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

Hwang, Do Sik; Zeng, G.L.

doi:10.1088/0031-9155/51/2/004

Cited by 31 publications

(44 citation statements)

References 18 publications

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“…, . Although bigger step size is effective for accelerating IIR method, the algorithm diverges or oscillates if it is too big [12,13]. The value of ℎ was chosen to characterize the difference between lower-and higher-order discretization methods (i.e., OS-EM and RK, resp.)…”

Section: Numerical Examplementioning

confidence: 99%

“…To accelerate the ML-EM algorithm, which has a drawback of slow convergence, the orderedsubset variation of the ML-EM, known as the orderedsubsets expectation-maximization (OS-EM) [7,8], is an effective and popular method. In addition to the OS-EM method, a larger power factor that does not cause divergence in the iterative process was introduced [9][10][11][12][13] to further accelerate the convergence rate. It was asserted [12] that a power-based ML-EM algorithm with increased power (step size) resulted in not only accelerating the convergence rate but also maximizing the likelihood values.…”

Section: Introductionmentioning

confidence: 99%

“…In addition to the OS-EM method, a larger power factor that does not cause divergence in the iterative process was introduced [9][10][11][12][13] to further accelerate the convergence rate. It was asserted [12] that a power-based ML-EM algorithm with increased power (step size) resulted in not only accelerating the convergence rate but also maximizing the likelihood values. However, there is currently no general formula for optimizing the convergence rate by choosing appropriate values of the subsets number and the step size, which depend on the tomography system condition.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Continuous Analog of Accelerated OS‐EM Algorithm for Computed Tomography

Tateishi

Yamaguchi

Al-Ola

et al. 2017

Mathematical Problems in Engineering

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The maximum-likelihood expectation-maximization (ML-EM) algorithm is used for an iterative image reconstruction (IIR) method and performs well with respect to the inverse problem as cross-entropy minimization in computed tomography. For accelerating the convergence rate of the ML-EM, the ordered-subsets expectation-maximization (OS-EM) with a power factor is effective. In this paper, we propose a continuous analog to the power-based accelerated OS-EM algorithm. The continuoustime image reconstruction (CIR) system is described by nonlinear differential equations with piecewise smooth vector fields by a cyclic switching process. A numerical discretization of the differential equation by using the geometric multiplicative first-order expansion of the nonlinear vector field leads to an exact equivalent iterative formula of the power-based OS-EM. The convergence of nonnegatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem for consistent inverse problems. We illustrate through numerical experiments that the convergence characteristics of the continuous system have the highest quality compared with that of discretization methods. We clarify how important the discretization method approximates the solution of the CIR to design a better IIR method.

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Section: Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Continuous Analog of Accelerated OS‐EM Algorithm for Computed Tomography

Tateishi

Yamaguchi

Al-Ola

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…For example, an enlarged step size with the form of exponential power was proposed for ML-EM reconstruction. 50 The algorithm lacks monotonicity, hence may have a problem with stability. The idea of over-relaxed step size was also mentioned in Yu et al 30 for the ICD framework, where a factor of 1 to 2 was used to scale up the step size.…”

Section: E Computation Of the Solutionmentioning

confidence: 99%

“…(25) varied from 1 to K, a value larger than 1. That is, the optimal scaling factor ρ * , which produces the optimal step size to achieve the fastest convergence rate at each iteration, is not scaled down gradually, but needs to be successively increased iteratively, which is fundamentally different from other methods 50 where an exponential factor is supposed to be more conservative with increasing iterations.…”

Section: E Computation Of the Solutionmentioning

confidence: 99%

Statistical iterative reconstruction to improve image quality for digital breast tomosynthesis

Zhou

et al. 2015

Medical Physics

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Purpose: Digital breast tomosynthesis (DBT) is a novel modality with the potential to improve early detection of breast cancer by providing three-dimensional (3D) imaging with a low radiation dose. 3D image reconstruction presents some challenges: cone-beam and flat-panel geometry, and highly incomplete sampling. A promising means to overcome these challenges is statistical iterative reconstruction (IR), since it provides the flexibility of accurate physics modeling and a general description of system geometry. The authors' goal was to develop techniques for applying statistical IR to tomosynthesis imaging data. Methods: These techniques include the following: a physics model with a local voxel-pair based prior with flexible parameters to fine-tune image quality; a precomputed parameter λ in the prior, to remove data dependence and to achieve a uniform resolution property; an effective ray-driven technique to compute the forward and backprojection; and an oversampled, ray-driven method to perform high resolution reconstruction with a practical region-of-interest technique. To assess the performance of these techniques, the authors acquired phantom data on the stationary DBT prototype system. To solve the estimation problem, the authors proposed an optimization-transfer based algorithm framework that potentially allows fewer iterations to achieve an acceptably converged reconstruction. Results: IR improved the detectability of low-contrast and small microcalcifications, reduced crossplane artifacts, improved spatial resolution, and lowered noise in reconstructed images. Conclusions: Although the computational load remains a significant challenge for practical development, the superior image quality provided by statistical IR, combined with advancing computational techniques, may bring benefits to screening, diagnostics, and intraoperative imaging in clinical applications. C 2015 American Association of Physicists in Medicine.

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SPECT reconstruction with sub‐sinogram acquisitions

Hwang

Lee

Zeng

2011

Int J Imaging Syst Tech

Self Cite

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Described herein are the advantages of using sub-sinograms for single photon emission computed tomography image reconstruction. A sub-sinogram is a sinogram acquired with an entire data acquisition protocol, but in a fraction of the total acquisition time. A total-sinogram is the summation of all sub-sinograms. Images can be reconstructed from the total-sinogram or from sub-sinograms and then be summed to produce the final image. For a linear reconstruction method such as the filtered backprojection algorithm, there is no advantage of using sub-sinograms. However, for nonlinear methods such as the maximum likelihood (ML) expectation maximization algorithm, the use of sub-sinograms can produce better results. The ML estimator is a random variable, and one ML reconstruction is one realization of the random variable. The ML solution is better obtained via the mean value of the random variable of the ML estimator. Sub-sinograms can provide many realizations of the ML estimator. We show that the use of sub-sinograms can produce better estimations for the ML solution than can the total-sinogram and can also reduce the statistical noise within iteratively reconstructed images.

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

Cited by 31 publications

References 18 publications

Continuous Analog of Accelerated OS‐EM Algorithm for Computed Tomography

Continuous Analog of Accelerated OS‐EM Algorithm for Computed Tomography

Statistical iterative reconstruction to improve image quality for digital breast tomosynthesis

SPECT reconstruction with sub‐sinogram acquisitions

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