Evolution of computer technology for fast cone beam backprojection

Goddard, Iain; Berman, Ari; Bockenbach, Olivier; Lauginiger, Frank; Schuberth, Sebastian; Thieret, Scott

doi:10.1117/12.722160

Cited by 6 publications

(3 citation statements)

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“…We use SI prefixes, i.e., 1 GUP/s means 10 9 updates per second. This is inconsistent with a large part of the literature on medical image reconstruction, where "G" is used as a binary prefix for 2 30 ≈ 1.074 • 10 9[20] …”

mentioning

confidence: 90%

Pushing the limits for medical image reconstruction on recent standard multicore processors

Treibig¹,

Hager²,

Hofmann

et al. 2012

The International Journal of High Performance Computing Applica

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Volume reconstruction by backprojection is the computational bottleneck in many interventional clinical computed tomography (CT) applications. Today vendors in this field replace special purpose hardware accelerators with standard hardware such as multicore chips and GPGPUs. Medical imaging algorithms are on the verge of employing highperformance computing (HPC) technology, and are therefore an interesting new candidate for optimization. This paper presents low-level optimizations for the backprojection algorithm, guided by a thorough performance analysis on four generations of Intel multicore processors (Harpertown, Westmere, Westmere EX, and Sandy Bridge). We choose the RABBITCT benchmark, a standardized testcase well supported in industry, to ensure transparent and comparable results. Our aim is to provide not only the fastest possible implementation but also compare with performance models and hardware counter data in order to fully understand the results. We separate the influence of algorithmic optimizations, parallelization, SIMD vectorization, and microarchitectural issues and pinpoint problems with current SIMD instruction set extensions on standard CPUs (SSE, AVX). The use of assembly language is mandatory for best performance. Finally, we compare our results to the best GPGPU implementations available for this open competition benchmark.

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mentioning

confidence: 90%

Pushing the limits for medical image reconstruction on recent standard multicore processors

Treibig¹,

Hager²,

Hofmann

et al. 2012

The International Journal of High Performance Computing Applica

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“…This parameter is the most important one in a clinical environment as it tells how long the physician has to wait for the result of the reconstruction, depending on the number of acquired projections. Other performance measures, e.g., GUPS, 19 can be derived from it. Comparing the GUPS between different problem sizes, one can assess the scalability of a specific implementation.…”

Section: Iid Evaluation Metricsmentioning

confidence: 99%

Technical Note: RabbitCT—an open platform for benchmarking 3D cone‐beam reconstruction algorithmsa)

et al. 2009

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“…As indicated in the listings, an update is a summation of the rawdata value to the final voxel. After a time measurement, we calculate the number of giga updates that our algorithms can process per second (giga updates per second (GUPS)); this useful measure was initially proposed in Goddard et al (2007). To give a simple and intuitive example of these figures, let us make an example for a simple circle scan: assume that 512 projections per 360 • have to be backprojected and let the volume contain 512 3 voxels.…”

Section: Time Measurements and Implementation Detailsmentioning

confidence: 99%

High performance cone-beam spiral backprojection with voxel-specific weighting

2009

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Cone-beam spiral backprojection is computationally highly demanding. At first sight, the backprojection requirements are similar to those of cone-beam backprojection from circular scans such as it is performed in the widely used Feldkamp algorithm. However, there is an additional complication: the illumination of each voxel, i.e. the range of angles the voxel is seen by the x-ray cone, is a complex function of the voxel position. In general, one needs to multiply a voxel-specific weight w(x, y, z, alpha) prior to adding a projection from angle alpha to a voxel at position x, y, z. Often, the weight function has no analytically closed form and must be numerically determined. Storage of the weights is prohibitive since the amount of memory required equals the number of voxels per spiral rotation times the number of projections a voxel receives contributions and therefore is in the order of up to 10(12) floating point values for typical spiral scans. We propose a new algorithm that combines the spiral symmetry with the ability of today's 64 bit operating systems to store large amounts of precomputed weights, even above the 4 GB limit. Our trick is to backproject into slices that are rotated in the same manner as the spiral trajectory rotates. Using the spiral symmetry in this way allows one to exploit data-level paralellism and thereby to achieve a very high level of vectorization. An additional postprocessing step rotates these slices back to normal images. Our new backprojection algorithm achieves up to 17 giga voxel updates per second on our systems that are equipped with four standard Intel X7460 hexa core CPUs (Intel Xeon 7300 platform, 2.66 GHz, Intel Corporation). This equals the reconstruction of 344 images per second assuming that each slice consists of 512 x 512 pixels and receives contributions from 512 projections. Thereby, it is an order of magnitude faster than a highly optimized code that does not make use of the spiral symmetry. In its present version, the spiral backprojection algorithm is pixel-driven. A ray-driven version and a corresponding high performance forward projector can be easily designed. Thus, our findings can be used to speed up any type of image reconstruction algorithm (approximate or exact analytical algorithms and iterative algorithms) and therefore yield a versatile and valuable component of future image reconstruction pipelines.

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Evolution of computer technology for fast cone beam backprojection

Cited by 6 publications

References 0 publications

Pushing the limits for medical image reconstruction on recent standard multicore processors

Pushing the limits for medical image reconstruction on recent standard multicore processors

Technical Note: RabbitCT—an open platform for benchmarking 3D cone‐beam reconstruction algorithmsa)

High performance cone-beam spiral backprojection with voxel-specific weighting

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