Three-dimensional iterative reconstruction algorithms with attenuation and geometric point response correction

Zeng, G.L.; Gullberg, Grant T.; Tsui, B.M.W.; Terry, J.A.

doi:10.1109/23.289376

Cited by 232 publications

(106 citation statements)

References 14 publications

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“…Now, we give a requirement for a valid projector/backprojector pair. We call a projector/ backprojector pair valid if algorithm (1) converges to (11), which is guaranteed by inequality (4).…”

Section: Theorymentioning

confidence: 99%

“…Equation (5) can be rewritten as (11) This result implies that the projection data are first filtered by F b , and then the pseudoinverse operator of C is applied to the result. When m and n are close in value, the prefiltering does not have a significant effect on the result.…”

Section: Theorymentioning

confidence: 99%

“…No scatter was modeled in the projector. The projector C remained unchanged for all examples and used line-length weighting with attenuation and 3-D detector response modeling [11]. The backprojection matrix was B T .…”

Section: B Examples Verifying Valid Projector/backprojector Pairsmentioning

confidence: 99%

“…The geometric response was depth dependent. The point response function was modeled by a 7 × 7 inverse-cone (see [11] for details). A constant attenuation coefficient of μ = 0.1 per pixel-length was used, the attenuator was an ellipsoid of semiaxes of 19.5, 19.5, and 3.5 pixels, and the pixel size was 0.67 cm.…”

Section: B Examples Verifying Valid Projector/backprojector Pairsmentioning

confidence: 99%

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Unmatched projector/backprojector pairs in an iterative reconstruction algorithm

Zeng

Gullberg

2000

IEEE Trans. Med. Imaging

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192

154

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Computational burden is a major concern when an iterative algorithm is used to reconstruct a three-dimensional (3-D) image with attenuation, detector response, and scatter corrections. Most of the computation time is spent executing the projector and backprojector of an iterative algorithm. Usually, the projector and the backprojector are transposed operators of each other. The projector should model the imaging geometry and physics as accurately as possible. Some researchers have used backprojectors that are computationally less expensive than the projectors to reduce computation time. This paper points out that valid backprojectors should satisfy a condition that the projector/backprojector matrix must not contain negative eigenvalues. This paper also investigates the effects when unmatched projector/backprojector pairs are used.

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Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: B Examples Verifying Valid Projector/backprojector Pairsmentioning

confidence: 99%

Section: B Examples Verifying Valid Projector/backprojector Pairsmentioning

confidence: 99%

See 2 more Smart Citations

Unmatched projector/backprojector pairs in an iterative reconstruction algorithm

Zeng

Gullberg

2000

IEEE Trans. Med. Imaging

Self Cite

192

154

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show abstract

“…Resolution recovery methods have been used successfully in iterative reconstruction methods for single photon emission computed tomography (SPECT) [19,20], positron emission tomography (PET) [21,22] and computed tomography (CT) [23,24]. The general idea behind these methods is that by taking into account the size of the x-ray source size, collimation effects and detector characteristics, the final reconstruction is improved.…”

Section: Introductionmentioning

confidence: 99%

Patchwork reconstruction with resolution modeling for digital breast tomosynthesis

2013

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Purpose: Digital breast tomosynthesis is a relatively new diagnostic x-ray modality that allows high resolution breast imaging while suppressing interference from overlapping anatomical structures. However, proper visualization of micro-calcifications remains a challenge. For the subset of systems we consider, the main cause of deterioration is movement of the x-ray source during exposures. We propose a modified grouped coordinate ascent algorithm that includes a specific acquisition model to compensate for this deterioration.Methods: We create a resolution model based on the movement of the x-ray source during image acquisition and combine this with a grouped coordinate ascent algorithm. Choosing planes parallel to the detector surface as the groups enables efficient implementation of the position dependent resolution model. In the current implementation, the resolution model is approximated by a Gaussian smoothing kernel.The effect of the resolution model on the iterative reconstruction is evaluated by measuring contrast to noise ratio (CNR) of spherical micro-calcifications in a homogeneous background. After this, our new reconstruction method is compared to the optimized filtered backprojection method for the considered system, by performing two observer studies: the first study simulates clusters of spherical micro-calcifications in a power law background for a free search task; the second study simulates smooth or irregular micro-calcifications in the same type of backgrounds for a classification task.Results: Including the resolution model in the iterative reconstruction methods increases the CNR of micro-calcifications. The first observer study shows a significant improvement in detection of micro-calcifications (p = 0.029) while the second study shows that performance on a classification task remains the same (p = 0.935) compared to the filtered backprojection method.Conclusions: Our method shows higher CNR and improved visualization of micro-calcifications in an observer experiment on synthetic data. Further study of the negative results of the classification task showed performance variations throughout the volume linked to the changing noise structure introduced by the combination of the resolution model and the smoothing prior.

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Application of Krylov subspaces to SPECT imaging

Calvini¹,

Bertero

2002

Int J Imaging Syst Tech

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ABSTRACT:The application of the conjugate gradient (CG) algorithm to the problem of data reconstruction in SPECT imaging indicates that most of the useful information is already contained in Krylov subspaces of small dimension, ranging from 9 (two-dimensional case) to 15 (three-dimensional case). On this basis, a new, proposed approach can be basically summarized as follows: construction of a basis spanning a Krylov subspace of suitable dimension and projection of the projector-backprojector matrix (a 10 6 ϫ 10 6 matrix in the three-dimensional case) onto such a subspace. In this way, one is led to a problem of low dimensionality, for which regularized solutions can be easily and quickly obtained. The required SPECT activity map is expanded as a linear combination of the basis elements spanning the Krylov subspace and the regularization acts by modifying the coefficients of such an expansion. By means of a suitable graphical interface, the tuning of the regularization parameter(s) can be performed interactively on the basis of the visual inspection of one or some slices cut from a reconstruction.

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Three-dimensional iterative reconstruction algorithms with attenuation and geometric point response correction

Cited by 232 publications

References 14 publications

Unmatched projector/backprojector pairs in an iterative reconstruction algorithm

Unmatched projector/backprojector pairs in an iterative reconstruction algorithm

Patchwork reconstruction with resolution modeling for digital breast tomosynthesis

Application of Krylov subspaces to SPECT imaging

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