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Medical Imaging

Medical Imaging. Mohammad Dawood Department of Computer Science University of Münster Germany. Image Reconstruction. Reconstruction Law of Attenuation. Reconstruction Parallel projections of a plane. y. Reconstruction Radon Transformation. s. f. r. n. θ. x. Reconstruction

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Medical Imaging

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  1. Medical Imaging Mohammad Dawood Department of Computer Science University of Münster Germany

  2. Image Reconstruction

  3. Reconstruction Law of Attenuation

  4. Reconstruction Parallel projections of a plane

  5. y Reconstruction Radon Transformation s f r n θ x

  6. Reconstruction Radon Transformation (Line Integrals at different angles)

  7. Reconstruction Radon Transformation Original Sinogram (Radon Transform)

  8. Reconstruction Inverse Radon Transformation H: Hilbert transform

  9. Reconstruction Filtered Back Projection

  10. Reconstruction Filtered Back Projection

  11. Reconstruction Filtered Back Projection 2D/3D filtering is costly Backproject Filter 2D Projections Image Filter 1D Backproject

  12. Reconstruction Fourier Slice Theorem

  13. Reconstruction Fourier slice theorem Take a two-dimensional function f(r), project it onto a line, and do a Fourier transform of that projection Take that same function, but do a two-dimensional Fourier transform first, and then slice it through its origin parallel to the projection line

  14. Reconstruction Fourier Slice Theorem

  15. Reconstruction FBP: Commonly used filters 1=Ram-Lak (ramp), 2=Shepp-Logan, 3=Cosine, and 4=Hamming

  16. Reconstruction Iterative Reconstruction b: measured values x: unknown attenuation coefficients aij: weights

  17. Reconstruction Iterative Reconstruction Kaczmarz Method (=ART: Algebraic Reconstruction Technique)

  18. Reconstruction Iterative Reconstruction Kaczmarz Method (=ART: Algebraic Reconstruction Technique) 1. Start by setting x(0) = 0 2. Compute the forward projection from the n-th estimate, i.e. b(n) = A x(n) 3. Choose i and correct the current estimate x(n) 4. Iterate steps 2,3 until the difference between new forward projection b(n), computed in 2, and the old one is below tolerance

  19. Reconstruction Iterative Reconstruction EM (Expectation Maximization)

  20. Reconstruction Iterative Reconstruction OSEM (Ordered Subset Expectation Maximization)

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