Minimal residual cone-beam reconstruction with attenuation correction in SPECT

La, Valérie; Grangeat, Pierre

doi:10.1088/0031-9155/43/4/002

Cited by 8 publications

(4 citation statements)

References 12 publications

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“…Other approaches to solve Eq. ͑1͒ with a better convergence rate than the OS-EM algorithm are the conjugate gradient minimum residual ͑CG-MR͒ approaches, 4,15,16 which are constructed based on the least-squares criteria. 8 They provide least-squares solutions by solving the asymmetric system equations ͑19͒ generalized from ͑1͒:…”

Section: F Computer Simulationsmentioning

confidence: 99%

Study of noise propagation and the effects of insufficient numbers of projection angles and detector samplings for iterative reconstruction using planar-integral data

Zhang

Zeng

2006

Med. Phys.

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A rotating slat collimator can be used to acquire planar-integral data. It achieves higher geometric efficiency than a parallel-hole collimator by accepting more photons, but the planar-integral data contain less tomographic information that may result in larger noise amplification in the reconstruction. Lodge evaluated the rotating slat system and the parallel-hole system based on noise behavior for an FBP reconstruction. Here, we evaluate the noise propagation properties of the two collimation systems for iterative reconstruction. We extend Huesman's noise propagation analysis of the line-integral system to the planar-integral case, and show that approximately 2.0(D/dp) SPECT angles, 2.5(D/dp) self-spinning angles at each detector position, and a 0.5dp detector sampling interval are required in order for the planar-integral data to be efficiently utilized. Here, D is the diameter of the object and dp is the linear dimension of the voxels that subdivide the object. The noise propagation behaviors of the two systems are then compared based on a least-square reconstruction using the ratio of the SNR in the image reconstructed using a planar-integral system to that reconstructed using a line-integral system. The ratio is found to be proportional to the square root of F/D, where F is a geometric efficiency factor. This result has been verified by computer simulations. It confirms that for an iterative reconstruction, the noise tradeoff of the two systems is not only dependent on the increase of the geometric efficiency afforded by the planar projection method, but also dependent on the size of the object. The planar-integral system works better for small objects, while the line-integral system performs better for large ones. This result is consistent with Lodge's results based on the FBP method.

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Section: F Computer Simulationsmentioning

confidence: 99%

Study of noise propagation and the effects of insufficient numbers of projection angles and detector samplings for iterative reconstruction using planar-integral data

Zhang

Zeng

2006

Med. Phys.

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“…If this requirement is satisfied, we can have a local iterative reconstruction based on solving . In this paper, the unsymmetric system (4) is solved with the CG algorithm as suggested in [10] and [11].…”

Section: B Image Reconstruction Algorithmmentioning

confidence: 99%

“…For example, the matrix can model the attenuation effect while does not model the attenuation [5], or the matrix models the attenuation while is the regular filtered backprojection algorithm [10]. Recently a method has been developed to design a preconditioner to model and control the projection noise [11].…”

Section: Introductionmentioning

confidence: 99%

Local tomography property of residual minimization reconstruction with planar integral data

Zeng

Gagnon

Natterer

et al. 2003

IEEE Trans. Nucl. Sci.

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Residual minimization with the well-known conjugate gradient (CG) algorithm has been applied to medical image reconstruction for years. The main advantage of this method is its fast convergence rate. In this paper, we point out that this method has another property-local tomography, when this image reconstruction method is applied to planar integral projections. By local tomography we mean the following: The object is relatively large, the entire object is not sufficiently measured, and the projections are truncated due to a small detector size. However, a small region-of-interest (ROI) is sufficiently measured. The small ROI is able to be exactly reconstructed. This local tomographic property is found for planar integral data only and is not found for line-integral measurements. Iterative local tomography has been applied to cos weighted planar integral data through computer simulations and phantom experiments. An efficient projector that models the cos weighting factor is also developed.

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“…Unfortunately, these significant achievements cannot be easily adapted to the cone-beam problem in SPECT since gamma ray photons are attenuated before they are captured by the detector. In cone-beam SPECT, the most representative works in image reconstruction with attenuation compensation are inefficient iterative algorithms [7]- [10] and approximate analytical algorithms [11]- [14]. With the greater computing power that is now available, iterative methods are the algorithms of choice because they model the physics of the imaging detection process better and provide more accurate reconstructions.…”

Section: Introductionmentioning

confidence: 99%

Exact Reconstruction From Uniformly Attenuated Helical Cone-Beam Projections in SPECT

Gullberg¹,

Huang²,

You³

et al. 2008

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In recent years the development of cone-beam reconstruction algorithms has been an active research area in x-ray computed tomography (CT), and significant progress has been made in the advancement of algorithms. Theoretically exact and computationally efficient analytical algorithms can be found in the literature. However, in single photon emission computed tomography (SPECT), published cone-beam reconstruction algorithms are either approximate or involve iterative methods. The SPECT reconstruction problem is more complicated due to degradations in the imaging detection process, one of which is the effect of attenuation of gamma ray photons. Attenuation should be compensated for to obtain quantitative results. In this paper, an analytical reconstruction algorithm for uniformly attenuated cone-beam projection data is presented for SPECT imaging. The algorithm adopts the DBH method, a procedure consisting of differentiation and backprojection followed by a finite inverse cosh-weighted Hilbert transform. The significance of the proposed approach is that a selected region of interest can be reconstructed even with a detector with a reduced field of view. The algorithm is designed for a general trajectory. However, to validate the algorithm, a numerical study was performed using a helical trajectory. The implementation is efficient and the simulation result is promising.

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Minimal residual cone-beam reconstruction with attenuation correction in SPECT

Cited by 8 publications

References 12 publications

Study of noise propagation and the effects of insufficient numbers of projection angles and detector samplings for iterative reconstruction using planar-integral data

Study of noise propagation and the effects of insufficient numbers of projection angles and detector samplings for iterative reconstruction using planar-integral data

Local tomography property of residual minimization reconstruction with planar integral data

Exact Reconstruction From Uniformly Attenuated Helical Cone-Beam Projections in SPECT

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