A true three-dimensional reconstruction algorithm for the spherical positron emission tomograph

Beom, Jong; Lim, C.B.; Cho, Zh; Hilal, S. K.; Correll, James W.

doi:10.1088/0031-9155/27/1/004

Cited by 59 publications

(25 citation statements)

References 13 publications

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“…Such a reconstruction can be achieved by splitting the reconstruction volume into a set of slices orthogonal to and applying a conventional 2-D algorithm for reconstruction of each slice. Using the 2-D FBP reconstruction formula of Tretiak and Metz [14], one gets the following expression for from data on : let and be the detector axes used to describe ; then (12) where (13) With detector-independent notations, the filtering step of (13) is rewritten as (14) and (15) since and for . Conceptually, a reconstruction formula such as (15) can be written for any vector .…”

Section: Algorithm Derivationmentioning

confidence: 99%

“…In each case, only the part is displayed. The expression of the filter in the nonattenuated case can be found in [12] or by taking the limit for tending to zero in the expression of the A-TTR filter. Fig.…”

Section: B the Equatorial Bandmentioning

confidence: 99%

“…Although unusual, we note that this data acquisition geometry could be easily implemented on existing SPECT scanners. Thederivationof ourformulafollows thesamelinesasthework of Ra et al [12] for image reconstruction from nonattenuated projections. From the theory for 2-D radon transform, Ra et al derived the first true three-dimensional reconstruction (TTR) algorithm for nonattenuated X-ray projections.…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional image reconstruction from exponential parallel-beam projections

Wagner

Noo

2001

IEEE Trans. Nucl. Sci.

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In this paper, we present a filtered-backprojection (FBP) algorithm suitable for image reconstruction from exponential X-ray (parallel-beam) projections sampled on any subset of the sphere that includes great circles. This algorithm is similar to the true three-dimensional reconstruction algorithm of Ra et al. (1982) for nonattenuated projections. It is derived by combining all reconstructions that can be obtained from subsets of measurements corresponding to great circles. Our results generalize those published by Hazou (1988) and Weng et al. (1996) for reconstruction from projections sampled on the unit sphere. However, they remain modest, as they only apply to specific sets of measurements.Index Terms-Attenuation, parallel-beam projections, three-dimensional reconstruction.

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Section: Algorithm Derivationmentioning

confidence: 99%

Section: B the Equatorial Bandmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Three-dimensional image reconstruction from exponential parallel-beam projections

Wagner

Noo

2001

IEEE Trans. Nucl. Sci.

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“…Since the number of PE's which can be allocated in iPSCI2 for every application must be a power of 2, we have employed only three different sizes of cubes, 8,16, and 32 in this study. For a cube of size k, the PE's are numbered from 0 to k-1.…”

Section: Communication Patternsmentioning

confidence: 99%

A parallel implementation of 3-D CT image reconstruction on hypercube multiprocessor

Chen

Lee

Cho

1990

IEEE Trans. Nucl. Sci.

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In this paper, we describe how image reconstruction in Computerized Tomography (CT) can be parallelized on a message-passing multiprocessor. In particular, the results obtained from parallel implementation of 3-D CT image reconstruction for parallel beam geometries on the Intel hypercube, iPSC/2, are presented. A two stage pipelining approach is employed for filtering (convolution) and backprojection. The conventional sequential convolution algorithm is modified such that the symmetry of the filter kernel is fully utilized for parallelization.In the backprojection stage, the 3-D Incremental algorithm, our recently developed backprojection scheme which is shown to be faster than conventional algorithm, is parallelized. The speed-up, defined as (sequential processing time)/(parallel processing time), ranging from 5 to 27, and the efficiency, defined as (speed-up)/(the number of processing elements), ranging from 60% to 92%, have been achieved, depending on the size of image and the number of processing elements employed.

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“…However, only cylinder or similar cylinder systems with smaller ring structure were fabricated for brain PET imaging [5][6][7][8][9]. Furthermore, a spherical PET (S-PET) can achieve an even higher geometrical sensitivity and a lower parallax error than conventional cylindrical ring PET scanners, thus making it a good candidate for high performance dedicated brain imaging [10][11][12]. However, the S-PET system has not yet been implemented because of the difficulties in designing the detector, S616 gantry and electronics.…”

Section: Introductionmentioning

confidence: 99%

Design study of dedicated brain PET with polyhedron geometry

Han

et al. 2015

THC

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Abstract. BACKGROUND: Despite being the conventional choice, whole body PET cameras with a 76 cm diameter ring are not the optimal means of human brain imaging. OBJECTIVE: In fact, a dedicated brain PET with a better geometrical structure has the potential to achieve a higher sensitivity, a higher signal-to-noise ratio, and a better imaging performance. METHODS: In this study, a polyhedron geometrical dedicated brain PET (a dodecahedron design) is compared to three other candidates via their geometrical efficiencies by calculating the Solid Angle Fractions (SAF); the three other candidates include a spherical cap design, a cylindrical design, and the conventional whole body PET. RESULTS: The spherical cap and the dodecahedron have an identical SAF that is 58.4% higher than that of a 30 cm diameter cylinder and 5.44 times higher than that of a 76 cm diameter cylinder. The conceptual polygon-shape detectors (including pentagon and hexagon detectors based on the PMT-light-sharing scheme instead of the conventional square-shaped block detector module) are presented for the polyhedron PET design. Monte Carlo simulations are performed in order to validate the detector decoding. CONCLUSIONS:The results show that crystals in a pentagon-shape detector can be successfully decoded by Anger Logic. The new detector designs support the polyhedron PET investigation.

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A true three-dimensional reconstruction algorithm for the spherical positron emission tomograph

Cited by 59 publications

References 13 publications

Three-dimensional image reconstruction from exponential parallel-beam projections

Three-dimensional image reconstruction from exponential parallel-beam projections

A parallel implementation of 3-D CT image reconstruction on hypercube multiprocessor

Design study of dedicated brain PET with polyhedron geometry

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