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Regularization For Inverting The Radon Transform With Wedge Consideration

Regularization For Inverting The Radon Transform With Wedge Consideration. I. Aganj 1 , A. Bartesaghi 2 , M. Borgnia 2 , H.Y. Liao 3 , G. Sapiro 1 , S. Subramaniam 2. Department of Electrical Engineering, University of Minnesota Center for Cancer Research, National Institutes of Health

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Regularization For Inverting The Radon Transform With Wedge Consideration

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  1. Regularization For Inverting The RadonTransform With Wedge Consideration I. Aganj1, A. Bartesaghi2, M. Borgnia2, H.Y. Liao3, G. Sapiro1, S. Subramaniam2 Department of Electrical Engineering, University of Minnesota Center for Cancer Research, National Institutes of Health Institute for Mathematics and Its Applications, University of Minnesota

  2. Radon Transform

  3. Radon Transform

  4. Missing Wedge Problem

  5. Missing Wedge Problem

  6. Reconstruction R: Radon Transformf: Reconstructed Image w: Projections

  7. Reconstruction R: Radon Transformf: Reconstructed Image w: Projections

  8. Reconstruction R: Radon Transformf: Reconstructed Image w: ProjectionsP(f):Penalty Function

  9. Total Variation Introduced in: L. Rudin, S. Osher, and CFatemi “Nonlinear total variation . based noise removal algorithms” Physica D, vol. 60, pp. 259-–268, 1992. Low TV High TV

  10. Reconstruction by Total Variation Minimization fidelity penalty R: Radon Transformf: Reconstructed Image w: Projections

  11. Reconstruction by Total Variation Minimization Original image Weighted Back Projection TV minimization Phantom image originally from: A.H. Delaney and Y. Bresler, “Globally convergent edge-preserving regularized reconstruction: an application to limited-angle tomography,” IEEE. Trans. Imag. Proc., vol. 7, pp. 204-221, 1998.

  12. Anisotropic Regularization Isotropic Total Variation: Anisotropic Total Variation:

  13. Reconstruction by Anisotropic Regularization R: Radon Transformf: Reconstructed Image w: Projections

  14. Reconstruction by Anisotropic Regularization This is the optimum direction, choosing more than one direction is redundant! R: Radon Transformf: Reconstructed Image w: Projections

  15. Reconstruction by Anisotropic Regularization Original image Weighted Back Projection Anisotropic Regularization TV minimization

  16. Results on Real Data (Bdellovibrio Bacterium) ART SIRT Anisotropic TV

  17. THANK YOU!

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