Utilization of Non-Negativity Constraints in Reconstruction of Emission Tomograms

Tanaka, Eiichi; Nohara, Norimasa; Tomitani, Takehiro; Yamamoto, Mikio

doi:10.1007/978-94-009-4261-5_27

Cited by 10 publications

(11 citation statements)

References 7 publications

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“…Many researchers have studied how to increase the step size. Vishampayan et al (1985), Tanaka et al (1985) and Tanaka (1987) tried to raise the correction factor of ML-EM to a certain power, and Lewitt and Muehllehner (1986) and Kaufman (1987) increased the step size of the correction factor in an additive form of ML-EM. The additive form of ML-EM has been modified to be applied to various OS-type algorithms for further acceleration and a decreased step size, rather than an increased one, is used to control their convergence characteristics (Browne andDe Pierro 1996, Tanaka andKudo 2003).…”

Section: Introductionmentioning

confidence: 99%

Convergence study of an accelerated ML-EM algorithm using bigger step size

Hwang

Zeng

2005

Phys. Med. Biol.

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In SPECT/PET, the maximum-likelihood expectation-maximization (ML-EM) algorithm is getting more attention as the speed of computers increases. This is because it can incorporate various physical aspects into the reconstruction process leading to a more accurate reconstruction than other analytical methods such as filtered-backprojection algorithms. However, the convergence rate of the ML-EM algorithm is very slow. Several methods have been developed to speed it up, such as the ordered-subset expectation-maximization (OS-EM) algorithm. Even though OS-type algorithms can bring about significant acceleration in the iterative reconstruction, it is generally believed that ML-EM produces better images, in terms of statistical noise in the reconstruction. In this paper, we present an accelerated ML-EM algorithm with bigger step size and show its convergence characteristics in terms of variance noise and log-likelihood values. We also show some advantages of our method over other accelerating methods using additive forms.

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Section: Introductionmentioning

confidence: 99%

Convergence study of an accelerated ML-EM algorithm using bigger step size

Hwang

Zeng

2005

Phys. Med. Biol.

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“…This speedup strategy may destroy a good property of the emission EM algorithm which conserves the total forward projection counts at every iteration. One remedy is to renormalize the image according to the total count at every iteration …”

Section: Resultsmentioning

confidence: 99%

Technical Note: Emission expectation maximization look‐alike algorithms for x‐rayCTand other applications

Zeng

2018

Medical Physics

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“…Because of the high quality of image reconstruction afforded by the MLEM algorithm, improved MLEM methods have been presented for accelerating convergence. Some schemes accelerate the convergence rate by increasing a relaxation parameter or the step-size in iterative operations [14,17,18] or by introducing a parameter with a power exponent related to the projection for controlling the noise model [19,20]. However, no theory has explained the divergence and oscillation phenomena affecting solutions when the step-size parameter is large.…”

Section: Introductionmentioning

confidence: 99%

Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures

Kasai

Yamaguchi

Kojima

et al. 2021

Entropy

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The problem of tomographic image reconstruction can be reduced to an optimization problem of finding unknown pixel values subject to minimizing the difference between the measured and forward projections. Iterative image reconstruction algorithms provide significant improvements over transform methods in computed tomography. In this paper, we present an extended class of power-divergence measures (PDMs), which includes a large set of distance and relative entropy measures, and propose an iterative reconstruction algorithm based on the extended PDM (EPDM) as an objective function for the optimization strategy. For this purpose, we introduce a system of nonlinear differential equations whose Lyapunov function is equivalent to the EPDM. Then, we derive an iterative formula by multiplicative discretization of the continuous-time system. Since the parameterized EPDM family includes the Kullback–Leibler divergence, the resulting iterative algorithm is a natural extension of the maximum-likelihood expectation-maximization (MLEM) method. We conducted image reconstruction experiments using noisy projection data and found that the proposed algorithm outperformed MLEM and could reconstruct high-quality images that were robust to measured noise by properly selecting parameters.

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Utilization of Non-Negativity Constraints in Reconstruction of Emission Tomograms

Cited by 10 publications

References 7 publications

Convergence study of an accelerated ML-EM algorithm using bigger step size

Convergence study of an accelerated ML-EM algorithm using bigger step size

Technical Note: Emission expectation maximization look‐alike algorithms for x‐rayCTand other applications

Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures

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