Accelerated penalized weighted least-squares and maximum likelihood algorithms for reconstructing transmission images from PET transmission data

Anderson, J.M.M.; Srinivasan, R.; Mair, B.A.; Votaw, John R.

doi:10.1109/tmi.2004.842453

Cited by 8 publications

(12 citation statements)

References 30 publications

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“…In other words, this algorithm monotonically increases the objective function with increasing iterations. Later, in [24] a de-coupled surrogate function (i.e., no terms of the form , except when ) satisfying (C1) and (C2) was suggested (25) where is a constant and is the number of nonzero elements in the row of . Additional definitions are: and , where the diagonal matrix and vector are defined by (23)- (26) in [24].…”

Section: Cse Algorithmmentioning

confidence: 99%

“…Additional definitions are: and , where the diagonal matrix and vector are defined by (23)- (26) in [24]. For details on (25), see (75) in Appendix B of [24]. The advantage of using the de-coupled surrogate functions is that the updates for the algorithm have closed form solutions and the algorithm is monotonic.…”

Section: Cse Algorithmmentioning

confidence: 99%

“…To complete our development of the CSE algorithm, we now address the optimization problem in (24). Since attenuation is a nonnegative quantity, the gamma density function may be an appropriate choice for the class density functions .…”

Section: Cse Algorithmmentioning

confidence: 99%

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Concurrent Segmentation and Estimation of Transmission Images for Attenuation Correction in Positron Emission Tomography

Anderson

Kim

Votaw

2009

IEEE Trans. Nucl. Sci.

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When transmission images are obtained using conventional reconstruction methods in stand alone PET scanners, such as standard clinical PET, microPET, and dedicated brain scanners, the results may be noisy and/or inaccurate. For example, the popular penalized maximum-likelihood method effectively reduces noise, but it does not address the bias problem that results from the incorporation of a penalty function and contamination from emission data due to patient activity. In this paper, we present an algorithm that simultaneously reconstructs transmission images and performs a "soft" segmentation of voxels into the classes: air, patient bed, lung, soft-tissue, and bone. It is through the segmentation step that the algorithm, which we refer to as the concurrent segmentation and estimation (CSE) algorithm, provides a means for incorporating accurate attenuation coefficients. The CSE algorithm is obtained by applying an expectation-maximization like formulation to a certain maximum a posterior objective function. This formulation enables us to show that the CSE algorithm monotonically increases the objective function. In experiments using real phantom and synthetic data, the CSE images produced attenuation correction factors and emission images that were more accurate than those obtained using a popular segmentation based attenuation correction method, and the penalized maximum likelihood and filtered backprojection methods.Index Terms-Expectation maximization (EM) algorithm, image reconstruction, penalized maximum likelihood (PML) method, positron emission tomography (PET), segmentation.

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Section: Cse Algorithmmentioning

confidence: 99%

Section: Cse Algorithmmentioning

confidence: 99%

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Concurrent Segmentation and Estimation of Transmission Images for Attenuation Correction in Positron Emission Tomography

Anderson

Kim

Votaw

2009

IEEE Trans. Nucl. Sci.

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“…Iterative image reconstruction methods have attracted considerable attention in the past decades for applications in positron emission tomography (PET) due to the feasibility of incorporating the physical and statistical properties of the imaging process more completely [4,25]. So far, all statistical reconstruction algorithms are based on the maximum likelihood (ML) or the least squares cost function.…”

Section: Introductionmentioning

confidence: 99%

“…Another class of iterative image reconstruction methods made use of the weighted least squares (WLS) method [4,13]. Recently, Anderson et al [4] developed a WLS algorithm and demonstrated that this algorithm converged faster than the ML-EM and produced images that were significantly of better resolution and contrast.…”

Section: Introductionmentioning

confidence: 99%

Image reconstruction for positron emission tomography using fuzzy nonlinear anisotropic diffusion penalty

Zhu

Zhou

et al. 2006

Med Bio Eng Comput

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Iterative algorithms such as maximum likelihood-expectation maximization (ML-EM) become the standard for the reconstruction in emission computed tomography. However, such algorithms are sensitive to noise artifacts so that the reconstruction begins to degrade when the number of iterations reaches a certain value. In this paper, we have investigated a new iterative algorithm for penalized-likelihood image reconstruction that uses the fuzzy nonlinear anisotropic diffusion (AD) as a penalty function. The proposed algorithm does not suffer from the same problem as that of ML-EM algorithm, and it converges to a low noisy solution even if the iteration number is high. The fuzzy reasoning instead of a nonnegative monotonically decreasing function was used to calculate the diffusion coefficients which control the whole diffusion. Thus, the diffusion strength is controlled by fuzzy rules expressed in a linguistic form. The proposed method makes use of the advantages of fuzzy set theory in dealing with uncertain problems and nonlinear AD techniques in removing the noise as well as preserving the edges. Quantitative analysis shows that the proposed reconstruction algorithm is suitable to produce better reconstructed images when compared with ML-EM, ordered subsets EM (OS-EM), Gaussian-MAP, MRP, TV-EM reconstructed images.

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MRT letter: A unified accelerated maximum likelihood technique for widefield, confocal, and super‐resolution 4Pi microscopy

Rajan

Mondal

2015

Microscopy Res & Technique

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We propose an algorithmic technique for accelerating maximum likelihood (ML) algorithm for image reconstruction in fluorescence microscopy. This is made possible by integrating Biggs-Andrews (BA) method with ML approach. The results on widefield, confocal, and super-resolution 4Pi microscopy reveal substantial improvement in the speed of 3D image reconstruction (the number of iterations has reduced by approximately one-half). Moreover, the quality of reconstruction obtained using accelerated ML closely resembles with nonaccelerated ML method. The proposed technique is a step closer to realize real-time reconstruction in 3D fluorescence microscopy.

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Accelerated penalized weighted least-squares and maximum likelihood algorithms for reconstructing transmission images from PET transmission data

Cited by 8 publications

References 30 publications

Concurrent Segmentation and Estimation of Transmission Images for Attenuation Correction in Positron Emission Tomography

Concurrent Segmentation and Estimation of Transmission Images for Attenuation Correction in Positron Emission Tomography

Image reconstruction for positron emission tomography using fuzzy nonlinear anisotropic diffusion penalty

MRT letter: A unified accelerated maximum likelihood technique for widefield, confocal, and super‐resolution 4Pi microscopy

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