Lecture-by-lecture list of topics EECS 516 Medical Imaging Systems, F09 'X' means a topic covered in a previous year's lecture but not this year! (such topics are usually still in the lecture notes and are recommended reading) 1 (1) Introduction Overview of course Systems view of imaging systems Ideal imaging systems Preview of major modalities (lecture ends early due to EE:S orientation) (2) 2d signals and systems X Vector spaces X Examples of important vector spaces X Linear operator 2d signal transformations 2 2d signals: circ, gaussian, sinusoid, etc. 2d Dirac impulse, comb function 2d systems Shift invariance, or space invariance Rotation invariance Linearity Point spread function (PSF) example: magnifier (overhead projector) FOV issues 2d superposition integral X example: 1D pinhole camera 2d convolution integral for LSI systems 3 new properties in 2d PSF and spatial resolution Magnification and 2d pinhole camera Eigenfunctions of LSI systems: frequency response Two-dimensional Fourier transforms 2d Fourier transform properties Hankel transform Sampling bandlimited functions, non-bandlimited functions 4 Recovering bandlimited signal from its samples X DSFT, DFT FFT for computing FT (see notes) X (p) Probability review (not in lecture; students should review) X Radioactive decay statistics X Binomial counting process X Half-life X Poisson process X Noise in medical imaging systems X Statistics of point photon emitter and line detector (M9, P10) Ultrasound imaging (reflection mode) Ultrasound overview Object: what does ultrasound image? Surface reflections Volumetric scattering A-mode scan X M-mode scan 5 Source considerations Attenuation and dispersion Narrowband pulses Gaussian envelopes B-mode scans (reflection imaging) Near-field signal model Image formation expression Attenuation correction Near-field PSF X Depth variance of PSF X A scan, PSF of A scan Diffraction analysis of PSF of A-scan or B-scan Introduction X Huygens-Fresnel principle X Rayleigh-Sommerfield equations X Reciprocity theorem of Helmholtz Insonification Narrowband approximation for AM pulses Steady-state approximation X Paraxial approximation X Diffraction in Cartesian coordinates Diffraction in polar coordinates Fresnel approximation Fraunhofer approximation (far-field) Rect/Sinc example 6 Design tradeoffs X Physical interpretation of PSF Focusing (mechanical) Steering (mechanical) Speckle artifact Rayleigh distribution 7 Signal to noise ratio Summary (M10, P11) Ultrasound imaging with arrays Imaging array Steering and focusing viewed as propagation delays Forming sector scan Beamforming with real signals 8 Demodulation/baseband approach Scan conversion Diffraction with ultrasound arrays (PSF analysis) 9 X Linear array, simple sum Linear array with deflection (beam steering) Transducer sampling (design) Angular sampling Radial sampling 10 Focusing and quadratic phase errors Summary MRI (Nishimura) NMR physics overview spins, Zeeman diagram Main field, magentization, Larmor equation 11 RF field Relaxation, T1, T2 Field gradients, spatial location encoded into frequencies Selective and nonselective excitation X Chemical shift X RF Signal X k-space X spin-echos 12 Bloch equation Solutions when RF=0 Free induction decay (G=0 solution) Fundamental equation of MR Signal equation narrowband approximation T2 weighting based on TE k-space interpretation 13 (MR review) Pulse sequences 2d projection-reconstruction sequence Design parameters 2d FT (spin warp) sequence Sampling vs FOV Spatial Resolution (Dirichlet) X T2 weighting 14 (+ extra 35 minutes) Excitation Overview Bloch in rotating frame Nonselective excitation Selective excitation Refocusing lobe of Gz 15 Off-resonance effects Generalized form of Fund. Eq. of MR T2* Spin echo Spin echos and imaging 16 X T2 weighting and T2 mapping (TE) X Field mapping X T1 contrast (TR) NMR Spectroscopy Separation of fat and water Overview of project 17 (M3) Overview of Projection Radiography X-ray source physics Continuum spectrum, X-ray line spectra Beer's law Parallel-beam geometry Attenuation coefficient 18 Coherent scatter, Photoelectric absorption, Compton scattering (M4): Overview of assumptions Point-source geometry Solid angle depth-dependent (object) magnification thin-object example X example with wedge-shaped rod, magnification distortion X rectangular rod example planar source of finite size parallel to detector source magnification factor tradeoffs: scatter, resolution, noise, motion 19 (M5): Recorder resolution considerations screen film systems dual-screen file systems resolution/efficiency tradeoff critical angle considerations overall system response 20 (M6): Noise in X-ray projection radiography relative contrast / absolute contrast SNR = absolute contrast / signal std. dev. coefficient of variation SNR = C * sqrt(N) poisson(N) -> binomial thinning(p) -> poisson(Np) effect of recorder spatial resolution statistics for counting detector X SNR of line integral statistics for scintillators general expression for SNR for multiple quantum-limited stages X flouroscopy - viewing by eye X image intensifier scatter - contrast and SNR reduction (brief) 21 (M7): Tomography X Motion tomography (planigraphy) (brief) X PSF for linear motion X tomosynthesis (brief) Computed Tomography X statistical image reconstruction methods projections and line integrals circle and Dirac examples Radon transform properties sinogram Fourier-slice theorem 22 Fourier-slice (Gridding) reconstruction method Backprojection laminogram Backprojection-filtering (BPF) reconstruction method cone filter, DC value, noise PSF when apodized Filtered-backprojection (FBP) reconstruction method derivation zero-padding, ramp filter convolution backprojection formula bandlimited ramp filter Practical backprojection rotation X pixel driven, ray driven, continuous vs discrete 23 [John Seamans CT/PET overview] Sampling: angular and radial quarter-detector offset 24 PSF analysis: spatial resolution effects due to windowing BPF: 2D apodization and Hankel FBP: 1D apodization and 2D effect ultrasound beamforming is like backprojection speed of sound tomography (propagation time) X [course eval.] X X-ray CT practical considerations finite source size scan time - systems object motion fan-beam, cone-beam scatter beam-hardening X bowtie filter dual-energy CT source fluctuations X noise (brief) 25 (M8) Nuclear Imaging overview radiotracers basic physics X single-bore gamma detector Anger camera / photo-multiplier tube SPECT: mechanical collimation PET: electronic collimation Compton scatter imaging ML-EM image reconstruction algorithm statistical / iterative / model-based image reconstruction --------------- below here is from F07. This line will evolve ----------- 26 (missed one lecture due to p41 review trip; only partially made it up)