relationship of implanted devices to the aneurysm, parent artery, and other branch vessels during the treatment. Intraprocedural C-arm CT imaging has been shown to provide such information. However, its repeated use is limited due to increasing radiation exposure to the patient. The goal of this study was to evaluate a new volume-of-interest C-arm CT imaging technique, which would provide device-specific information through multiple 3D acquisitions of only the region of interest, thus reducing cumulative radiation exposure to the patient.

MATERIALS AND METHODS

VOI C-arm CT images were obtained in 28 patients undergoing endovascular treatment of intracranial aneurysms. VOI images were acquired with the x-ray source collimated around the deployed device, both horizontally and vertically. The images were reconstructed by using a novel prototype robust reconstruction algorithm to minimize truncation artifacts from double collimation. The reconstruction accuracy of VOI C-arm CT images was assessed quantitatively by comparing them with the full-head noncollimated images.

RESULTS

Quantitative analysis showed that the quality of VOI C-arm CT images is comparable with that of the standard Feldkamp, Davis, and Kress reconstruction of noncollimated C-arm CT images (correlation coefficient = 0.96 and structural similarity index = 0.92). Furthermore, 91.5% reduction in dose-area product was achieved with VOI imaging compared with the full-head acquisition.

CONCLUSIONS

VOI imaging allows multiple 3D C-arm CT acquisitions and provides information related to device expansion, parent wall apposition, and neck coverage during the procedure, with very low additional radiation exposure to the patient.

Axial Cone-Beam Reconstruction by Weighted BPF/DBPF and Orthogonal Butterfly Filtering

GOAL

The backprojection-filtration (BPF) and the derivative backprojection filtered (DBPF) algorithms, in which Hilbert filtering is the common algorithmic feature, are originally derived for exact helical reconstruction from cone-beam (CB) scan data and axial reconstruction from fan beam data, respectively. These two algorithms can be heuristically extended for image reconstruction from axial CB scan data, but induce severe artifacts in images located away from the central plane, determined by the circular source trajectory. We propose an algorithmic solution herein to eliminate the artifacts.

METHODS

The solution is an integration of three-dimensional (3-D) weighted axial CB-BPF/DBPF algorithm with orthogonal butterfly filtering, namely axial CB-BPF/DBPF cascaded with orthogonal butterfly filtering. Using the computer simulated Forbild head and thoracic phantoms that are rigorous in inspecting the reconstruction accuracy, and an anthropomorphic thoracic phantom with projection data acquired by a CT scanner, we evaluate the performance of the proposed algorithm.

RESULTS

Preliminary results show that the orthogonal butterfly filtering can eliminate the severe streak artifacts existing in the images reconstructed by the 3-D weighted axial CB-BPF/DBPF algorithm located at off-central planes.

CONCLUSION

Integrated with orthogonal butterfly filtering, the 3-D weighted CB-BPF/DBPF algorithm can perform at least as well as the 3-D weighted CB-FBP algorithm in image reconstruction from axial CB scan data.

SIGNIFICANCE

The proposed 3-D weighted axial CB-BPF/DBPF cascaded with orthogonal butterfly filtering can be an algorithmic solution for CT imaging in extensive clinical and preclinical applications.

Dental cone beam CT: A review

For the maxillofacial region, there are various indications that cannot be interpreted from 2D images and will benefit from multiplanar viewing. Dental cone beam CT (CBCT) utilises a cone- or pyramid-shaped X-ray beam using mostly flat-panel detectors for 3D image reconstruction with high spatial resolution. The vast increase in availability and amount of these CBCT devices offers many clinical benefits, and their ongoing development has potential to bring various new clinical applications for medical imaging. Additionally, there is also a need for high quality research and education. European guidelines promote the use of a medical physics expert for advice on radiation protection, patient dose optimisation, and equipment testing. In this review article, we perform a comparison of technical equipment based on manufacturer data, including scanner specific X-ray spectra, and describe issues concerning CBCT image reconstruction and image quality, and also address radiation dose issues, dosimetry, and optimisation. We also discuss clinical needs and what type of education users should have in order to operate CBCT systems safely. We will also take a look into the future and discuss the issues that still need to be solved.

Reconstruction of four-dimensional computed tomography lung images by applying spatial and temporal anatomical constraints using a Bayesian model

Current four-dimensional computed tomography (4-D CT) lung image reconstruction methods rely on respiratory gating, such as surrogate, to sort the large number of axial images captured during multiple breathing cycles into serial three-dimensional CT images of different respiratory phases. Such sorting methods may be subject to external surrogate signal noises due to poor reproducibility of breathing cycles. New image-matching-based reconstruction algorithms refine the 4-D CT reconstruction by matching neighboring image slices, and they generally work better for the cine mode of 4-D CT acquisition than the helical mode due to different table positions of axial images in the helical mode. We propose a Bayesian model (BM) based automated 4-D CT lung image reconstruction for helical mode scans. BM allows for applying new spatial and temporal anatomical constraints in the optimization procedure. Using an iterative optimization procedure, each axial image is assigned to a respiratory phase to make sure the anatomical structures are spatially and temporally smooth based on the BM framework. In experiments, we visually and quantitatively compared the results of the proposed BM-based 4-D CT reconstruction with the respiratory surrogate and the normalized cross-correlation based image matching method using both simulated and actual 4-D patient scans. The results indicated that the proposed algorithm yielded more accurate reconstruction and fewer artifacts in the 4-D CT image series.

Region-of-interest cone beam computed tomography (ROI CBCT) with a high resolution CMOS detector

Cone beam computed tomography (CBCT) systems with rotational gantries that have standard flat panel detectors (FPD) are widely used for the 3D rendering of vascular structures using Feldkamp cone beam reconstruction algorithms. One of the inherent limitations of these systems is limited resolution (<3 lp/mm). There are systems available with higher resolution but their small FOV limits them to small animal imaging only. In this work, we report on region-of-interest (ROI) CBCT with a high resolution CMOS detector (75 μm pixels, 600 μm HR-CsI) mounted with motorized detector changer on a commercial FPD-based C-arm angiography gantry (194 μm pixels, 600 μm HL-CsI). A cylindrical CT phantom and neuro stents were imaged with both detectors. For each detector a total of 209 images were acquired in a rotational protocol. The technique parameters chosen for the FPD by the imaging system were used for the CMOS detector. The anti-scatter grid was removed and the incident scatter was kept the same for both detectors with identical collimator settings. The FPD images were reconstructed for the 10 cm x10 cm FOV and the CMOS images were reconstructed for a 3.84 cm × 3.84 cm FOV. Although the reconstructed images from the CMOS detector demonstrated comparable contrast to the FPD images, the reconstructed 3D images of the neuro stent clearly showed that the CMOS detector improved delineation of smaller objects such as the stent struts (~70 μm) compared to the FPD. Further development and the potential for substantial clinical impact are suggested.

Prior-based artifact correction (PBAC) in computed tomography

PURPOSE

Image quality in computed tomography (CT) often suffers from artifacts which may reduce the diagnostic value of the image. In many cases, these artifacts result from missing or corrupt regions in the projection data, e.g., in the case of metal, truncation, and limited angle artifacts. The authors propose a generalized correction method for different kinds of artifacts resulting from missing or corrupt data by making use of available prior knowledge to perform data completion.

METHODS

The proposed prior-based artifact correction (PBAC) method requires prior knowledge in form of a planning CT of the same patient or in form of a CT scan of a different patient showing the same body region. In both cases, the prior image is registered to the patient image using a deformable transformation. The registered prior is forward projected and data completion of the patient projections is performed using smooth sinogram inpainting. The obtained projection data are used to reconstruct the corrected image.

RESULTS

The authors investigate metal and truncation artifacts in patient data sets acquired with a clinical CT and limited angle artifacts in an anthropomorphic head phantom data set acquired with a gantry-based flat detector CT device. In all cases, the corrected images obtained by PBAC are nearly artifact-free. Compared to conventional correction methods, PBAC achieves better artifact suppression while preserving the patient-specific anatomy at the same time. Further, the authors show that prominent anatomical details in the prior image seem to have only minor impact on the correction result.

CONCLUSIONS

The results show that PBAC has the potential to effectively correct for metal, truncation, and limited angle artifacts if adequate prior data are available. Since the proposed method makes use of a generalized algorithm, PBAC may also be applicable to other artifacts resulting from missing or corrupt data.

Towards clinical application of a Laplace operator-based region of interest reconstruction algorithm in C-arm CT

It is known that a reduction of the field-of-view in 3-D X-ray imaging is proportional to a reduction in radiation dose. The resulting truncation, however, is incompatible with conventional reconstruction algorithms. Recently, a novel method for region of interest reconstruction that uses neither prior knowledge nor extrapolation has been published, named approximated truncation robust algorithm for computed tomography (ATRACT). It is based on a decomposition of the standard ramp filter into a 2-D Laplace filtering and a 2-D Radon-based residual filtering step. In this paper, we present two variants of the original ATRACT. One is based on expressing the residual filter as an efficient 2-D convolution with an analytically derived kernel. The second variant is to apply ATRACT in 1-D to further reduce computational complexity. The proposed algorithms were evaluated by using a reconstruction benchmark, as well as two clinical data sets. The results are encouraging since the proposed algorithms achieve a speed-up factor of up to 245 compared to the 2-D Radon-based ATRACT. Reconstructions of high accuracy are obtained, e.g., even real-data reconstruction in the presence of severe truncation achieve a relative root mean square error of as little as 0.92% with respect to nontruncated data.

Dual-exposure technique for extending the dynamic range of x-ray flat panel detectors

This work presents an approach to extend the dynamic range of x-ray flat panel detectors by combining two acquisitions of the same sample taken with two different x-ray photon flux levels and the same beam spectral configuration. In order to combine both datasets, the response of detector pixels was modelled in terms of mean and variance using a linear model. The model was extended to take into account the effect of pixel saturation. We estimated a joint probability density function (j-pdf) of the pixel values by assuming that each dataset follows an independent Gaussian distribution. This j-pdf was used for estimating the final pixel value of the high-dynamic-range dataset using a maximum likelihood method. The suitability of the pixel model for the representation of the detector signal was assessed using experimental data from a small-animal cone-beam micro-CT scanner equipped with a flat panel detector. The potential extension in dynamic range offered by our method was investigated for generic flat panel detectors using analytical expressions and simulations. The performance of the proposed dual-exposure approach in realistic imaging environments was compared with that of a regular single-exposure technique using experimental data from two different phantoms. Image quality was assessed in terms of signal-to-noise ratio, contrast, and analysis of profiles drawn on the images. The dynamic range, measured as the ratio between the exposure for saturation and the exposure equivalent to instrumentation noise, was increased from 76.9 to 166.7 when using our method. Dual-exposure results showed higher contrast-to-noise ratio and contrast resolution than the single-exposure acquisitions for the same x-ray dose. In addition, image artifacts were reduced in the combined dataset. This technique to extend the dynamic range of the detector without increasing the dose is particularly suited to image samples that contain both low and high attenuation regions.

Accelerating ordered subsets image reconstruction for X-ray CT using spatially nonuniform optimization transfer

Statistical image reconstruction algorithms in X-ray computed tomography (CT) provide improved image quality for reduced dose levels but require substantial computation time. Iterative algorithms that converge in few iterations and that are amenable to massive parallelization are favorable in multiprocessor implementations. The separable quadratic surrogate (SQS) algorithm is desirable as it is simple and updates all voxels simultaneously. However, the standard SQS algorithm requires many iterations to converge. This paper proposes an extension of the SQS algorithm that leads to spatially nonuniform updates. The nonuniform (NU) SQS encourages larger step sizes for the voxels that are expected to change more between the current and the final image, accelerating convergence, while the derivation of NU-SQS guarantees monotonic descent. Ordered subsets (OS) algorithms can also accelerate SQS, provided suitable "subset balance" conditions hold. These conditions can fail in 3-D helical cone-beam CT due to incomplete sampling outside the axial region-of-interest (ROI). This paper proposes a modified OS algorithm that is more stable outside the ROI in helical CT. We use CT scans to demonstrate that the proposed NU-OS-SQS algorithm handles the helical geometry better than the conventional OS methods and "converges" in less than half the time of ordinary OS-SQS.

Approximate truncation robust computed tomography--ATRACT

We present an approximate truncation robust algorithm to compute tomographic images (ATRACT). This algorithm targets at reconstructing volumetric images from cone-beam projections in scenarios where these projections are highly truncated in each dimension. It thus facilitates reconstructions of small subvolumes of interest, without involving prior knowledge about the object. Our method is readily applicable to medical C-arm imaging, where it may contribute to new clinical workflows together with a considerable reduction of x-ray dose. We give a detailed derivation of ATRACT that starts from the conventional Feldkamp filtered-backprojection algorithm and that involves, as one component, a novel original formula for the inversion of the two-dimensional Radon transform. Discretization and numerical implementation are discussed and reconstruction results from both, simulated projections and first clinical data sets are presented.

Achieving routine submillisievert CT scanning: report from the summit on management of radiation dose in CT

This Special Report presents the consensus of the Summit on Management of Radiation Dose in Computed Tomography (CT) (held in February 2011), which brought together participants from academia, clinical practice, industry, and regulatory and funding agencies to identify the steps required to reduce the effective dose from routine CT examinations to less than 1 mSv. The most promising technologies and methods discussed at the summit include innovations and developments in x-ray sources; detectors; and image reconstruction, noise reduction, and postprocessing algorithms. Access to raw projection data and standard data sets for algorithm validation and optimization is a clear need, as is the need for new, clinically relevant metrics of image quality and diagnostic performance. Current commercially available techniques such as automatic exposure control, optimization of tube potential, beam-shaping filters, and dynamic z-axis collimators are important, and education to successfully implement these methods routinely is critically needed. Other methods that are just becoming widely available, such as iterative reconstruction, noise reduction, and postprocessing algorithms, will also have an important role. Together, these existing techniques can reduce dose by a factor of two to four. Technical advances that show considerable promise for additional dose reduction but are several years or more from commercial availability include compressed sensing, volume of interest and interior tomography techniques, and photon-counting detectors. This report offers a strategic roadmap for the CT user and research and manufacturer communities toward routinely achieving effective doses of less than 1 mSv, which is well below the average annual dose from naturally occurring sources of radiation.

Cone-beam artifact evaluation of the factorization method

PURPOSE

The authors investigate the CB artifact behavior of the factorization approach recently suggested for image reconstruction in circular cone-beam computed tomography. This investigation is carried out in a typical C-arm geometry and involves simulated data and for the first time also phantom and clinical CB data acquired with a commercially available angiographic system.

METHODS

The CB artifact level is first measured using quantitative figures-of-merit that are computed from the reconstructions of the mathematical FORBILD head phantom and of a modified disk phantom. The authors then show reconstructions from a physical thorax phantom and clinical head data sets for a visual assessment of image quality. The performance of the factorization method is primarily compared to that of short-scan FDK, but the authors also show the results obtained with the full-scan FDK and the virtual PI-line BPF method for the simulation studies, as a benchmark.

RESULTS

Quantitatively, the FORBILD head phantom reconstructions of both FDK methods show a spatially averaged bias of up to 1.2% in the axial slices about 9 cm away from the plane of the scan, which is placed 4 cm below the central slice through the phantom. The artifact level for the short-scan FDK method and the virtual PI-line BPF method noticeably depends on the scan orientation. The factorization approach can significantly reduce both, this dependency as well as the reconstruction bias. It also shows visually an improved quality of the clinical images compared to short-scan FDK, particularly close to the spine and in the subcranial regions of the clinical data sets.

CONCLUSIONS

The factorization approach comes with noticeably lower reconstruction bias than the FDK methods and is least sensitive to the scan orientation among all considered short-scan methods. The data inconsistencies contained in the real data sets, such as scatter, beam hardening, or data truncation, show only little impact on the factorization results. Hence, in both, reconstructions from real and simulated data, the factorization method yields better image quality than short-scan FDK, albeit at the cost of some slight, directed high-frequency artifacts that are mostly visible in axial slices.

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.

Radiation dose reduction in computed tomography: techniques and future perspective

Despite universal consensus that computed tomography (CT) overwhelmingly benefits patients when used for appropriate indications, concerns have been raised regarding the potential risk of cancer induction from CT due to the exponentially increased use of CT in medicine. Keeping radiation dose as low as reasonably achievable, consistent with the diagnostic task, remains the most important strategy for decreasing this potential risk. This article summarizes the general technical strategies that are commonly used for radiation dose management in CT. Dose-management strategies for pediatric CT, cardiac CT, dual-energy CT, CT perfusion and interventional CT are specifically discussed, and future perspectives on CT dose reduction are presented.

Region-of-interest image reconstruction with intensity weighting in circular cone-beam CT for image-guided radiation therapy

Imaging plays a vital role in radiation therapy and with recent advances in technology considerable emphasis has been placed on cone-beam CT (CBCT). Attaching a kV x-ray source and a flat panel detector directly to the linear accelerator gantry has enabled progress in target localization techniques, which can include daily CBCT setup scans for some treatments. However, with an increasing number of CT scans there is also an increasing concern for patient exposure. An intensity-weighted region-of-interest (IWROI) technique, which has the potential to greatly reduce CBCT dose, in conjunction with the chord-based backprojection-filtration (BPF) reconstruction algorithm, has been developed and its feasibility in clinical use is demonstrated in this article. A nonuniform filter is placed in the x-ray beam to create regions of two different beam intensities. In this manner, regions outside the target area can be given a reduced dose but still visualized with a lower contrast to noise ratio. Image artifacts due to transverse data truncation, which would have occurred in conventional reconstruction algorithms, are avoided and image noise levels of the low- and high-intensity regions are well controlled by use of the chord-based BPF reconstruction algorithm. The proposed IWROI technique can play an important role in image-guided radiation therapy.

An Investigation of Compressive-sensing Image Reconstruction from Flying-focal-spot CT Data

Flying-focal-spot (FFS) technique has been used for improving the sampling condition in advanced clinical CT by collecting multiple cone-beam data sets with the focal-spot at different locations at each "projection view". It has been demonstrated that the increased sampling rate in FFS scans can substantially reduce aliasing artifacts in reconstructed images. However, the increase of the sampling density through multiple illuminations at each view can result in the increase of radiation dose to the imaged subject. In this work, we have applied a compressive-sensing (CS)-based algorithm to image reconstruction from data acquired in FFS scans. The results of the study demonstrate that aliasing artifacts observed images reconstructed by use of analytic algorithms can be suppressed effectively in images reconstructed with this CS-based algorithm from only data acquired at one FFS scan.

Rotational micro-CT using a clinical C-arm angiography gantry

Rotational angiography (RA) gantries are used routinely to acquire sequences of projection images of patients from which 3D renderings of vascular structures are generated using Feldkamp cone-beam reconstruction algorithms. However, these systems have limited resolution (<4 lp/mm). Micro-computed tomography (micro-CT) systems have better resolution (>10 lp/mm) but to date have relied either on rotating object imaging or small bore geometry for small animal imaging, and thus are not used for clinical imaging. The authors report here the development and use of a 3D rotational micro-angiography (RMA) system created by mounting a micro-angiographic fluoroscope (MAF) [35 microm pixel, resolution >10 microp/mm, field of view (FOV)=3.6 cm] on a standard clinical FPD-based RA gantry (Infinix, Model RTP12303J-G9E, Toshiba Medical Systems Corp., Tustin, CA). RA image sequences are obtained using the MAF and reconstructed. To eliminate artifacts due to image truncation, lower-dose (compared to MAF acquisition) full-FOV (FFOV) FPD RA sequences (194 microm pixel, FOV=20 cm) were also obtained to complete the missing data. The RA gantry was calibrated using a helical bead phantom. To ensure high-quality high-resolution reconstruction, the high-resolution images from the MAF were aligned spatially with the lower-dose FPD images, and the pixel values in the FPD image data were scaled to match those of the MAF. Images of a rabbit with a coronary stent placed in an artery in the Circle of Willis were obtained and reconstructed. The MAF images appear well aligned with the FPD images (average correlation coefficient before and after alignment: 0.65 and 0.97, respectively) Greater details without any visible truncation artifacts are seen in 3D RMA (MAF-FPD) images than in those of the FPD alone. The FWHM of line profiles of stent struts (100 microm diameter) are approximately 192+/-21 and 313+/-38 microm for the 3D RMA and FPD data, respectively. In addition, for the dual-acquisition 3D RMA, FFOV FPD data need not be of the highest quality, and thus may be acquired at lower dose compared to a standard FPD acquisition. These results indicate that this system could provide the basis for high resolution images of regions of interest in patients with a reduction in the integral dose compared to the standard FPD approach.

Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization

An iterative algorithm, based on recent work in compressive sensing, is developed for volume image reconstruction from a circular cone-beam scan. The algorithm minimizes the total variation (TV) of the image subject to the constraint that the estimated projection data is within a specified tolerance of the available data and that the values of the volume image are non-negative. The constraints are enforced by the use of projection onto convex sets (POCS) and the TV objective is minimized by steepest descent with an adaptive step-size. The algorithm is referred to as adaptive-steepest-descent-POCS (ASD-POCS). It appears to be robust against cone-beam artifacts, and may be particularly useful when the angular range is limited or when the angular sampling rate is low. The ASD-POCS algorithm is tested with the Defrise disk and jaw computerized phantoms. Some comparisons are performed with the POCS and expectation-maximization (EM) algorithms. Although the algorithm is presented in the context of circular cone-beam image reconstruction, it can also be applied to scanning geometries involving other x-ray source trajectories.

Region-of-interest image reconstruction in circular cone-beam microCT

Cone-beam microcomputed tomography (microCT) is one of the most popular choices for small animal imaging which is becoming an important tool for studying animal models with transplanted diseases. Region-of-interest (ROI) imaging techniques in CT, which can reconstruct an ROI image from the projection data set of the ROI, can be used not only for reducing imaging-radiation exposure to the subject and scatters to the detector but also for potentially increasing spatial resolution of the reconstructed images. Increasing spatial resolution in microCT images can facilitate improved accuracy in many assessment tasks. A method proposed previously for increasing CT image spatial resolution entails the exploitation of the geometric magnification in cone-beam CT. Due to finite detector size, however, this method can lead to data truncation for a large geometric magnification. The Feldkamp-Davis-Kress (FDK) algorithm yields images with artifacts when truncated data are used, whereas the recently developed backprojection filtration (BPF) algorithm is capable of reconstructing ROI images without truncation artifacts from truncated cone-beam data. We apply the BPF algorithm to reconstructing ROI images from truncated data of three different objects acquired by our circular cone-beam microCT system. Reconstructed images by use of the FDK and BPF algorithms from both truncated and nontruncated cone-beam data are compared. The results of the experimental studies demonstrate that, from certain truncated data, the BPF algorithm can reconstruct ROI images with quality comparable to that reconstructed from nontruncated data. In contrast, the FDK algorithm yields ROI images with truncation artifacts. Therefore, an implication of the studies is that, when truncated data are acquired with a configuration of a large geometric magnification, the BPF algorithm can be used for effective enhancement of the spatial resolution of a ROI image.

Tiny a priori knowledge solves the interior problem in computed tomography

Based on the concept of differentiated backprojection (DBP) (Noo et al 2004 Phys. Med. Biol. 49 3903, Pan et al 2005 Med. Phys. 32 673, Defrise et al 2006 Inverse Problems 22 1037), this paper shows that the solution to the interior problem in computed tomography is unique if a tiny a priori knowledge on the object f(x, y) is available in the form that f(x, y) is known on a small region located inside the region of interest. Furthermore, we advance the uniqueness result to obtain more general uniqueness results which can be applied to a wider class of imaging configurations. We also develop a reconstruction algorithm which can be considered an extension of the DBP-POCS (projection onto convex sets) method described by Defrise et al (2006 Inverse Problems 22 1037), where we not only extend this method to the interior problem but also introduce a new POCS algorithm to reduce computational cost. Finally, we present experimental results which show evidence that the inversion corresponding to each obtained uniqueness result is stable.

A factorization approach for cone-beam reconstruction on a circular short-scan

In this paper, we introduce a new algorithm for 3-D image reconstruction from cone-beam (CB) projections acquired along a partial circular scan. Our algorithm is based on a novel, exact factorization of the initial 3-D reconstruction problem into a set of independent 2-D inversion problems, each of which corresponds to finding the object density on one, single plane. Any such 2-D inversion problem is solved numerically using a projected steepest descent iteration scheme. We present a numerical evaluation of our factorization algorithm using computer-simulated CB data, without and with noise, of the FORBILD head phantom and of a disk phantom. First, we study quantitatively the impact of the reconstruction parameters on the algorithm performance. Next, we present reconstruction results for visual assessment of the achievable image quality and provide, for comparison, results obtained with two other state-of-the-art reconstruction algorithms for the circular short-scan.

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.

Circular CT in combination with a helical segment

The combination of circular CT with a helical trajectory segment results in a mathematically complete data set. We present a reconstruction algorithm which is mathematically exact and of the filtered back-projection type. The algorithm ensures that only Radon planes which are not covered along the circle are taken into account, when data from the helical segment are back-projected. Therefore, the helical segment contributes only to low-frequency parts of trans-axial slices. Data along the helix can be obtained with a very low acquisition dose.