Parallelization Of The EM Algorithm For 3D PEt Image Reconstruction

Chen, C.M.; Lee, S.-Y.; Cho, Z.H.

doi:10.1109/nssmic.1990.693601

Cited by 8 publications

(8 citation statements)

References 12 publications

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“…While this leads to substantial cost savings, Fourier rebinning again assumes that the data are measurements of line integrals so that the potential for resolution recovery is lost with this approach. Several other investigators have approached the problem using a combination of sparse matrix structures and in-plane and axial symmetries to reduce computation and storage requirements (Chen et al 1991, Johnson et al 1995, 1997, Ollinger and Goggin 1996, Terstegge et al 1996. These methods model the detection process using geometrical computations based either on the intersection of detection 'tubes' with each voxel (Ollinger and Goggin 1996) or on depth dependent geometric sensitivity calculations based on the solid angles subtended at the detectors by each voxel (Chen et al 1991, Terstegge et al 1996.…”

Section: Introductionmentioning

confidence: 99%

“…Many of the statistically based 3D reconstruction methods are based on the EM (Chen et al 1991, Johnson et al 1995 or OSEM (Johnson et al 1997) algorithms. Both approaches can exhibit high-variance behaviour at high iteration numbers and are regularized through early termination of the algorithm or by subsequent smoothing of the reconstructed images.…”

Section: Introductionmentioning

confidence: 99%

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High-resolution 3D Bayesian image reconstruction using the microPET small-animal scanner

Leahy

Cherry³

et al. 1998

Phys. Med. Biol.

584

483

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A Bayesian method is described for reconstruction of high-resolution 3D images from the microPET small-animal scanner. Resolution recovery is achieved by explicitly modelling the depth dependent geometric sensitivity for each voxel in combination with an accurate detector response model that includes factors due to photon pair non-collinearity and inter-crystal scatter and penetration. To reduce storage and computational costs we use a factored matrix in which the detector response is modelled using a sinogram blurring kernel. Maximum a posteriori (MAP) images are reconstructed using this model in combination with a Poisson likelihood function and a Gibbs prior on the image. Reconstructions obtained from point source data using the accurate system model demonstrate a potential for near-isotropic FWHM resolution of approximately 1.2 mm at the center of the field of view compared with approximately 2 mm when using an analytic 3D reprojection (3DRP) method with a ramp filter. These results also show the ability of the accurate system model to compensate for resolution loss due to crystal penetration producing nearly constant radial FWHM resolution of 1 mm out to a 4 mm radius. Studies with a point source in a uniform cylinder indicate that as the resolution of the image is reduced to control noise propagation the resolution obtained using the accurate system model is superior to that obtained using 3DRP at matched background noise levels. Additional studies using pie phantoms with hot and cold cylinders of diameter 1-2.5 mm and 18FDG animal studies appear to confirm this observation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

High-resolution 3D Bayesian image reconstruction using the microPET small-animal scanner

Leahy

Cherry³

et al. 1998

Phys. Med. Biol.

584

483

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“…By choosing the voxel size in the z direction to be an integer fraction of the ring distance, we have in-plane rotation symmetries, axial reflection symmetry, and parallel symmetry in P geom as described in [4,5,7]. The non-zero elements of P geom are stored using automated voxel indexing in a ray-driven projector format.…”

Section: A Factorization Of the Projection Matrixmentioning

confidence: 99%

“…fY g RM p;q k;l = f Y g R p;q 2k;l + f Y g R p;q 2k + 1 ; l (5) In contrast to FBP methods based on the line integral model, the statistically based approach allows us to explicitly model these data compression procedures in our geometric projection matrix, P geom . To do this, we first compute p geom i; j for all ring differences, d = 0 ; 1 ; 2 ; : : : ; d max = 2 2 .…”

Section: B Axial Rebinning and Angular Mashingmentioning

confidence: 99%

“…The full size of the system matrix for a clinical whole body scanner is huge (see Table 2) but it can be efficiently stored by exploiting its sparseness and the high degree of symmetry [4,5]. Further reductions in size can be realized by using automated indexing schemes and a factored system model so that a spatially variant detector response can be included at little additional cost compared to a simple strip-integral model [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Fully 3D Bayesian image reconstruction for the ECAT EXACT HR+

Qi¹,

Leahy²,

Hsu³

et al.

1997 IEEE Nuclear Science Symposium Conference Record

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A fully 3D Bayesian method is described for high resolution reconstruction of images from the Siemens/CTI ECAT EXACT HR+ whole body positron emission tomography (PET) scanner. To maximize resolution recovery from the system we model depth dependent geometric efficiency, intrinsic detector efficiency, photon pair non-colinearity, crystal penetration and inter-crystal scatter. We also explicitly model the effects of axial rebinning and angular mashing on the detection probability or system matrix. By fully exploiting sinogram symmetries and using a factored system matrix and automated indexing schemes, we are able to achieve substantial savings in both the storage size and time required to compute forward and backward projections. Reconstruction times are further reduced using multi-threaded programming on a four processor Unix server. Bayesian reconstructions are computed using a Huber prior and a shifted-Poisson likelihood model that accounts for the effects of randoms subtraction and scatter. Reconstructions of phantom data show that the 3D Bayesian method can achieve improved FWHM resolution and contrast recovery ratios at matched background noise levels compared to both the 3D reprojection method and an OSEM method based on the shifted-Poisson model.

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