Statistical iterative methods for image reconstruction like maximum likelihood expectation maximization (ML-EM) are more robust and flexible than analytical inversion methods and allow for accurately modeling the coun...
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Statistical iterative methods for image reconstruction like maximum likelihood expectation maximization (ML-EM) are more robust and flexible than analytical inversion methods and allow for accurately modeling the counting statistics and the photon transport during acquisition. They are rapidly becoming the standard for image reconstruction in emission computed tomography. The maximum likelihood approach provides images with superior noise characteristics compared to the conventional filtered back projection algorithm. But a major drawback of the statistical iterative image reconstruction is its high computational cost. In this paper, a fast algorithm is proposed as a modified OS-EM (MOS-EM) using a penalized function, which is applied to the least squares merit function to accelerate image reconstruction and to achieve better convergence. The experimental results show that the algorithm can provide high quality reconstructed images with a small number of iterations. (c) 2005 IPEM. Published by Elsevier Ltd. All rights reserved.
Iterative algorithms such as maximum likelihood expectation maximization (ML-EM) algorithm are rapidly becoming the standard for image reconstruction in emission computed tomography. The maximum likelihood approach pr...
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Iterative algorithms such as maximum likelihood expectation maximization (ML-EM) algorithm are rapidly becoming the standard for image reconstruction in emission computed tomography. The maximum likelihood approach provides images with superior noise characteristics compared to conventional filtered backprojection algorithm. A major drawback of the iterative image reconstruction methods is their high computational cost. In this paper, we develop a new algorithm called the improved ordered subset expectation maximization (IOS-EM) algorithm. This algorithm modifies the number of projections in each subset and the step size (i.e., the relaxation factor) for each iteration in order to recover various frequency components in early iteration steps. In the method presented in this paper, the number of projections in a subset increases and the step size decreases after each iteration. In addition, pixel data are grouped into subdivisions to accelerate image reconstruction. Experimental results show that the IOS-EM algorithm can provide high quality reconstructed images at a small number of iterations.
In this paper, we discuss the solution of a system of fuzzy linear equations, X = AX + U, and its iteration algorithms where A is a real n x n matrix, the unknown vector X and the constant U are all vectors consisting...
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In this paper, we discuss the solution of a system of fuzzy linear equations, X = AX + U, and its iteration algorithms where A is a real n x n matrix, the unknown vector X and the constant U are all vectors consisting of n fuzzy numbers, and the addition, scale-multiplication are defined by Zadeh's extension principle. After introducing a metric between two fuzzy vectors, we prove that the system has unique solution if \\A\\(infinity) < 1 We also give the convergence and the error estimation for using simple iteration to obtain the solution. Finally, we give the convergence and the error estimation of successive iteration sequence for obtaining the solution. (C) 2001 Elsevier Science B.V. All rights reserved.
The numerical treatment of nonlinear model fitting problems often can be simplified by manipulating the model equations. Algebraic manipulations including nonlinear transformations of model parameters, do not change t...
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The numerical treatment of nonlinear model fitting problems often can be simplified by manipulating the model equations. Algebraic manipulations including nonlinear transformations of model parameters, do not change the numerical result of the adjustment and can be a powerful method to improve the performance of solution algorithms. Nonlinear transformations of the observations, on the other hand, do change the numerical results unless the normal equations are transformed accordingly. The latter transformation has been neglected by previous authors and this article provides a complete set of formulas that are needed to implement transformations of observations. The transformations are in general less useful than parameter transformations for the improvement of algorithms but may have other applications in particular situations.
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