An accelerated convergent ordered subsets algorithm for emission tomography

Hsiao, Ing‐Tsung; Rangarajan, Anand; Khurd, Parmeshwar; Gindi, Gene

doi:10.1088/0031-9155/49/11/002

Cited by 51 publications

(49 citation statements)

References 11 publications

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“…This allows us to choose the latest and fastest optimization algorithm for image reconstruction, including the convergent versions of subset-based algorithms. [49][50][51] A common intuition is that any approximations in the system matrix will always slow down the convergence to the true solution. However, as shown in Fig.…”

Section: Discussionmentioning

confidence: 99%

A residual correction method for high‐resolution PET reconstruction with application to on‐the‐fly Monte Carlo based model of positron range

2010

Medical Physics

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Purpose: The quality of tomographic images is directly affected by the system model being used in image reconstruction. An accurate system matrix is desirable for high-resolution image reconstruction, but it often leads to high computation cost. In this work the authors present a maximum a posteriori reconstruction algorithm with residual correction to alleviate the tradeoff between the model accuracy and the computation efficiency in image reconstruction. Methods: Unlike conventional iterative methods that assume that the system matrix is accurate, the proposed method reconstructs an image with a simplified system matrix and then removes the reconstruction artifacts through residual correction. Since the time-consuming forward and back projection operations using the accurate system matrix are not required in every iteration, image reconstruction time can be greatly reduced. Results:The authors apply the new algorithm to high-resolution positron emission tomography reconstruction with an on-the-fly Monte Carlo ͑MC͒ based positron range model. Computer simulations show that the new method is an order of magnitude faster than the traditional MC-based method, whereas the visual quality and quantitative accuracy of the reconstructed images are much better than that obtained by using the simplified system matrix alone. Conclusions:The residual correction method can reconstruct high-resolution images and is computationally efficient.

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Section: Discussionmentioning

confidence: 99%

A residual correction method for high‐resolution PET reconstruction with application to on‐the‐fly Monte Carlo based model of positron range

2010

Medical Physics

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“…They include, mainly, ordered subset EM (OSEM) [25], row action maximum likelihood algorithm (RAMLA) [26], block sequential regularized EM (BSREM) [27], modified BSREM and relaxed OS separable paraboloidal surrogates (OS-SPS) [18], and complete data ordered subsets EM (COSEM-ML and COSEM-MAP [28]). Among these algorithms, OSEM, RAMLA and COSEM-ML are for ML reconstructions, while BSREM, modified BSREM, relaxed OS-SPS and COSEM-MAP are for MPL reconstructions.…”

Section: Ordered Subset Formulationsmentioning

confidence: 99%

“…For COSIB, of (24) can be cheaply computed using since, for all , (28) This demonstrates that the computational burden of COSIB is tantamount to that of OSIB. However, we must note that (28) is true only if is computed using (24).…”

Section: Ordered Subset Formulationsmentioning

confidence: 99%

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On Iterative Bayes Algorithms for Emission Tomography

2008

IEEE Trans. Nucl. Sci.

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In this paper we formulate a new approach to medical image reconstruction from projections in emission tomography. This approach conceptually differs from the traditional methods such as filtered backprojection, maximum likelihood or maximum penalized likelihood. Similar to the Richardson-Lucy algorithm ([1], [2]), our method develops directly from the Bayes formula with the final result being an iterative algorithm, for which the maximum likelihood expectation-maximization of [3] (or [4]) is a special case. Although there are different ways to enforce smoothness in the reconstructions using this method, in this paper we opt to focus only on the way which smoothes the camera bin measurements before reconstruction. In fact, this method can be explicated as maximizing a special penalized log-likelihood function. Its theoretical properties are also analyzed in the paper.

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“…The C-OS-3 algorithm belongs to the framework of convergent incremental optimization transfer methods described in [6]. Specifically, it is an extension of the convergent C-OSEM algorithm of [7] that is based on an incremental version of the complete-data space used in the EM-3 algorithm described in [8]. The algorithm is available in Matlab code in the Image Reconstruction Toolbox written by Fessler [5].…”

Section: Regularization Through Side Informationmentioning

confidence: 99%

Nature of Ringing Artifacts in Spect Reconstruction and Their Reduction by the Use of Side Information

Koral

2007

2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro

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ML-EM iterative reconstruction algorithms tend towards ringing artifacts, and high noise, after a large number of iterations just as filtered backprojection algorithms tend toward streak artifacts. OS-EM is a type of ML-EM algorithm and an edge overshoot has been observed experimentally for uniform-activity spheres of large size but not smaller size. Herein, we shed light on such artifacts by showing that they are a function of the object size relative to the FWHM of the collimator-detector response function. That is, for a given number of iterations, an over-or undershoot can occur at a given spatial location or not depending on the value of the ratio. We further show that a new, regularized, penalized-likelihood algorithm based on ordered subsets and employing side information stabilizes the iterative procedure against the development of artifacts.

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An accelerated convergent ordered subsets algorithm for emission tomography

Cited by 51 publications

References 11 publications

A residual correction method for high‐resolution PET reconstruction with application to on‐the‐fly Monte Carlo based model of positron range

A residual correction method for high‐resolution PET reconstruction with application to on‐the‐fly Monte Carlo based model of positron range

On Iterative Bayes Algorithms for Emission Tomography

Nature of Ringing Artifacts in Spect Reconstruction and Their Reduction by the Use of Side Information

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