Superiorization of the ML-EM Algorithm

Garduño, Edgar; Herman, Gabor T.

doi:10.1109/tns.2013.2283529

Cited by 36 publications

(43 citation statements)

References 34 publications

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“…Superiorization work with other target functions such as total variation (TV) appears in, e.g., [13, 15, 27]. Superiorization work on Case 3, where M is the solution set of a maximum likelihood optimization problem appears in [23, 28, 30]. …”

Section: The Superiorization Methodologymentioning

confidence: 99%

Can linear superiorization be useful for linear optimization problems?

Censor¹

2017

Inverse Problems

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Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are (i) Does linear superiorization provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? and (ii) How does linear superiorization fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: “yes” and “very well”, respectively.

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Section: The Superiorization Methodologymentioning

confidence: 99%

Can linear superiorization be useful for linear optimization problems?

Censor¹

2017

Inverse Problems

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“…We follow the same algorithm flowchart as in Censor et al (2014) and Garduno and Herman (2014). The superiorized SART algorithm is in table 1.…”

Section: Methodsmentioning

confidence: 99%

“…Specifically, the basic algorithm that solves the data fidelity term remains the same but the intermediate solution is steered towards the direction to reduce the penalty term. Several studies were performed to superiorize the ML-EM algorithm for emission reconstruction (Garduno and Herman 2014, Luo and Zhou 2014). TV and the l 1 -norm of a wavelet transform were implemented as the regularizers.…”

Section: Introductionmentioning

confidence: 99%

Superiorization-based multi-energy CT image reconstruction

2017

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The recently-developed superiorization approach is efficient and robust for solving various constrained optimization problems. This methodology can be applied to multi-energy CT image reconstruction with the regularization in terms of the prior rank, intensity and sparsity model (PRISM). In this paper, we propose a superiorized version of the simultaneous algebraic reconstruction technique (SART) based on the PRISM model. Then, we compare the proposed superiorized algorithm with the Split-Bregman algorithm in numerical experiments. The results show that both the Superiorized-SART and the Split-Bregman algorithms generate good results with weak noise and reduced artefacts.

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“…In the first of these, the saem [7] is compared with the em [15] considering two kind of superiorization sequences for non-negatively constrained Total Variation as a secondary criteria. The first superiorization sequence is produced according to Algorithm 2, following the ideas presented in [5], the second superiorization sequence is produced by the fgp algorithm from [1].…”

Section: Numerical Experimentationmentioning

confidence: 99%

Superiorization of incremental optimization algorithms for statistical tomographic image reconstruction

Helou¹,

Zibetti²,

Miqueles³

2017

Inverse Problems

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We propose the superiorization of incremental algorithms for tomographic image reconstruction. The resulting methods follow a better path in its way to finding the optimal solution for the maximum likelihood problem in the sense that they are closer to the Pareto optimal curve than the non-superiorized techniques. A new scaled gradient iteration is proposed and three superiorization schemes are evaluated. Theoretical analysis of the methods as well as computational experiments with both synthetic and real data are provided.

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Superiorization of the ML-EM Algorithm

Cited by 36 publications

References 34 publications

Can linear superiorization be useful for linear optimization problems?

Can linear superiorization be useful for linear optimization problems?

Superiorization-based multi-energy CT image reconstruction

Superiorization of incremental optimization algorithms for statistical tomographic image reconstruction

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