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Tomographic Model Based Iterative Reconstruction of Symmetric Objects

Kyle M. Champley, Ibrahim Oksuz, Matthew G. Bisbee, Joseph W. Tringe, Brian Maddox

Abstract

Computed Tomography (CT) reconstruction of objects with cylindrical symmetry can be performed with a single projection. When the measured rays are parallel, and the axis of symmetry is perpendicular to the optical axis, the data can be modeled with the so-called Abel Transform. The Abel Transform has been extensively studied and many methods exist for accurate reconstruction. However, most CT geometries are cone-beam rather than parallel-beam. Using Abel methods for reconstruction in these cases can lead to distortions and reconstruction artifacts. Here, we develop analytic and model-based iterative reconstruction (MBIR) methods to reconstruct symmetric objects with an arbitrary axis of symmetry from a cone-beam geometry. The MBIR methods demonstrate superior results relative to the analytic inversion methods by mitigating artifacts and reducing noise while retaining fine image features. We demonstrate the efficacy of our methods using simulated and experimentally-acquired x-ray and neutron projections.

Tomographic Model Based Iterative Reconstruction of Symmetric Objects

Abstract

Computed Tomography (CT) reconstruction of objects with cylindrical symmetry can be performed with a single projection. When the measured rays are parallel, and the axis of symmetry is perpendicular to the optical axis, the data can be modeled with the so-called Abel Transform. The Abel Transform has been extensively studied and many methods exist for accurate reconstruction. However, most CT geometries are cone-beam rather than parallel-beam. Using Abel methods for reconstruction in these cases can lead to distortions and reconstruction artifacts. Here, we develop analytic and model-based iterative reconstruction (MBIR) methods to reconstruct symmetric objects with an arbitrary axis of symmetry from a cone-beam geometry. The MBIR methods demonstrate superior results relative to the analytic inversion methods by mitigating artifacts and reducing noise while retaining fine image features. We demonstrate the efficacy of our methods using simulated and experimentally-acquired x-ray and neutron projections.

Paper Structure

This paper contains 9 sections, 19 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. X-ray and Abel Transforms and Assumptions of Symmetry
  3. Model-Based Iterative Reconstruction
  4. Adjoint Operators
  5. Analytic Inversion of the Axial Cone Beam Transform of Symmetric Objects
  6. Implementation of the Forward and Back Projection Algorithms
  7. Experimental Validation
  8. Conclusions and Discussion
  9. Acknowledgement

Figures (6)

  • Figure 1: Backprojection of a single projection of the (left) standard and (right) symmetric cone-beam X-ray Transform. The object here is a uniform cylinder and the images show a vertical two-dimensional slice through the center of the object.
  • Figure 2: Vertical slices of reconstructions of a uniform cylinder using the symmetric cone-beam transform using one hundred iterations of conjugate gradient. The image on the right uses the SQS preconditioner while the image on the left does not.
  • Figure 3: Cone-beam projector of symmetric objects is modeled by intersection lengths through annuli. The image on the left shows the intersection points through the set of annuli perpendicular to the axis of symmetry while the image on the right shows the intersections though a single annuli in three dimensions.
  • Figure 4: Reconstruction results for the simulated FORBILD head phantom.
  • Figure 5: Reconstruction results the dynamic explosive experiment at ALS.
  • ...and 1 more figures