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Improved Simultaneous Algebraic Reconstruction Technique Algorithm for Positron-Emission Tomography Image Reconstruction via Minimizing the Fast Total Variation

Published:November 01, 2017DOI:https://doi.org/10.1016/j.jmir.2017.09.005

      Abstract

      Context

      There has been considerable progress in the instrumentation for data measurement and computer methods for generating images of measured PET data. These computer methods have been developed to solve the inverse problem, also known as the “image reconstruction from projections” problem.

      Aim

      In this paper, we propose a modified Simultaneous Algebraic Reconstruction Technique (SART) algorithm to improve the quality of image reconstruction by incorporating total variation (TV) minimization into the iterative SART algorithm.

      Methodology

      The SART updates the estimated image by forward projecting the initial image onto the sinogram space. Then, the difference between the estimated sinogram and the given sinogram is back-projected onto the image domain. This difference is then subtracted from the initial image to obtain a corrected image. Fast total variation (FTV) minimization is applied to the image obtained in the SART step. The second step is the result obtained from the previous FTV update. The SART and the FTV minimization steps run iteratively in an alternating manner. Fifty iterations were applied to the SART algorithm used in each of the regularization-based methods. In addition to the conventional SART algorithm, spatial smoothing was used to enhance the quality of the image. All images were sized at 128 × 128 pixels.

      Results

      The proposed algorithm successfully accomplished edge preservation. A detailed scrutiny revealed that the reconstruction algorithms differed; for example, the SART and the proposed FTV-SART algorithm effectively preserved the hot lesion edges, whereas artifacts and deviations were more likely to occur in the ART algorithm than in the other algorithms.

      Conclusions

      Compared to the standard SART, the proposed algorithm is more robust in removing background noise while preserving edges to suppress the existent image artifacts. The quality measurements and visual inspections show a significant improvement in image quality compared to the conventional SART and Algebraic Reconstruction Technique (ART) algorithms.

      Résumé

      Contexte

      Il y a eu des progrès considérables dans l'instrumentation de mesure de données et les méthodes informatiques permettant de générer des images des données de TEP mesurées. Ces méthodes informatiques ont été développées pour résoudre le problème inverse, aussi appelé problème de « reconstruction de l'image à partir des projections ».

      But

      Dans cet article, les auteurs proposent un algorithme modifié pour la technique de reconstruction algébrique simultanée (SART), de façon à améliorer la qualité de la reconstruction de l'image en incorporant la minimisation de la variation totale (TV) dans l'algorithme itératif de SART.

      Méthodologie

      L'algorithme SART met à jour l'image estimative en faisant une projection avant de l'image sur l'espace du sinogramme. La différence entre le sinogramme estimé et le sinogramme donné est ensuite rétroprojetée sur le domaine de l'image. Cette différence est ensuite soustraite de l'image initiale pour obtenir une image corrigée. La minimisation rapide de la variation totale (FTV) est appliquée à l'image obtenue dans l’étape SART. La deuxième étape est le résultat obtenu de la mise à jour FTV précédente. Les étapes de SART et de minimisation FTV sont conduites de façon itérative, en alternance. Cinquante itérations ont été appliquées à l'algorithme SART utilisé dans chacune des méthodes fondées sur la régularisation. En plus de l'algorithme SART conventionnel, le lissage spatial a été utilisé pour améliorer la qualité de l'image. Toutes les images ont été produites en format 128 x 128 pixels.

      Résultats

      L'algorithme proposé a préservé les bordures avec succès. Un examen détaillé révèle que les algorithmes de reconstruction étaient différents; par exemple, l'algorithme SART et l'algorithme SART-FTV proposé ont préservé efficacement les bordures chaudes des lésions, tandis que les artefacts et les déviations étaient plus susceptibles d'apparaître dans l'algorithme ART que dans les autres algorithmes.

      Conclusion

      En comparaison de l'algorithme SART standard l'algorithme proposé réussit mieux à éliminer le bruit ambiant tout en préservant les bordures pour supprimer les artefacts existants. Les mesures de qualité et l'inspection visuelle montrent une amélioration significative de la qualité de l'image comparativement à l'algorithme SART traditionnel et à l'algorithme de technique de reconstruction algébrique (ART).

      Keywords

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