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k-space Data Pre-processing for Artifact Reduction in MRI

k-space Data Pre-processing for Artifact Reduction in MRI. SK Patch UW-Milwaukee. thanks KF King, L Estkowski, S Rand for comments on presentation A Gaddipatti and M Hartley for collaboration on Propeller productization. . 660Hz. 392Hz. G. E. C. 523.2Hz. pitch/frequency.

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k-space Data Pre-processing for Artifact Reduction in MRI

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  1. k-space Data Pre-processing for Artifact Reduction in MRI SK Patch UW-Milwaukee thanks KF King, L Estkowski, S Rand for comments on presentation A Gaddipatti and M Hartley for collaboration on Propeller productization.

  2. 660Hz 392Hz G E C 523.2Hz pitch/frequency temporal frequency time pitch/frequency

  3. apodized reconstructed image. checkerboard pattern  strong k-space signal along axes log of k-space magnitude data.

  4. Heisenberg Functions cannot be space- and band-limited. implies Riemann-Lebesgue k-space data decays with frequency Heisenberg, Riemann & Lebesgue

  5. Ringing near the edge of a disc. Solid line for k-space data sampled on 512x512; dashed for 128x128; dashed-dot on 64x64 grid. Cartesian sampling reconstruct directly with Fast Fourier Transform (FFT)

  6. spirals – fast acquisition From Handbook of MRI Pulse Sequences. Propeller – redundant data permits motion correction. non-Cartesian sampling requires gridding  additional errors

  7. CT errors high-frequency & localized MR errors low-frequency & global CT vs. MRI

  8. linear interpolation = convolve w/“tent” function “gridding” = convolve w/kernel (typically smooth, w/small support) naive k-space gridding low-order interp smooths corrected for gridding errors high-order interp overshoots

  9. convolution – “shift & sum”

  10. sinc interp in k-space 2x Field-of-View convolution – properties Avoid Aliasing Artifacts

  11. Avoid Aliasing Artifacts Propeller k-space data interpolated onto 4x fine grid

  12. sinc interp convolution – properties Image Space Upsampling

  13. Image Space Upsampling sinc-interpolated up to 64x512. image from a phase corrected Propeller blade with ETL=36 and readout length=320.

  14. k-space apodization Reprinted with permission from Handbook of MRI Pulse Sequences. Elsevier, 2004. PSF in image space. Tukey window function in k-space Ringing near the edge of a disc. Solid line for k-space data sampled on 512x512; dashed for 128x128; dashed-dot on 64x64 grid.

  15. high-order interp overshoots w/o gridding deconvolution after gridding deconv cubic interp cubic interp linear interp linear interp no interpolation no shading k-space data sampled at ‘X’s and linearly interpolated onto ‘’s. Low-frequency Gridding Errors no interpolation-no shading; interpolation onto Dk/4 lattice  4xFOV linear interpolation “tent” function against which k-space data is convolved

  16. sinc interp Cartesian sampling suited to sinc-interpolation

  17. Radial sampling (PR, spiral, Propeller) suited to jinc-interpolation

  18. perfect jinc kernel “fast” conv kernel 64 256 multiply image

  19. Propeller – Phase Correct Redundant data must agree, remove phase from each blade image

  20. CORRECTED Propeller – Phase Correct one blade RAW

  21. w/motion correction artifacts due to blade #1 errors sans motion correction Propeller - Motion Correct 2 scans – sans motion

  22. blade #1 Propeller – Blade Correlation throw out bad – or difficult to interpret - data Propeller – Blade Correlation throw out bad – or difficult to interpolate - data blade weights rotations in degrees 1 blade # 23 shifts in pixels

  23. Fourier Transform Properties shift image  phase roll across data b is blade image, r is reference image

  24. No correction, with correction shifts in pixels max at Dx

  25. “holes” in k-space Fourier Transform Properties rotate imagerotate data

  26. correlation correction only motion correction only full corrections no correction

  27. Backup Slides Simulations show Cartesian acquisitions are robust to field inhomogeneity. (top left) Field inhomogeneity translates and distorts k-space sampling more coherently than in spiral scans. (top right) magnitude image suffers fewer artifacts than spiral, despite (bottom left) severe phase roll. (bottom right) Image distortion displayed in difference image between magnitude images with and without field inhomogeneity. k-space stretching decreases the field-of-view (FOV), essentially stretching the imaging object.

  28. Backup Slides Propeller blades sample at points denoted with ‘o’ and are upsampled via sinc interpolation to the points denoted with ‘’

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