Rapid 3-D cone-beam reconstruction with the simultaneous algebraic reconstruction technique (SART) using 2-D texture mapping hardware

ATTRN: Acoustic Information Encoder and Temperature Field Reconstruction Decoder Network for Boiler Temperature Field Reconstruction

Accurate and swift evaluation of the temperature distribution in boiler furnaces is essential for maximizing energy efficiency and ensuring operational safety. Traditional temperature field reconstruction algorithms, while effective, often suffer from accumulated errors, difficulty in solving ill-posed problems, low accuracy, and poor generalization. To overcome these limitations, a Temperature Field Reconstruction Network based on an acoustic information encoder (AIE) and a temperature field reconstruction decoder (TFRD) is proposed (ATTRN). This method directly utilizes acoustic measurement data for temperature field prediction, effectively balancing global semantic capture and local detail preservation. The proposed approach avoids complex traditional mathematical processing and empirical parameter selection, enhancing both accuracy and generalization. Simulation studies and engineering validations demonstrate the performance and industrial applicability of the proposed method.

Three-dimensional reconstruction of integrated implosion targets from simulated small-angle pinhole images

To indirectly evaluate the asymmetry of the radiation drive under limited measurement conditions in inertial confinement fusion research, we have proposed an integral method to approximate the three-dimensional self-radiation distribution of the compressed plasma core using only four pinhole images from a single laser entrance hole at a maximum projection angle of 10°. The simultaneous algebraic reconstruction technique (SART) that uses spatial constraints provided by the prior structural information and the central pinhole image is utilized in the simulation. The simulation results showed that the normalized mean square deviation between the original distribution and reconstruction results of the central radiation area of the simulated cavity was 0.4401, and the structural similarity of the cavity radiation distribution was 0.5566. Meanwhile, using more diagnostic holes could achieve better structural similarity and lower reconstruction error. In addition, the results indicated that our new proposed method could reconstruct the distribution of a compressed plasma core in a vacuum hohlraum with high accuracy.

GPU-based Branchless Distance-Driven Projection and Backprojection

Projection and backprojection operations are essential in a variety of image reconstruction and physical correction algorithms in CT. The distance-driven (DD) projection and backprojection are widely used for their highly sequential memory access pattern and low arithmetic cost. However, a typical DD implementation has an inner loop that adjusts the calculation depending on the relative position between voxel and detector cell boundaries. The irregularity of the branch behavior makes it inefficient to be implemented on massively parallel computing devices such as graphics processing units (GPUs). Such irregular branch behaviors can be eliminated by factorizing the DD operation as three branchless steps: integration, linear interpolation, and differentiation, all of which are highly amenable to massive vectorization. In this paper, we implement and evaluate a highly parallel branchless DD algorithm for 3D cone beam CT. The algorithm utilizes the texture memory and hardware interpolation on GPUs to achieve fast computational speed. The developed branchless DD algorithm achieved 137-fold speedup for forward projection and 188-fold speedup for backprojection relative to a single-thread CPU implementation. Compared with a state-of-the-art 32-thread CPU implementation, the proposed branchless DD achieved 8-fold acceleration for forward projection and 10-fold acceleration for backprojection. GPU based branchless DD method was evaluated by iterative reconstruction algorithms with both simulation and real datasets. It obtained visually identical images as the CPU reference algorithm.

A review of GPU-based medical image reconstruction

Tomographic image reconstruction is a computationally demanding task, even more so when advanced models are used to describe a more complete and accurate picture of the image formation process. Such advanced modeling and reconstruction algorithms can lead to better images, often with less dose, but at the price of long calculation times that are hardly compatible with clinical workflows. Fortunately, reconstruction tasks can often be executed advantageously on Graphics Processing Units (GPUs), which are exploited as massively parallel computational engines. This review paper focuses on recent developments made in GPU-based medical image reconstruction, from a CT, PET, SPECT, MRI and US perspective. Strategies and approaches to get the most out of GPUs in image reconstruction are presented as well as innovative applications arising from an increased computing capacity. The future of GPU-based image reconstruction is also envisioned, based on current trends in high-performance computing.

A comparison of linear interpolation models for iterative CT reconstruction

PURPOSE

Recent reports indicate that model-based iterative reconstruction methods may improve image quality in computed tomography (CT). One difficulty with these methods is the number of options available to implement them, including the selection of the forward projection model and the penalty term. Currently, the literature is fairly scarce in terms of guidance regarding this selection step, whereas these options impact image quality. Here, the authors investigate the merits of three forward projection models that rely on linear interpolation: the distance-driven method, Joseph's method, and the bilinear method. The authors' selection is motivated by three factors: (1) in CT, linear interpolation is often seen as a suitable trade-off between discretization errors and computational cost, (2) the first two methods are popular with manufacturers, and (3) the third method enables assessing the importance of a key assumption in the other methods.

METHODS

One approach to evaluate forward projection models is to inspect their effect on discretized images, as well as the effect of their transpose on data sets, but significance of such studies is unclear since the matrix and its transpose are always jointly used in iterative reconstruction. Another approach is to investigate the models in the context they are used, i.e., together with statistical weights and a penalty term. Unfortunately, this approach requires the selection of a preferred objective function and does not provide clear information on features that are intrinsic to the model. The authors adopted the following two-stage methodology. First, the authors analyze images that progressively include components of the singular value decomposition of the model in a reconstructed image without statistical weights and penalty term. Next, the authors examine the impact of weights and penalty on observed differences.

RESULTS

Image quality metrics were investigated for 16 different fan-beam imaging scenarios that enabled probing various aspects of all models. The metrics include a surrogate for computational cost, as well as bias, noise, and an estimation task, all at matched resolution. The analysis revealed fundamental differences in terms of both bias and noise. Task-based assessment appears to be required to appreciate the differences in noise; the estimation task the authors selected showed that these differences balance out to yield similar performance. Some scenarios highlighted merits for the distance-driven method in terms of bias but with an increase in computational cost. Three combinations of statistical weights and penalty term showed that the observed differences remain the same, but strong edge-preserving penalty can dramatically reduce the magnitude of these differences.

CONCLUSIONS

In many scenarios, Joseph's method seems to offer an interesting compromise between cost and computational effort. The distance-driven method offers the possibility to reduce bias but with an increase in computational cost. The bilinear method indicated that a key assumption in the other two methods is highly robust. Last, strong edge-preserving penalty can act as a compensator for insufficiencies in the forward projection model, bringing all models to similar levels in the most challenging imaging scenarios. Also, the authors find that their evaluation methodology helps appreciating how model, statistical weights, and penalty term interplay together.

3D alternating direction TV-based cone-beam CT reconstruction with efficient GPU implementation

Iterative image reconstruction (IIR) with sparsity-exploiting methods, such as total variation (TV) minimization, claims potentially large reductions in sampling requirements. However, the computation complexity becomes a heavy burden, especially in 3D reconstruction situations. In order to improve the performance for iterative reconstruction, an efficient IIR algorithm for cone-beam computed tomography (CBCT) with GPU implementation has been proposed in this paper. In the first place, an algorithm based on alternating direction total variation using local linearization and proximity technique is proposed for CBCT reconstruction. The applied proximal technique avoids the horrible pseudoinverse computation of big matrix which makes the proposed algorithm applicable and efficient for CBCT imaging. The iteration for this algorithm is simple but convergent. The simulation and real CT data reconstruction results indicate that the proposed algorithm is both fast and accurate. The GPU implementation shows an excellent acceleration ratio of more than 100 compared with CPU computation without losing numerical accuracy. The runtime for the new 3D algorithm is about 6.8 seconds per loop with the image size of 256 × 256 × 256 and 36 projections of the size of 512 × 512.

GPU-based high-performance computing for radiation therapy

Recent developments in radiotherapy therapy demand high computation powers to solve challenging problems in a timely fashion in a clinical environment. The graphics processing unit (GPU), as an emerging high-performance computing platform, has been introduced to radiotherapy. It is particularly attractive due to its high computational power, small size, and low cost for facility deployment and maintenance. Over the past few years, GPU-based high-performance computing in radiotherapy has experienced rapid developments. A tremendous amount of study has been conducted, in which large acceleration factors compared with the conventional CPU platform have been observed. In this paper, we will first give a brief introduction to the GPU hardware structure and programming model. We will then review the current applications of GPU in major imaging-related and therapy-related problems encountered in radiotherapy. A comparison of GPU with other platforms will also be presented.

Soft-tissue imaging with C-arm cone-beam CT using statistical reconstruction

The potential for statistical image reconstruction methods such as penalized-likelihood (PL) to improve C-arm cone-beam CT (CBCT) soft-tissue visualization for intraoperative imaging over conventional filtered backprojection (FBP) is assessed in this work by making a fair comparison in relation to soft-tissue performance. A prototype mobile C-arm was used to scan anthropomorphic head and abdomen phantoms as well as a cadaveric torso at doses substantially lower than typical values in diagnostic CT, and the effects of dose reduction via tube current reduction and sparse sampling were also compared. Matched spatial resolution between PL and FBP was determined by the edge spread function of low-contrast (∼ 40-80 HU) spheres in the phantoms, which were representative of soft-tissue imaging tasks. PL using the non-quadratic Huber penalty was found to substantially reduce noise relative to FBP, especially at lower spatial resolution where PL provides a contrast-to-noise ratio increase up to 1.4-2.2 × over FBP at 50% dose reduction across all objects. Comparison of sampling strategies indicates that soft-tissue imaging benefits from fully sampled acquisitions at dose above ∼ 1.7 mGy and benefits from 50% sparsity at dose below ∼ 1.0 mGy. Therefore, an appropriate sampling strategy along with the improved low-contrast visualization offered by statistical reconstruction demonstrates the potential for extending intraoperative C-arm CBCT to applications in soft-tissue interventions in neurosurgery as well as thoracic and abdominal surgeries by overcoming conventional tradeoffs in noise, spatial resolution, and dose.

Technical note: algebraic iterative image reconstruction using a cylindrical image grid for tetrahedron beam computed tomography

PURPOSE

To accelerate iterative algebraic reconstruction algorithms using a cylindrical image grid.

METHODS

Tetrahedron beam computed tomography (TBCT) is designed to overcome the scatter and detector problems of cone beam computed tomography (CBCT). Iterative algebraic reconstruction algorithms have been shown to mitigate approximate reconstruction artifacts that appear at large cone angles, but clinical implementation is limited by their high computational cost. In this study, a cylindrical voxelization method on a cylindrical grid is developed in order to take advantage of the symmetries of the cylindrical geometry. The cylindrical geometry is a natural fit for the circular scanning trajectory employed in volumetric CT methods such as CBCT and TBCT. This method was implemented in combination with the simultaneous algebraic reconstruction technique (SART). Both two- and three-dimensional numerical phantoms as well as a patient CT image were utilized to generate the projection sets used for reconstruction. The reconstructed images were compared to the original phantoms using a set of three figures of merit (FOM).

RESULTS

The cylindrical voxelization on a cylindrical reconstruction grid was successfully implemented in combination with the SART reconstruction algorithm. The FOM results showed that the cylindrical reconstructions were able to maintain the accuracy of the Cartesian reconstructions. In three dimensions, the cylindrical method provided better accuracy than the Cartesian methods. At the same time, the cylindrical method was able to provide a speedup factor of approximately 40 while also reducing the system matrix storage size by 2 orders of magnitude.

CONCLUSIONS

TBCT image reconstruction using a cylindrical image grid was able to provide a significant improvement in the reconstruction time and a more compact system matrix for storage on the hard drive and in memory while maintaining the image quality provided by the Cartesian voxelization on a Cartesian grid.

Medical image processing on the GPU - past, present and future

Graphics processing units (GPUs) are used today in a wide range of applications, mainly because they can dramatically accelerate parallel computing, are affordable and energy efficient. In the field of medical imaging, GPUs are in some cases crucial for enabling practical use of computationally demanding algorithms. This review presents the past and present work on GPU accelerated medical image processing, and is meant to serve as an overview and introduction to existing GPU implementations. The review covers GPU acceleration of basic image processing operations (filtering, interpolation, histogram estimation and distance transforms), the most commonly used algorithms in medical imaging (image registration, image segmentation and image denoising) and algorithms that are specific to individual modalities (CT, PET, SPECT, MRI, fMRI, DTI, ultrasound, optical imaging and microscopy). The review ends by highlighting some future possibilities and challenges.

Evaluation of Algebraic Iterative Image Reconstruction Methods for Tetrahedron Beam Computed Tomography Systems

Tetrahedron beam computed tomography (TBCT) performs volumetric imaging using a stack of fan beams generated by a multiple pixel X-ray source. While the TBCT system was designed to overcome the scatter and detector issues faced by cone beam computed tomography (CBCT), it still suffers the same large cone angle artifacts as CBCT due to the use of approximate reconstruction algorithms. It has been shown that iterative reconstruction algorithms are better able to model irregular system geometries and that algebraic iterative algorithms in particular have been able to reduce cone artifacts appearing at large cone angles. In this paper, the SART algorithm is modified for the use with the different TBCT geometries and is tested using both simulated projection data and data acquired using the TBCT benchtop system. The modified SART reconstruction algorithms were able to mitigate the effects of using data generated at large cone angles and were also able to reconstruct CT images without the introduction of artifacts due to either the longitudinal or transverse truncation in the data sets. Algebraic iterative reconstruction can be especially useful for dual-source dual-detector TBCT, wherein the cone angle is the largest in the center of the field of view.

Panoramic cone beam computed tomography

PURPOSE

Cone-beam computed tomography (CBCT) is the main imaging tool for image-guided radiotherapy but its functionality is limited by a small imaging volume and restricted image position (imaged at the central instead of the treatment position for peripheral lesions to avoid collisions). In this paper, the authors present the concept of "panoramic CBCT," which can image patients at the treatment position with an imaging volume as large as practically needed.

METHODS

In this novel panoramic CBCT technique, the target is scanned sequentially from multiple view angles. For each view angle, a half scan (180° + θ(cone) where θ(cone) is the cone angle) is performed with the imaging panel positioned in any location along the beam path. The panoramic projection images of all views for the same gantry angle are then stitched together with the direct image stitching method (i.e., according to the reported imaging position) and full-fan, half-scan CBCT reconstruction is performed using the stitched projection images. To validate this imaging technique, the authors simulated cone-beam projection images of the Mathematical Cardiac Torso (MCAT) thorax phantom for three panoramic views. Gaps, repeated/missing columns, and different exposure levels were introduced between adjacent views to simulate imperfect image stitching due to uncertainties in imaging position or output fluctuation. A modified simultaneous algebraic reconstruction technique (modified SART) was developed to reconstruct CBCT images directly from the stitched projection images. As a gold standard, full-fan, full-scan (360° gantry rotation) CBCT reconstructions were also performed using projection images of one imaging panel large enough to encompass the target. Contrast-to-noise ratio (CNR) and geometric distortion were evaluated to quantify the quality of reconstructed images. Monte Carlo simulations were performed to evaluate the effect of scattering on the image quality and imaging dose for both standard and panoramic CBCT.

RESULTS

Truncated images with artifacts were observed for the CBCT reconstruction using projection images of the central view only. When the image stitching was perfect, complete reconstruction was obtained for the panoramic CBCT using the modified SART with the image quality similar to the gold standard (full-scan, full-fan CBCT using one large imaging panel). Imperfect image stitching, on the other hand, lead to (streak, line, or ring) reconstruction artifacts, reduced CNR, and/or distorted geometry. Results from Monte Carlo simulations showed that, for identical imaging quality, the imaging dose was lower for the panoramic CBCT than that acquired with one large imaging panel. For the same imaging dose, the CNR of the three-view panoramic CBCT was 50% higher than that of the regular CBCT using one big panel.

CONCLUSIONS

The authors have developed a panoramic CBCT technique and demonstrated with simulation data that it can image tumors of any location for patients of any size at the treatment position with comparable or less imaging dose and time. However, the image quality of this CBCT technique is sensitive to the reconstruction artifacts caused by imperfect image stitching. Better algorithms are therefore needed to improve the accuracy of image stitching for panoramic CBCT.

Mapping iterative medical imaging algorithm on cell accelerator

Algebraic reconstruction techniques require about half the number of projections as that of Fourier backprojection methods, which makes these methods safer in terms of required radiation dose. Algebraic reconstruction technique (ART) and its variant OS-SART (ordered subset simultaneous ART) are techniques that provide faster convergence with comparatively good image quality. However, the prohibitively long processing time of these techniques prevents their adoption in commercial CT machines. Parallel computing is one solution to this problem. With the advent of heterogeneous multicore architectures that exploit data parallel applications, medical imaging algorithms such as OS-SART can be studied to produce increased performance. In this paper, we map OS-SART on cell broadband engine (Cell BE). We effectively use the architectural features of Cell BE to provide an efficient mapping. The Cell BE consists of one powerPC processor element (PPE) and eight SIMD coprocessors known as synergetic processor elements (SPEs). The limited memory storage on each of the SPEs makes the mapping challenging. Therefore, we present optimization techniques to efficiently map the algorithm on the Cell BE for improved performance over CPU version. We compare the performance of our proposed algorithm on Cell BE to that of Sun Fire ×4600, a shared memory machine. The Cell BE is five times faster than AMD Opteron dual-core processor. The speedup of the algorithm on Cell BE increases with the increase in the number of SPEs. We also experiment with various parameters, such as number of subsets, number of processing elements, and number of DMA transfers between main memory and local memory, that impact the performance of the algorithm.

GPU computing in medical physics: a review

The graphics processing unit (GPU) has emerged as a competitive platform for computing massively parallel problems. Many computing applications in medical physics can be formulated as data-parallel tasks that exploit the capabilities of the GPU for reducing processing times. The authors review the basic principles of GPU computing as well as the main performance optimization techniques, and survey existing applications in three areas of medical physics, namely image reconstruction, dose calculation and treatment plan optimization, and image processing.

A fast CT reconstruction scheme for a general multi-core PC

Expensive computational cost is a severe limitation in CT reconstruction for clinical applications that need real-time feedback. A primary example is bolus-chasing computed tomography (CT) angiography (BCA) that we have been developing for the past several years. To accelerate the reconstruction process using the filtered backprojection (FBP) method, specialized hardware or graphics cards can be used. However, specialized hardware is expensive and not flexible. The graphics processing unit (GPU) in a current graphic card can only reconstruct images in a reduced precision and is not easy to program. In this paper, an acceleration scheme is proposed based on a multi-core PC. In the proposed scheme, several techniques are integrated, including utilization of geometric symmetry, optimization of data structures, single-instruction multiple-data (SIMD) processing, multithreaded computation, and an Intel C++ compilier. Our scheme maintains the original precision and involves no data exchange between the GPU and CPU. The merits of our scheme are demonstrated in numerical experiments against the traditional implementation. Our scheme achieves a speedup of about 40, which can be further improved by several folds using the latest quad-core processors.

GPU-accelerated 3D Bayesian image reconstruction from Compton scattered data

This paper describes the development of fast Bayesian reconstruction methods for Compton cameras using commodity graphics hardware. For fast iterative reconstruction, not only is it important to increase the convergence rate, but also it is equally important to accelerate the computation of time-consuming and repeated operations, such as projection and backprojection. Since the size of the system matrix for a typical Compton camera is intractably large, it is impractical to use a conventional caching scheme that stores the pre-calculated elements of a system matrix and uses them for the calculation of projection and backprojection. In this paper we propose GPU (graphics processing unit)-accelerated methods that can rapidly perform conical projection and backprojection on the fly. Since the conventional ray-based backprojection method is inefficient for parallel computing on GPUs, we develop voxel-based conical backprojection methods using two different approximation schemes. In the first scheme, we approximate the intersecting chord length of the ray passing through a voxel by the perpendicular distance from the center to the ray. In the second scheme, each voxel is regarded as a dimensionless point rather than a cube so that the backprojection can be performed without the need for calculating intersecting chord lengths or their approximations. Our simulation studies show that the GPU-based method dramatically improves the computational speed with only minor loss of accuracy in reconstruction. With the development of high-resolution detectors, the difference in the reconstruction accuracy between the GPU-based method and the CPU-based method will eventually be negligible.

3D forward and back-projection for X-ray CT using separable footprints

Iterative methods for 3D image reconstruction have the potential to improve image quality over conventional filtered back projection (FBP) in X-ray computed tomography (CT). However, the computation burden of 3D cone-beam forward and back-projectors is one of the greatest challenges facing practical adoption of iterative methods for X-ray CT. Moreover, projector accuracy is also important for iterative methods. This paper describes two new separable footprint (SF) projector methods that approximate the voxel footprint functions as 2D separable functions. Because of the separability of these footprint functions, calculating their integrals over a detector cell is greatly simplified and can be implemented efficiently. The SF-TR projector uses trapezoid functions in the transaxial direction and rectangular functions in the axial direction, whereas the SF-TT projector uses trapezoid functions in both directions. Simulations and experiments showed that both SF projector methods are more accurate than the distance-driven (DD) projector, which is a current state-of-the-art method in the field. The SF-TT projector is more accurate than the SF-TR projector for rays associated with large cone angles. The SF-TR projector has similar computation speed with the DD projector and the SF-TT projector is about two times slower.

A multiresolution approach to iterative reconstruction algorithms in X-ray computed tomography

In computed tomography, the application of iterative reconstruction methods in practical situations is impeded by their high computational demands. Especially in high resolution X-ray computed tomography, where reconstruction volumes contain a high number of volume elements (several giga voxels), this computational burden prevents their actual breakthrough. Besides the large amount of calculations, iterative algorithms require the entire volume to be kept in memory during reconstruction, which quickly becomes cumbersome for large data sets. To overcome this obstacle, we present a novel multiresolution reconstruction, which greatly reduces the required amount of memory without significantly affecting the reconstructed image quality. It is shown that, combined with an efficient implementation on a graphical processing unit, the multiresolution approach enables the application of iterative algorithms in the reconstruction of large volumes at an acceptable speed using only limited resources.

On the efficiency of iterative ordered subset reconstruction algorithms for acceleration on GPUs

Expectation Maximization (EM) and the Simultaneous Iterative Reconstruction Technique (SIRT) are two iterative computed tomography reconstruction algorithms often used when the data contain a high amount of statistical noise, have been acquired from a limited angular range, or have a limited number of views. A popular mechanism to increase the rate of convergence of these types of algorithms has been to perform the correctional updates within subsets of the projection data. This has given rise to the method of Ordered Subsets EM (OS-EM) and the Simultaneous Algebraic Reconstruction Technique (SART). Commodity graphics hardware (GPUs) has shown great promise to combat the high computational demands incurred by iterative reconstruction algorithms. However, we find that the special architecture and programming model of GPUs add extra constraints on the real-time performance of ordered subsets algorithms, counteracting the speedup benefits of smaller subsets observed on CPUs. This gives rise to new relationships governing the optimal number of subsets as well as relaxation factor settings for obtaining the smallest wall-clock time for reconstruction-a factor that is likely application-dependent. In this paper we study the generalization of SIRT into Ordered Subsets SIRT and show that this allows one to optimize the computational performance of GPU-accelerated iterative algebraic reconstruction methods.

Lung perfusion imaging in small animals using 4D micro-CT at heartbeat temporal resolution

PURPOSE

Quantitative in vivo imaging of lung perfusion in rodents can provide critical information for preclinical studies. However, the combined challenges of high temporal and spatial resolution have made routine quantitative perfusion imaging difficult in small animals. The purpose of this work is to demonstrate 4D micro-CT for perfusion imaging in rodents at heartbeat temporal resolution and isotropic spatial resolution.

METHODS

We have recently developed a dual tube/detector micro-CT scanner that is well suited to capture first pass kinetics of a bolus of contrast agent used to compute perfusion information. Our approach is based on the paradigm that similar time density curves can be reproduced in a number of consecutive, small volume injections of iodinated contrast agent at a series of different angles. This reproducibility is ensured by the high-level integration of the imaging components of our system with a microinjector, a mechanical ventilator, and monitoring applications. Sampling is controlled through a biological pulse sequence implemented in LABVIEW. Image reconstruction is based on a simultaneous algebraic reconstruction technique implemented on a graphic processor unit. The capabilities of 4D micro-CT imaging are demonstrated in studies on lung perfusion in rats.

RESULTS

We report 4D micro-CT imaging in the rat lung with a heartbeat temporal resolution (approximately 150 ms) and isotropic 3D reconstruction with a voxel size of 88 microm based on sampling using 16 injections of 50 microL each. The total volume of contrast agent injected during the experiments (0.8 mL) was less than 10% of the total blood volume in a rat. This volume was not injected in a single bolus, but in multiple injections separated by at least 2 min interval to allow for clearance and adaptation. We assessed the reproducibility of the time density curves with multiple injections and found that these are very similar. The average time density curves for the first eight and last eight injections are slightly different, i.e., for the last eight injections, both the maximum of the average time density curves and its area under the curve are decreased by 3.8% and 7.2%, respectively, relative to the average time density curves based on the first eight injections. The radiation dose associated with our 4D micro-CT imaging is 0.16 Gy and is therefore in the range of a typical micro-CT dose.

CONCLUSIONS

4D micro-CT-based perfusion imaging demonstrated here has immediate application in a wide range of preclinical studies such as tumor perfusion, angiogenesis, and renal function. Although our imaging system is in many ways unique, we believe that our approach based on the multiple injection paradigm can be used with the newly developed flat-panel slip-ring-based micro-CT to increase their temporal resolution in dynamic perfusion studies.

Visualization and computer graphics on isotropically emissive volumetric displays

The availability of commodity volumetric displays provides ordinary users with a new means of visualizing 3D data. Many of these displays are in the class of isotropically emissive light devices, which are designed to directly illuminate voxels in a 3D frame buffer, producing X-ray-like visualizations. While this technology can offer intuitive insight into a 3D object, the visualizations are perceptually different from what a computer graphics or visualization system would render on a 2D screen. This paper formalizes rendering on isotropically emissive displays and introduces a novel technique that emulates traditional rendering effects on isotropically emissive volumetric displays, delivering results that are much closer to what is traditionally rendered on regular 2D screens. Such a technique can significantly broaden the capability and usage of isotropically emissive volumetric displays. Our method takes a 3D dataset or object as the input, creates an intermediate light field, and outputs a special 3D volume dataset called a lumi-volume. This lumi-volume encodes approximated rendering effects in a form suitable for display with accumulative integrals along unobtrusive rays. When a lumi-volume is fed directly into an isotropically emissive volumetric display, it creates a 3D visualization with surface shading effects that are familiar to the users. The key to this technique is an algorithm for creating a 3D lumi-volume from a 4D light field. In this paper, we discuss a number of technical issues, including transparency effects due to the dimension reduction and sampling rates for light fields and lumi-volumes. We show the effectiveness and usability of this technique with a selection of experimental results captured from an isotropically emissive volumetric display, and we demonstrate its potential capability and scalability with computer-simulated high-resolution results.

Accelerating Advanced MRI Reconstructions on GPUs

Computational acceleration on graphics processing units (GPUs) can make advanced magnetic resonance imaging (MRI) reconstruction algorithms attractive in clinical settings, thereby improving the quality of MR images across a broad spectrum of applications. This paper describes the acceleration of such an algorithm on NVIDIA's Quadro FX 5600. The reconstruction of a 3D image with 128(3) voxels achieves up to 180 GFLOPS and requires just over one minute on the Quadro, while reconstruction on a quad-core CPU is twenty-one times slower. Furthermore, relative to the true image, the error exhibited by the advanced reconstruction is only 12%, while conventional reconstruction techniques incur error of 42%.

Real-time 3D computed tomographic reconstruction using commodity graphics hardware

The recent emergence of various types of flat-panel x-ray detectors and C-arm gantries now enables the construction of novel imaging platforms for a wide variety of clinical applications. Many of these applications require interactive 3D image generation, which cannot be satisfied with inexpensive PC-based solutions using the CPU. We present a solution based on commodity graphics hardware (GPUs) to provide these capabilities. While GPUs have been employed for CT reconstruction before, our approach provides significant speedups by exploiting the various built-in hardwired graphics pipeline components for the most expensive CT reconstruction task, backprojection. We show that the timings so achieved are superior to those obtained when using the GPU merely as a multi-processor, without a drop in reconstruction quality. In addition, we also show how the data flow across the graphics pipeline can be optimized, by balancing the load among the pipeline components. The result is a novel streaming CT framework that conceptualizes the reconstruction process as a steady flow of data across a computing pipeline, updating the reconstruction result immediately after the projections have been acquired. Using a single PC equipped with a single high-end commodity graphics board (the Nvidia 8800 GTX), our system is able to process clinically-sized projection data at speeds meeting and exceeding the typical flat-panel detector data production rates, enabling throughput rates of 40-50 projections s(-1) for the reconstruction of 512(3) volumes.

Three-dimensional focus of attention for iterative cone-beam micro-CT reconstruction

Three-dimensional iterative reconstruction of high-resolution, circular orbit cone-beam x-ray CT data is often considered impractical due to the demand for vast amounts of computer cycles and associated memory. In this paper, we show that the computational burden can be reduced by limiting the reconstruction to a small, well-defined portion of the image volume. We first discuss using the support region defined by the set of voxels covered by all of the projection views. We then present a data-driven preprocessing technique called focus of attention that heuristically separates both image and projection data into object and background before reconstruction, thereby further reducing the reconstruction region of interest. We present experimental results for both methods based on mouse data and a parallelized implementation of the SIRT algorithm. The computational savings associated with the support region are substantial. However, the results for focus of attention are even more impressive in that only about one quarter of the computer cycles and memory are needed compared with reconstruction of the entire image volume. The image quality is not compromised by either method.

Comparison of methods for suppressing edge and aliasing artefacts in iterative x-ray CT reconstruction

X-ray CT images obtained with iterative reconstruction (IR) can be hampered by the so-called edge and aliasing artefacts, which appear as interference patterns and severe overshoots in the areas of sharp intensity transitions. Previously, we have demonstrated that these artefacts are caused by discretization errors during the projection simulation step in IR. Although these errors are inherent to IR, they can be adequately suppressed by reconstruction on an image grid that is finer than that typically used for analytical methods such as filtered back-projection. Two other methods that may prevent edge artefacts are: (i) smoothing the projections prior to reconstruction or (ii) using an image representation different from voxels; spherically symmetric Kaiser-Bessel functions are a frequently employed example of such a representation. In this paper, we compare reconstruction on a fine grid with the two above-mentioned alternative strategies for edge artefact reduction. We show that the use of a fine grid results in a more adequate suppression of artefacts than the smoothing of projections or using the Kaiser-Bessel image representation.

Noise simulation in cone beam CT imaging with parallel computing

We developed a computer noise simulation model for cone beam computed tomography imaging using a general purpose PC cluster. This model uses a mono-energetic x-ray approximation and allows us to investigate three primary performance components, specifically quantum noise, detector blurring and additive system noise. A parallel random number generator based on the Weyl sequence was implemented in the noise simulation and a visualization technique was accordingly developed to validate the quality of the parallel random number generator. In our computer simulation model, three-dimensional (3D) phantoms were mathematically modelled and used to create 450 analytical projections, which were then sampled into digital image data. Quantum noise was simulated and added to the analytical projection image data, which were then filtered to incorporate flat panel detector blurring. Additive system noise was generated and added to form the final projection images. The Feldkamp algorithm was implemented and used to reconstruct the 3D images of the phantoms. A 24 dual-Xeon PC cluster was used to compute the projections and reconstructed images in parallel with each CPU processing 10 projection views for a total of 450 views. Based on this computer simulation system, simulated cone beam CT images were generated for various phantoms and technique settings. Noise power spectra for the flat panel x-ray detector and reconstructed images were then computed to characterize the noise properties. As an example among the potential applications of our noise simulation model, we showed that images of low contrast objects can be produced and used for image quality evaluation.

Evaluation of accelerated iterative x-ray CT image reconstruction using floating point graphics hardware

Statistical reconstruction methods offer possibilities to improve image quality as compared with analytical methods, but current reconstruction times prohibit routine application in clinical and micro-CT. In particular, for cone-beam x-ray CT, the use of graphics hardware has been proposed to accelerate the forward and back-projection operations, in order to reduce reconstruction times. In the past, wide application of this texture hardware mapping approach was hampered owing to limited intrinsic accuracy. Recently, however, floating point precision has become available in the latest generation commodity graphics cards. In this paper, we utilize this feature to construct a graphics hardware accelerated version of the ordered subset convex reconstruction algorithm. The aims of this paper are (i) to study the impact of using graphics hardware acceleration for statistical reconstruction on the reconstructed image accuracy and (ii) to measure the speed increase one can obtain by using graphics hardware acceleration. We compare the unaccelerated algorithm with the graphics hardware accelerated version, and for the latter we consider two different interpolation techniques. A simulation study of a micro-CT scanner with a mathematical phantom shows that at almost preserved reconstructed image accuracy, speed-ups of a factor 40 to 222 can be achieved, compared with the unaccelerated algorithm, and depending on the phantom and detector sizes. Reconstruction from physical phantom data reconfirms the usability of the accelerated algorithm for practical cases.

Speedup OS-EM Image Reconstruction by PC Graphics Card Technologies for Quantitative SPECT with Varying Focal-Length Fan-Beam Collimation

In the paper, we present a new hardware acceleration method to speedup the ordered-subsets expectation-maximization (OS-EM) algorithm for quantitative SPECT (single photon emission computed tomography) image reconstruction with varying focal-length fan-beam (VFF) collimation. By utilizing the geometrical symmetry of VFF point-spread function (PSF), compensation for object-specific attenuation and system-specific PSF are accelerated using currently available PC video/graphics card technologies. A ten-fold acceleration of quantitative SPECT reconstruction is achieved.

Statistical image reconstruction for transmission tomography using relaxed ordered subset algorithms

Statistical reconstruction methods offer possibilities for improving image quality as compared to analytical methods, but current reconstruction times prohibit routine clinical applications in x-ray computed tomography (CT). To reduce reconstruction times, we have applied (under) relaxation to ordered subset algorithms. This enables us to use subsets consisting of only single projection angle, effectively increasing the number of image updates within an entire iteration. A second advantage of applying relaxation is that it can help improve convergence by removing the limit cycle behaviour of ordered subset algorithms, which normally do not converge to an optimal solution but rather a suboptimal limit cycle consisting of as many points as there are subsets. Relaxation suppresses the limit cycle behaviour by decreasing the stepsize for approaching the solution. A simulation study for a 2D mathematical phantom and three different ordered subset algorithms shows that all three algorithms benefit from relaxation: equal noise-to-resolution trade-off can be achieved using fewer iterations than the conventional algorithms, while a lower minimal normalized mean square error (NMSE) clearly indicates a better convergence. Two different schemes for setting the relaxation parameter are studied, and both schemes yield approximately the same minimal NMSE.

Characterization and suppression of edge and aliasing artefacts in iterative x-ray CT reconstruction

For the purpose of obtaining x-ray tomographic images, statistical reconstruction (SR) provides a general framework with possible advantages over analytical algorithms such as filtered backprojection (FBP) in terms of flexibility, resolution, contrast and image noise. However, SR images may be seriously affected by some artefacts that are not present in FBP images. These artefacts appear as aliasing patterns and as severe overshoots in the areas of sharp intensity transitions ('edge artefacts'). We characterize this inherent property of iterative reconstructions and hypothesize how discretization errors during reconstruction contribute to the formation of the artefacts. An adequate solution to the problem is to perform the reconstructions on an image grid that is finer than that typically employed for FBP reconstruction, followed by a downsampling of the resulting image to a granularity normally used for display. Furthermore, it is shown that such a procedure is much more effective than post-filtering of the reconstructions. Resulting SR images have superior noise-resolution trade-off compared to FBP, which may facilitate dose reduction during CT examinations.

Experiments with the nonlinear and chaotic behaviour of the multiplicative algebraic reconstruction technique (MART) algorithm for computed tomography

Among the iterative reconstruction algorithms for tomography, the multiplicative algebraic reconstruction technique (MART) has two advantages that make it stand out from other algorithms: it confines the image (and therefore the projection data) to the convex hull of the patient, and it maximizes entropy. In this paper, we have undertaken a series of experiments to determine the importance of MART nonlinearity to image quality. Variants of MART were implemented aiming to exploit and exaggerate the nonlinear properties of the algorithm. We introduce the Power MART, Boxcar Averaging MART and Bouncing MART algorithms. Power MART is linked to the relaxation concept. Its behaviour is similar to that of the chaos of a logistic equation. There appears to be an antagonism between increasing nonlinearity and noise in the projection data. The experiments confirm our general observation that regularization as a means of solving simultaneous linear equations that are underdetermined is suboptimal: it does not necessarily select the correct image from the hyperplane of solutions, and so does not maximize the image quality:x-ray dose ratio. Our investigations prove that there is scope to optimize CT algorithms and thereby achieve greater dose reduction.