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Medical Imaging Dr. Mohammad Dawood Department of Computer Science University of Münster Germany Medical Imaging, SS-2014 Recap Dr. Mohammad Dawood 2 Medical Imaging, SS-2014 α decay Gamma scintigraphy Dr. Mohammad Dawood β- decay PET β+ decay Sinogram 3 Medical Imaging, SS-2014 Ultrasound / Sonography Dr. Mohammad Dawood 4 Medical Imaging, SS-2014 Sound spectrum The frequency range of sound above 20kHz is known as ultrasound Dr. Mohammad Dawood 5 Medical Imaging, SS-2014 Sound wave propagation Dr. Mohammad Dawood 6 Medical Imaging, SS-2014 Ultrasound Dr. Mohammad Dawood 7 Medical Imaging, SS-2014 Ultrasound Dr. Mohammad Dawood 8 Medical Imaging, SS-2014 Ultrasound - is produced through the conversion of electrical energy into mechanical energy - is detected by the reverse process, by converting mechanical energy into electrical energy. - The transducer is a device that is both a transmitter and receiver of the ultrasound signal and it serves a dual role in pulse echo imaging. Dr. Mohammad Dawood 9 Medical Imaging, SS-2014 Inge Edler und Helmut Hertz Dr. Mohammad Dawood (1954) 10 Medical Imaging, SS-2014 Ultrasound Dr. Mohammad Dawood 11 Medical Imaging, SS-2014 Ultrasound Reflexion Dr. Mohammad Dawood Scatter Transmission 12 Medical Imaging, SS-2014 Ultrasound Depth Resolution Frequency Dr. Mohammad Dawood 13 Medical Imaging, SS-2014 Ultrasound Dr. Mohammad Dawood 14 Medical Imaging, SS-2014 Ultrasound Dr. Mohammad Dawood 15 Medical Imaging, SS-2014 Medium Speed of sound m/s Air 331 Water 1483 Tissue 1540-1595 Liver 1549 Blood 1570 Glycerin 1923 Bones (Compact) 3600 Dr. Mohammad Dawood 16 Medical Imaging, SS-2014 Dr. Mohammad Dawood 17 Medical Imaging, SS-2014 Ultrasound - A mode (amplitude) - B mode (brightness) - M mode (moving) Dr. Mohammad Dawood 18 Medical Imaging, SS-2014 Ultrasound - no functional information - Bone / gas - fast - Obesity - cheap - Operator dependence - no radiation - portable - no injection Dr. Mohammad Dawood 19 Medical Imaging, SS-2014 Image Reconstruction Dr. Mohammad Dawood 20 Medical Imaging, SS-2014 Reconstruction Tomography detector x-ray source collimator object Dr. Mohammad Dawood 21 Medical Imaging, SS-2014 Reconstruction Law of Attenuation Dr. Mohammad Dawood 22 Medical Imaging, SS-2014 Reconstruction Parallel projections of a plane Dr. Mohammad Dawood 23 Medical Imaging, SS-2014 Reconstruction y s Radon Transformation f n r θ x Dr. Mohammad Dawood 24 Medical Imaging, SS-2014 Reconstruction Radon Transformation (Line Integrals at different angles) Dr. Mohammad Dawood 25 Medical Imaging, SS-2014 Reconstruction Radon Transformations Dr. Mohammad Dawood 26 Medical Imaging, SS-2014 Reconstruction Radon Transformation 32 128 512 Dr. Mohammad Dawood 27 Medical Imaging, SS-2014 Reconstruction Inverse Radon Transformation H: Hilbert transform Dr. Mohammad Dawood 28 Medical Imaging, SS-2014 Reconstruction Inverse Radon Transformation Problems with Missing data and Noise! Dr. Mohammad Dawood 29 Medical Imaging, SS-2014 Reconstruction Filtered Back Projection Dr. Mohammad Dawood 30 Medical Imaging, SS-2014 Reconstruction Projections A A+B B 1 D C+D C 2 4 A B 3 B+D A+C D C A+D B+C Dr. Mohammad Dawood 31 Medical Imaging, SS-2014 Reconstruction Back projections 2A+B 3A+B 4A+B A+3B A+4B A+B+ A+C+ C+2D C+D ? C+4D 3D A+B+ A+2C C+D ? 3C+D 4C+D +D A+2B A+B ? A+B ? +C+D +C +C+D +C A+B 1 C+D 4 2 A B B+D 3 C A+C D A+D B+C Dr. Mohammad Dawood 32 Medical Imaging, SS-2014 Reconstruction Back projections Dr. Mohammad Dawood 4A+B +C+D A+4B +C+D A+B+ C+4D A+B+ 4C+D 3A 3B - (A+B+C+D) = A B D C / (n-1) = 3D 3C 33 Medical Imaging, SS-2014 Reconstruction Filtered Back Projection Dr. Mohammad Dawood 34 Medical Imaging, SS-2014 Reconstruction FBP: Commonly used filters 1=Ram-Lak (ramp), 2=Shepp-Logan, 3=Cosine, and 4=Hamming Dr. Mohammad Dawood 35 Medical Imaging, SS-2014 Reconstruction Filtered Back Projection 2D/3D filtering is costly Backproject Filter 2D Projections Image Filter 1D Dr. Mohammad Dawood Backproject 36 Medical Imaging, SS-2014 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 Dr. Mohammad Dawood 37 Medical Imaging, SS-2014 Dr. Mohammad Dawood 38 Medical Imaging, SS-2014 Dr. Mohammad Dawood 39 Medical Imaging, SS-2014 Reconstruction Iterative Reconstruction Kaczmarz Method (=ART: Algebraic Reconstruction Technique) 1. Start by setting x(0) = 0 2. Compute the forward projection 3. Update the current estimate 4. Iterate steps 2,3 until the difference between new forward projection, computed in 2, and the old one is below tolerance Dr. Mohammad Dawood 40 Medical Imaging, SS-2014 Dr. Mohammad Dawood 41