Maximum a Posteriori Image Reconstruction from Projections

Herman, Gabor T.; Chan, M.; Censor, Yair; Levitan, E.; Lewitt, R.M.; Narayan, T. K.

doi:10.1007/978-1-4612-4056-3_3

Cited by 4 publications

(4 citation statements)

References 55 publications

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“…Cross log entropy maximization has been suggested by Herman et al [12] in tomography, together with the algorithm (5) where is a relaxation parameter with the same dimension as . The above algorithm's convergence is still a subject of study.…”

Section: Consider the System Of Equationsmentioning

confidence: 99%

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Cross Burg entropy maximization and its application to ringing suppression in image reconstruction

Cao

Eggermont²,

Terebey³

1999

IEEE Trans. on Image Process.

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Section: Consider the System Of Equationsmentioning

confidence: 99%

“…Second, we write (10) Now observe that (11) where . Now is strictly convex for , and so by Jensen's inequality (12) with equality if and only if is independent of , for those indices for which . Consequently (13) with equality if and only if is the constant vector.…”

Section: A Derivationmentioning

confidence: 99%

Cross Burg entropy maximization and its application to ringing suppression in image reconstruction

Cao

Eggermont²,

Terebey³

1999

IEEE Trans. on Image Process.

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“…Also, there is a need for comparing the outcomes of numerical observer evaluations and human observer evaluations of reconstruction algorithms. There have been some reports in this direction [2,7,15,28] and such work is part of our ongoing research [29].…”

Section: Calculation Of the Levels Of Statistical Significance Based Onmentioning

confidence: 99%

Computerized evaluation of image reconstruction algorithms

Browne

Herman

1996

Int. J. Imaging Syst. Technol.

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In medical imaging an enormous variety of algorithms have been proposed to reconstruct a cross section of the human body. In assessing the relative task‐oriented performance of reconstruction algorithms, it is desirable to assign statistical significance to claims of superiority of one algorithm over another. However, very often the achievement of statistical significance demands a large number of observations. Performing such an evaluation on mathematical phantoms requires a means of running the competing algorithms on projection data obtained from a large number of randomly generated phantoms. Thereafter, various numerical measures of agreement between the reconstructed images and the original phantoms may be used to reach a conclusion which has some statistical substance. In this article we describe the software SuperSNARK, which automates an evaluation methodology for assigning statistical significance to the observed differences in performance of two or more image reconstruction algorithms. As a demonstration, we compare the relative efficacy of the maximum likelihood expectation maximization (ML‐EM) algorithm and the filtered backprojection (FBP) method for performing three medical tasks in positron emission tomography (PET)—estimation of total uptake by structures, detection of relatively higher uptake between pairs of symmetric structures, and estimation of uptake at individual points within structures. We find that for estimating total uptake ML‐EM outperforms FBP, for detecting relatively higher uptake there is not a statistically significant difference between the two methods, and for estimating pointwise uptake FBP outperforms ML‐EM. It is demonstrated that SuperSNARK makes it easy to apply the methodology of statistical hypothesis testing to substantiate such claims of task‐specific superiority of one reconstruction algorithm over another. © 1996 John Wiley & Sons, Inc.

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“…Matej, Vardi, Herman, and Vardi [60] suggested representing the image function f by a hexagonal grid, which is assumed to have a Gibbs distribution with known local properties, as described in [29]. Other reconstruction methods are based on Bayesian probability principles, and apply maximum a posteriori expectation maximization [34,58] or maximum likelihood [68] techniques. Kuba, Nagy and Balogh were interested in the reconstruction of hv-convex binary patterns and published reconstruction algorithms [46,[48][49][50] using two orthogonal projections.…”

Section: Historical Overviewmentioning

confidence: 99%

A Pixel-based Discrete Tomographic Technique and Its Applications

Kiss¹

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Maximum a Posteriori Image Reconstruction from Projections

Cited by 4 publications

References 55 publications

Cross Burg entropy maximization and its application to ringing suppression in image reconstruction

Cross Burg entropy maximization and its application to ringing suppression in image reconstruction

Computerized evaluation of image reconstruction algorithms

A Pixel-based Discrete Tomographic Technique and Its Applications

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