FDK Algorithm Research Articles

Joint denoising and interpolating network for low-dose cone-beam CT reconstruction under hybrid dose-reduction strategy

Cone-beam computed tomography (CBCT) is generally reconstructed with hundreds of two-dimensional X-Ray projections through the FDK algorithm, and its excessive ionizing radiation of X-Ray may impair patients’ health. Two common dose-reduction strategies are to either lower the intensity of X-Ray, i.e., low-intensity CBCT, or reduce the number of projections, i.e., sparse-view CBCT. Existing efforts improve the low-dose CBCT images only under a single dose-reduction strategy. In this paper, we argue that applying the two strategies simultaneously can reduce dose in a gentle manner and avoid the extreme degradation of the projection data in a single dose-reduction strategy, especially under ultra-low-dose situations. Therefore, we develop a Joint Denoising and Interpolating Network (JDINet) in projection domain to improve the CBCT quality with the hybrid low-intensity and sparse-view projections. Specifically, JDINet mainly includes two important components, i.e., denoising module and interpolating module, to respectively suppress the noise caused by the low-intensity strategy and interpolate the missing projections caused by the sparse-view strategy. Because FDK actually utilizes the projection information after ramp-filtering, we develop a filtered structural similarity constraint to help JDINet focus on the reconstruction-required information. Afterward, we employ a Postprocessing Network (PostNet) in the reconstruction domain to refine the CBCT images that are reconstructed with denoised and interpolated projections. In general, a complete CBCT reconstruction framework is built with JDINet, FDK, and PostNet. Experiments demonstrate that our framework decreases RMSE by approximately 8 %, 15 %, and 17 %, respectively, on the 1/8, 1/16, and 1/32 dose data, compared to the latest methods. In conclusion, our learning-based framework can be deeply imbedded into the CBCT systems to promote the development of CBCT. Source code is available at https://github.com/LianyingChao/FusionLowDoseCBCT.

Development and validation of a 3D anthropomorphic phantom for dental CBCT imaging research.

Optimization of dental cone beam computed tomography (CBCT) imaging is still in a preliminary stage and should be addressed using task-based methods. Dedicated models containing relevant clinical tasks for image quality studies have yet to be developed. To present a methodology to develop and validate a virtual adult anthropomorphic voxel phantom for use in task-based image quality optimization studies in dental CBCT imaging research, focusing on root fracture (RF) detection tasks in the presence of metal artefacts. The phantom was developed from a CBCT scan with an isotropic voxel size of 0.2mm, from which the main dental structures, mandible and maxilla were segmented. The missing large anatomical structures, including the spine, skull and remaining soft tissues, were segmented from a lower resolution full skull scan. Anatomical abnormalities were absent in the areas of interest. Fine detailed dental structures, that could not be segmented due to the limited resolution and noise in the clinical data, were modelled using a-priori anatomical knowledge. Model resolution of the teeth was therefore increased to 0.05mm. Models of RFs as well as dental restorations to create the artefacts, were developed, and could be inserted in the phantom in any desired configuration. Simulated CBCT images of the models were generated using a newly developed multi-resolution simulation framework that incorporated the geometry, beam quality, noise and spatial resolution characteristics of a real dental CBCT scanner. Ray-tracing and Monte Carlo techniques were used to create the projection images, which were reconstructed using the classical FDK algorithm. Validation of the models was assessed by measurements of different tooth lengths, the pulp volume and the mandible, and comparison with reference values. Additionally, the simulated images were used in a reader study in which two oral radiologists had to score the realism level of the model's normal anatomy, as well as the modelled RFs and restorations. A model of an adult head, as well as models of RFs and different types of dental restorations were created. Anatomical measurements were consistent with ranges reported in literature. For the tooth length measurements, the deviations from the mean reference values were less than 20%. In 77% of all the measurements, the deviations were within 10.1%. The pulp volumes, and mandible measurements were within one standard deviation of the reference values. Regarding the normal anatomy, both readers considered the realism level of the dental structures to be good. Background structures received a lower realism score due to the lack of detailed enough trabecular bone structure, which was expected but not the focus of this study. All modelled RFs were scored at least adequate by at least one of the readers, both in appearance and position. The realism level of the modelled restorations was considered to be good. A methodology was proposed to develop and validate an anthropomorphic voxel phantom for image quality optimization studies in dental CBCT imaging, with a main focus on RF detection tasks. The methodology can be extended further to create more models representative of the clinical population.

A Hybrid FDK (H-FDK) Algorithm for Circular Cone-beam CT that Combines Variable Filtering and Conjugate Rays

Circular cone-beam computed tomography (CT) is a popular configuration in industrial non-destructive testing. Corresponding to the circular cone-beam CT, the Feldkamp, Davis, and Kress (FDK) algorithm is the most popular reconstruction method. However, in the case of large cone angle scanning, the slice artifacts of the reconstruction using the FDK algorithm are visible because the data collected with the circular orbit scan mode do not satisfy the completeness conditions for exact reconstruction. To solve the problem, this study proposed a hybrid FDK (H-FDK) algorithm using a method that combines variable filtering and conjugate rays. First, the shape and curvature of the detector were changed for the filtering paths to be variable. Then, the conjugate weighting function for backprojection was constructed. Subsequently, optimization experiments were conducted to find optimal parameters for the detector and conjugate weighting function. Finally, the comparative experimental results demonstrated that the slices reconstructed by the H-FDK algorithm produced a discernible quality improvement.

Sparse-View Cone-Beam CT Reconstruction by Bar-by-Bar Neural FDK Algorithm

ABSTRACT The Feldkamp, Davis and Kress algorithm is a computationally efficient reconstruction method for three-dimensional cone-beam computed tomography. However, it suffers from severe artefacts when the number of projections is insufficient. Although recent deep learning–based methods have succeeded in reconstructing such sparse-view projections, it is still challenging to reconstruct a large 3D volume efficiently because of heavy memory consumption and difficulty in obtaining sufficient training data. Therefore, we propose a deep learning method to overcome these drawbacks. Our method consecutively reconstructs short bars in 3D CT volume using the intensities of pixels on the moving trajectory projected on the detector of these bars. Then, we feed such pixel intensities into a neural network and train it to simulate the filtering and back-projection processes of the FDK algorithm. Since the reconstruction volume is separated into bars, the neural network can be used with only a small amount of memory. Furthermore, the network can be trained sufficiently with only a few training samples because plenty of bar data can be extracted even from a single CT image. We experimentally demonstrate that our approach works efficiently for both simulated and actual sparse-view CBCT data using training data extracted from only a single CT image.

Sparse-View Cone Beam CT Reconstruction Using Data-Consistent Supervised and Adversarial Learning From Scarce Training Data

Reconstruction of CT images from a limited set of projections through an object is important in several applications ranging from medical imaging to industrial settings. As the number of available projections decreases, traditional reconstruction techniques such as the FDK algorithm and model-based iterative reconstruction methods perform poorly. Recently, data-driven methods such as deep learning-based reconstruction have garnered a lot of attention in applications because they yield better performance when enough training data is available. However, even these methods have their limitations when there is a scarcity of available training data. This work focuses on image reconstruction in such settings, i.e., when both the number of available CT projections and the training data is extremely limited. We adopt a sequential reconstruction approach over several stages using an adversarially trained shallow network for ‘destreaking’ followed by a data-consistency update in each stage. To deal with the challenge of limited data, we use image subvolumes to train our method, and patch aggregation during testing. To deal with the computational challenge of learning on 3D datasets for 3D reconstruction, we use a hybrid 3D-to-2D mapping network for the ‘destreaking’ part. Comparisons to other methods over several test examples indicate that the proposed method has much potential, when both the number of projections and available training data are highly limited.

3D-printed large-area focused grid for scatter reduction in cone-beam CT.

Cone-beam computed tomography (CBCT) systems acquire volumetric data more efficiently than fan-beam or multislice CT, particularly when the anatomy of interest resides within the axial field-of-view of the detector and data can be acquired in one rotation. For such systems, scattered radiation remains a source of image quality degradation leading to increased noise, image artifacts, and CT number inaccuracies. Recent advances in metal additive manufacturing allow the production of highly focused antiscatter grids (2D-ASGs) that can be used to reduce scatter intensity, while preserving primary radiation transmission. We present the first implementation of a large-area, 2D-ASG for flat-panel CBCT, including grid-line artifact removal and related improvements in image quality. A 245 × 194 × 10 mm 2D-ASG was manufactured from chrome-cobalt alloy using laser powder-bed fusion (LPBF) (AM-400; Renishaw plc, New Mills Wotton-under-Edge, UK). The 2D-ASG had a square profile with a pitch of 9.09 lines/cm and 10:1 grid-ratio. The nominal 0.1mm grid septa were focused to a 732 mm x-ray source to optimize primary x-ray transmission and reduce grid-line shadowing at the detector. Powder-bed fusion ensured the structural stability of the ASG with no need for additional interseptal support. The 2D-ASG was coupled to a 0.139-mm element pitch flat-panel detector (DRX 3543, Carestream Health) and proper alignment was confirmed by consistent grid-line shadow thickness across the whole detector array. A 154-mm diameter CBCT image-quality-assurance phantom was imaged using a rotary stage and a ceiling-mounted, x-ray unit (Proteus XR/a, GE Medical Systems, 80kVp, 0.5mAs). Grid-line artifacts were removed using a combination of exposure-dependent gain correction and spatial-frequency, Fourier filtering. Projections were reconstructed using a Parker-weighted, FDK algorithm and voxels were spatially averaged to 357 × 357 × 595 µm to improve the signal-to-noise characteristics of the CBCT reconstruction. Finally, in order to compare image quality with and without scatter, the phantom was scanned again under the same CBCT conditions but with no 2D-ASG. No additional antiscatter (i.e., air-gap, bowtie filtration) strategies were used to evaluate the effects in image quality caused by the 2D-ASG alone. The large-area, 2D-ASG prototype was successfully designed and manufactured using LPBF. CBCT image-quality improvements using the 2D-ASG included: an overall 14.5% CNR increase across the volume; up to 48.8% CNR increase for low-contrast inserts inside the contrast plate of the QA phantom; and a 65% reduction of cupping artifact in axial profiles of water-filled cross sections of the phantom. Advanced image processing strategies to remove grid line artifacts did not affect the spatial resolution or geometric accuracy of the system. LPBF can be used to manufacture highly efficient, 2D-focused ASGs that can be easily coupled to clinical, flat-panel detectors. The implementation of ASGs in CBCT leads to reduced scatter-related artifacts, improved CT number accuracy, and enhanced CNR with no increased equivalent dose to the patient. Further improvements to image quality might be achieved with a combination of scatter-correction algorithms and iterative-reconstruction strategies. Finally, clinical applications where other scatter removal strategies are unfeasible might now achieve superior soft-tissue visualization and quantitative capabilities.

Intelligent Reconstruction Algorithm-Based Computed Tomography Images for Automatic Detection of Gastric Tumor.

The aim of this study was to explore the application of computed tomography (CT) images in the diagnosis of gastric tumor under the intelligent reconstruction algorithm (IRA). 120 patients with gastric cancer were selected and all the patients underwent CT scanning, and CT images were analyzed based on the Feldkamp-Davis-Kress algorithm (FDK algorithm) to evaluate the imaging features of gastric lesions. According to biopsy or surgical pathology, the detection rate of CT images was calculated. The results showed that there were three pathological types of benign tumors (polyps, leiomyomas, and mesenchymomas) and three pathological types of malignant tumors (mesenchymomas, adenomas, and lymphomas). In addition, the detection rates of CT scans were different, reaching 94.2% on different orientations of the stomach, 90.7% of benign tumors, and 90.9% of malignant tumors, so the detection rate of different orientations was relatively high. CT images based on the FDK IRA could realize a high detection rate in diagnosis, accurately locate the lesion, and display the characteristics of the lesion and the metastasis of surrounding tissues; there were significant differences between benign and malignant gastric tumors in CT images, and the detection effect was obvious, which is worthy of clinical application and promotion.

Benchmarking of different reconstruction algorithms for industrial cone-beam CT

In the field of industrial computed tomography, there have been a lot of interests in different reconstruction algorithms which could perform better than the standard FDK algorithm in non-ideal conditions leading to faster CT acquisitions. However, the computation efforts required by iterative algorithms are quite high, which makes them less practical in industrial environments. In this work, we propose a benchmark of the performances of various reconstruction algorithms using Tomographic Iterative GPU-based Reconstruction (TIGRE) toolbox; the benchmarking criteria used include both image quality metrics and taskoriented post-reconstruction results (measurements, porosity, etc.). Furthermore, we have also tested their performances with limited projections and limited angular range to facilitate faster CT acquisitions. The preliminary results indicate several improvements in the reconstructions (better feature definitions) with one of the iterative algorithms (CGLS: conjugate gradient least squares) as compared to FDK.

Planning CT-guided robust and fast cone-beam CT scatter correction using a local filtration technique.

Cone-beam CT (CBCT) has been widely utilized in image-guided radiotherapy. Planning CT (pCT)-aided CBCT scatter correction could further enhance image quality and extend CBCT application to dose calculation and adaptive planning. Nevertheless, existing pCT-based approaches demand accurate registration between pCT and CBCT, leading to limited imaging performance and increased computational cost when large anatomical discrepancies exist. In this work, we proposed a robust and fast CBCT scatter correction method using local filtration technique and rigid registration between pCT and CBCT (LF-RR). First of all, the pCT was rigidly registered with CBCT, then forward projection was performed on registered pCT to create scatter-free projections. The raw scatter signals were obtained via subtracting the scatter-free projections from the measured CBCT projections. Based on frequency and intensity threshold criteria, reliable scatter signals were selected from the raw scatter signals, and further filtered for global scatter estimation via local filtration technique. Finally, corrected CBCT was reconstructed with the projections generated by subtracting the scatter estimation from the raw CBCT projections using FDK algorithm. The LF-RR method was evaluated via comparison with another pCT-based scatter correction method based on Median and Gaussian filters (MG method). Proposed method was first validated on an anthropomorphic pelvis phantom, and showed satisfied performance on scatter removal even when anatomical mismatches were intentionally created on pCT. The quantitative analysis was further performed on four clinical CBCT images. Compared with the uncorrected CBCT, CBCT corrected by MG with rigid registration (MG-RR), MG with deformable registration (MG-DR), and LF-RR reduced the CT number error from to , and HU for adipose and from to , , 3 HU for muscle, respectively. After correction, the spatial non-uniformity (SNU) of CBCT corrected with MG-RR, MG-DR and LF-RR was , , and HU for adipose, and , , and HU for muscle, respectively. Meanwhile, the contrast-to-noise ratio (CNR) between muscle and adipose was increased by a factor of 2.70, 2.89 and 2.56, respectively. Using the LF-RR method, the scatter correction of 656 projections can be finished within 10 s and the corrected volumetric images (200 slices) can be obtained within 2 min. We developed a fast and robust pCT-based CBCT scatter correction method which exploits the local-filtration technique to promote the accuracy of scatter estimation and is resistant to pCT-to-CBCT registration uncertainties. Both phantom and patient studies showed the superiority of the proposed correction in imaging accuracy and computational efficiency, indicating promisingfuture clinical application.

Computation and Storage Efficient Sparse MART Algorithm for 2-D, 3-D Reconstruction from Fan Beam, Cone-Beam Projection Data

ABSTRACT Algebraic reconstruction algorithms are a better choice compared to transform-based algorithms whenever projection data is limited in nature. High computational cost and huge memory requirements are two major downsides of iterative reconstruction methods. Among all algebraic techniques, the Multiplicative Algebraic Reconstruction Technique (MART) is most popular because it maximizes the entropy (of the image) in the limiting case. In the present work, our ultimate goal is to reduce computational complexity and cope with the huge storage scenario of the MART algorithm. We propose a new sparse MART algorithm (Sp-MART) and test it with two-dimensional and three-dimensional (2D/3D) numerical data. A more accurate and efficient geometrical formula for calculating intersection length is also presented. Experimental projection data of human tooth and drip irrigation pipe is processed for further validation of the Sp-MART algorithm. Reconstructions of real specimens are also done using the FDK algorithm. The difference between two algorithms are investigated by calculating the structural similarity index (SSIM) and the L2 error of the results.

StaticCodeCT: single coded aperture tensorial X-ray CT.

Coded aperture X-ray CT (CAXCT) is a new low-dose imaging technology that promises far-reaching benefits in industrial and clinical applications. It places various coded apertures (CA) at a time in front of the X-ray source to partially block the radiation. The ill-posed inverse reconstruction problem is then solved using l1-norm-based iterative reconstruction methods. Unfortunately, to attain high-quality reconstructions, the CA patterns must change in concert with the view-angles making the implementation impractical. This paper proposes a simple yet radically different approach to CAXCT, which is coined StaticCodeCT, that uses a single-static CA in the CT gantry, thus making the imaging system amenable for practical implementations. Rather than using conventional compressed sensing algorithms for recovery, we introduce a new reconstruction framework for StaticCodeCT. Namely, we synthesize the missing measurements using low-rank tensor completion principles that exploit the multi-dimensional data correlation and low-rank nature of a 3-way tensor formed by stacking the 2D coded CT projections. Then, we use the FDK algorithm to recover the 3D object. Computational experiments using experimental projection measurements exhibit up to 10% gains in the normalized root mean square distance of the reconstruction using the proposed method compared with those attained by alternative low-dose systems.

Four-dimensional cone-beam CT reconstruction based on motion-compensated robust principal component analysis

To propose a motion compensation reconstruction method based on robust principal component analysis (RPCA) to reduce the influence of streak artifacts on accurate estimation of interphase motion deformation fields. We propose a RPCA motion compensation reconstruction algorithm to improve the estimation of motion deformation fields based on the traditional MC-FDK algorithm. RPCA was used to decompose the cone-beam computed tomography (CBCT) images into low-rank and sparse components, and the motion deformation fields between different phase images were then estimated using Horn and Schunck optical flow method from the low-rank images to reduce the influence of striping artifacts on the accuracy of estimation of interphase motion deformation fields. The performance of the algorithm was evaluated using simulation data and real data. The simulation phantom data was obtained by back-projection of 4D-CT images acquired from Philips 16-slice spiral CT using MATLAB software programming according to the scanning geometry of Varian Edge accelerator. The real patient data were obtained using the Elekta Synergy system of CBCT scanning system with half-fan mode CB projection data from lung cancer patients. Compared with images reconstructed using the traditional MC-FDK algorithm, the reconstructed image using the proposed method had clearer tissue boundaries with reduced motion artifact was reduced. The results of phantom data reconstruction showed that compared with the MC- FDK algorithm, the proposed algorithms resulted in improvements of PSNR by 25.4% and SSIM by 7.6%; compared with the FDK algorithm, PSNR was improved by 37.9% and SSIM by 17.6%. The proposed algorithm can achieve accurate estimation of inter-phase motion deformation fields and improve the quality of the reconstructed CBCT images.

A Computationally Efficient Reconstruction Algorithm for Circular Cone-Beam Computed Tomography Using Shallow Neural Networks.

Circular cone-beam (CCB) Computed Tomography (CT) has become an integral part of industrial quality control, materials science and medical imaging. The need to acquire and process each scan in a short time naturally leads to trade-offs between speed and reconstruction quality, creating a need for fast reconstruction algorithms capable of creating accurate reconstructions from limited data. In this paper, we introduce the Neural Network Feldkamp–Davis–Kress (NN-FDK) algorithm. This algorithm adds a machine learning component to the FDK algorithm to improve its reconstruction accuracy while maintaining its computational efficiency. Moreover, the NN-FDK algorithm is designed such that it has low training data requirements and is fast to train. This ensures that the proposed algorithm can be used to improve image quality in high-throughput CT scanning settings, where FDK is currently used to keep pace with the acquisition speed using readily available computational resources. We compare the NN-FDK algorithm to two standard CT reconstruction algorithms and to two popular deep neural networks trained to remove reconstruction artifacts from the 2D slices of an FDK reconstruction. We show that the NN-FDK reconstruction algorithm is substantially faster in computing a reconstruction than all the tested alternative methods except for the standard FDK algorithm and we show it can compute accurate CCB CT reconstructions in cases of high noise, a low number of projection angles or large cone angles. Moreover, we show that the training time of an NN-FDK network is orders of magnitude lower than the considered deep neural networks, with only a slight reduction in reconstruction accuracy.

A residual dense network assisted sparse view reconstruction for breast computed tomography

To develop and investigate a deep learning approach that uses sparse-view acquisition in dedicated breast computed tomography for radiation dose reduction, we propose a framework that combines 3D sparse-view cone-beam acquisition with a multi-slice residual dense network (MS-RDN) reconstruction. Projection datasets (300 views, full-scan) from 34 women were reconstructed using the FDK algorithm and served as reference. Sparse-view (100 views, full-scan) projection data were reconstructed using the FDK algorithm. The proposed MS-RDN uses the sparse-view and reference FDK reconstructions as input and label, respectively. Our MS-RDN evaluated with respect to fully sampled FDK reference yields superior performance, quantitatively and visually, compared to conventional compressed sensing methods and state-of-the-art deep learning based methods. The proposed deep learning driven framework can potentially enable low dose breast CT imaging.

Automated FDK-Filter Selection for Cone-Beam CT in Research Environments

Users of X-ray (micro-)CT in research environments often study many different types of objects, with many different research questions. For each new scan, the settings of the scan (number of angles, dose, cone angle) are chosen by the user, often based on how much time is available, the dose sensitivity of the sample, and geometrical characteristics of the particular CT-scanner that is used. The FDK algorithm is the most common reconstruction method used for circular cone-beam data. Its filter is typically chosen based on characteristics of the object, the scan parameters, and task-specific metrics. This imposes a problem for case-by-case research use, as selecting an optimal filter requires manual and subjective user choices as well as considerable expertise. In this article we present a computationally efficient and automated method to compute an FDK-filter for a given measured projection dataset that is optimal with respect to an objectively defined quality criterion that is based on the difference between the measured projection data and the computed projections of the reconstructed volume. We show that for a variety of objects, scan settings (number of angles and noise levels), and tasks (porosity quantification, threshold-based segmentation), the FDK-filters computed by our approach yield accurate results in terms of several different metrics that are comparable to filters manually selected for the experiments.

Stability and performance of FDK algorithm for CBCT in multithreaded implementation

We have written, optimized and tested a C/C++ project designed to simulate a CBCT experiment with an arbitrary shaped and structured three dimensional radiological phantom with high resolution and precision. This phantom was generated and later used to simulate the recording of the multiple cone beam projections under successive rotations of the coupled source and detector around it. This radiological phantom can be used to generate projections in the various testing chambers conditions and configurations including the mammography case. The synthesized projections were used to reconstruct the internal structure of the phantom with FDK algorithm. Our simulation code is also able to accept an arbitrary set of projections from other simulation software or from the real computer tomography setup. The simulation code includes various filtering techniques and has been hardware accelerated using the OpenMP directives.

Scatter Correction in Cone Beam CT for Metal Additive Manufacturing Components

This paper provides an x-ray scatter correction method for cone beam computed tomography (CT) to reduce cupping artifacts and image inhomogeneity of metal additive manufacturing (AM) components. Firstly, projections in 360° were obtained by a cone beam CT system. Secondly, the corresponding virtual CT system was built on Geant4 to obtain scatter photons. Different from previous studies, the geometry of the metal AM component was set by importing a CAD model of the component into Geant4, which can not only assure the accuracy of geometry but also simplify the definition of the geometry. Finally, the corresponding scatter photons were subtracted from the experimental projections in 360° to obtain corrected projections. Corrected reconstruction images were acquired via an FDK algorithm. In the corrected images, the average sum of squares of deviation of regions of interest was about 79.5% of that in the uncorrected images. Corrected images showed that cupping-shaped artifacts and image inhomogeneity were effectively reduced.

QR-Factorization Algorithm for Computed Tomography (CT): Comparison With FDK and Conjugate Gradient (CG) Algorithms

Even though QR-factorization of the system matrix for tomographic devices has been already used for medical imaging, to date, no satisfactory solution has been found for solving large linear systems, such as those used in computed tomography (CT) (in the order of $10^{6}$ equations). In CT, the Feldkamp, Davis, and Kress back projection algorithm (FDK) and iterative methods like conjugate gradient (CG) are the standard methods used for image reconstruction. As the image reconstruction problem can be modeled by a large linear system of equations, QR-factorization of the system matrix could be used to solve this system. Current advances in computer science enable the use of direct methods for solving such a large linear system. The QR-factorization is a numerically stable direct method for solving linear systems of equations, which is beginning to emerge as an alternative to traditional methods, bringing together the best from traditional methods. QR-factorization was chosen because the core of the algorithm, from the computational cost point of view, is precalculated and stored only once for a given CT system, and from then on, each image reconstruction only involves a backward substitution process and the product of a vector by a matrix. Image quality assessment was performed comparing contrast to noise ratio and noise power spectrum; performances regarding sharpness were evaluated by the reconstruction of small structures using data measured from a small animal 3-D CT. Comparisons of QR-factorization with FDK and CG methods show that QR-factorization is able to reconstruct more detailed images for a fixed voxel size.

GPU based parallel acceleration for fast C-arm cone-beam CT reconstruction

BackgroundWith the introduction of Flat Panel Detector technology, cone-beam CT (CBCT) has become a novel image modality, and widely applied in clinical practices. C-arm mounted CBCT has shown extra suitability in image guided interventional surgeries. During practice, how to acquire high resolution and high quality 3D images with the real time requirement of clinical applications remain challenging.MethodsIn this paper, we propose a GPU based accelerated method for fast C-arm CBCT 3D image reconstructions. A filtered back projection method is optimized and implemented with GPU parallel acceleration technique. A distributed system is designed to make full use of the image acquisition consumption to hide the reconstruction delay to further improve system performance.ResultsWith the acceleration both in algorithm and system design, we show that our method significantly increases system efficiency. The optimized GPU accelerated FDK algorithm improves the reconstruction efficiency. The system performance is further enhanced with the proposed system design by 26% and reconstruction delay is accelerated by 2.1 times when 90 frames of projections are used. When the number of frames used increases to 120, the numbers are 39% and 3.3 times. We also show that when the projection acquisition consumption increases, the reconstruction acceleration rate increases significantly.

Fast parallel image reconstruction for cone‐beam FDK algorithm

SummaryFDK algorithm is a popular analytical reconstruction method for practical cone‐beam CT scanners. Compared with iterative methods, the FDK algorithm is computationally efficient. However, the reconstruction speed remains a limitation for its application when dealing with high resolution images. In this paper, we propose a fast method for parallel implementation of the FDK algorithm by the use of multi‐GPU. First, we optimize the backprojection operation of FDK according to the property of geometric symmetry and the correlation between adjacent slices. Then, we utilize the multi‐thread technology to realize the parallel implementation of the optimized FDK algorithm on multi‐GPU. Finally, we implement the proposed method on a multi‐GPU platform. Numerical experiment shows that the proposed multi‐GPU‐based approach can reconstruct a 512 cubed volume in 1.9 seconds from 360 projections of resolution 512 ×512, which is 511 times faster than a traditional CPU–based approach and 5 times faster than a single GPU–based approach. In addition, the reconstruction results also indicate that the proposed method can maintain the same precision with traditional method.