Fourier-based reprojection methods have the potential to reduce the computation time in iterative tomographic image reconstruction. Interpolation errors are a limitation of Fourier-based reprojection methods. We apply a min-max interpolation method for the nonuniform fast Fourier transform (NUFFT) to minimize the interpolation errors. Numerical results show that the min-max NUFFT approach provides substantially lower approximation errors in tomographic reprojection and backprojection than conventional interpolation methods.

The scanning of 3D geometry has become a popular way of capturing the shape of real-world objects. Transparent objects, however, pose problems for traditional scanning methods. We present a tomographic method for recovering the shape of objects made of

The introduction of programmability into commodity graphics hardware (GPUs) has enabled their use much beyond their native domain of computer graphics, in many areas of high performance computing. We have shown in previous work that many types of CT algorithms, both iterative and non-iterative, can also greatly benefit from the high degree of SIMD (Same Instruction Multiple Data) parallelism these platforms provide. In this paper, we extend this work by describing how one can deal with a number of challenges that frequently arise in practical application settings using the Feldkamp algorithm: large data, angle-dependent projection geometry, and the need for higher accuracy without compromising speed. For this, we combine our fast hardware-native 8-bit interpolation scheme with a higher precision dual-pass mechanism. This latest version of our RapidCT system runs on the most current GPU hardware, nearly eight times faster than the previous version. 1.

Abstract — In magnetic resonance imaging (MRI), non-Cartesian scan trajectories are advantageous in a wide variety of emerging applications. Advanced reconstruction algorithms that operate directly on non-Cartesian scan data using optimality criteria such as least-squares (LS) can produce significantly better images than conventional algorithms that apply a fast Fourier transform (FFT) after interpolating the scan data onto a Cartesian grid. However, advanced LS reconstructions require significantly more computation than conventional reconstructions based on the FFT. For example, one LS algorithm requires nearly six hours to reconstruct a single three-dimensional image on a modern CPU. Our work demonstrates that this advanced reconstruction can be performed quickly and efficiently on a modern GPU, with the reconstruction of a 64 3 3D image requiring just three minutes, an acceptable latency for key applications. This paper describes how the reconstruction algorithm leverages the resources of the GeForce 8800 GTX (G80) to achieve over 150 GFLOPS in performance. We find that the combination of tiling the data and storing the data in the G80’s constant memory dramatically reduces the algorithm’s required bandwidth to off-chip memory. The G80’s special functional units provide substantial acceleration for the trigonometric computations in the algorithm’s inner loops. Finally, experiment-driven code transformations increase the reconstruction’s performance by as much as 60 % to 80%. I.

Abstract—The mathematical problem posed by Computed Tomography (CT), which includes projecting radiation through an object resulting in an estimate of this object’s interior, is to calculate image data (the pixel values) from the projection values. Although for now the filtered back-projection algorithm is most widely used by manufacturers, efforts are being made to make iterative methods popular again due to their unique advantages, such as their performances with incomplete noisy data. The algebraic reconstruction technique (ART), the simultaneous algebraic reconstruction technique (SART) and the simultaneous iterative reconstruction technique (SIRT) are a few of those iterative methods and in this paper we discuss these techniques and how they can be implemented in MATLAB, a numerical computing environment and programming language, created by The MathWorks. We begin by creating the weight matrix. This is the matrix which holds the importance indicators per pixel. Then we move on to the actual reconstructions and we end by implementing these algorithms and calculations in a graphical user interface. I.

“As invenções são sobretudo os resultados de um trabalho teimoso.” “Inventions are above all the results of a stubborn work.”

The task of reconstructing an object from its projections via tomographic methods is a time-consuming process due to the vast complexity of the data. For this reason, manufacturers of equipment for computed tomography (CT), both medical and industrial, rely mostly on special ASICs to obtain the fast reconstruction times required in clinical, industrial, and security settings. Although modern CPUs have gained enough power in recent years to be competitive for 2D reconstruction, this is not the case for 3D reconstructions, especially not when iterative algorithms must be applied. Incidentally, this has prevented some very effective algorithms to be used in clinical practice, and the need for proprietary reconstruction hardware has also hampered new equipment manufacturers in their effort on entering the market. However, the recent evolution of GPUs has changed the picture in a very dramatic way. In this paper, we will show how floating point GPUs can be exploited to perform both analytical and iterative reconstruction from X-ray and functional imaging data at clinical rates and good quality. For this purpose, we derive a decomposition of three popular 3D reconstruction algorithms into a common set of base modules. All of these base modules can be executed on the GPU and their output linked internally. The data never leaves the GPU, which eliminates the previous GPU-CPU bottlenecks. Visualization of the reconstructed object is also easily done since the object already resides in the graphics hardware, and one can simply run a visualization module at any time to view the reconstruction results. Our implementation allows speedups at a factor of 20, compared to software implementations, at comparable image quality.

3D iterative CT reconstruction is an active research area in medical imaging. Compared with analytic reconstruction methods such as FDK, iterative methods may provide better reconstruction results for incomplete and noisy projection data. The simultaneous algebraic reconstruction technique (SART), one of the most popular iterative reconstruction methods, is applied in the cone-beam geometry for highresolution reconstruction, with the help of graphics hardware (GPU) and total variation (TV) regularization. GPU greatly improves the efficiency of SART, which is computationally intense for CPU, and thus makes it suitable for clinical applications. TV regularization reduces the effects of noise and helps the convergence of SART for noisy data. Experimental results for both synthetic and real data are provided to evaluate the accuracy and efficiency of the proposed framework. Index Terms — Cone-beam CT, iterative reconstruction, SART, GPU, TV regularization

Abstract not found

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. Copyright © 2007 Kai Zeng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.