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

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

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

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

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

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

8. high-order interp overshootslow-order interp smoothsnaive k-space griddingcorrected for gridding errors linear interpolation = convolve w/“tent” function “gridding” = convolve w/kernel (typically smooth, w/small support)

9. convolution – “shift & sum”

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

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

12. sinc interp convolution – properties Image Space Upsampling

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

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

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

16. sinc interp Cartesian sampling suited to sinc-interpolation

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

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

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

20. RAW Propeller – Phase Correct one blade CORRECTED

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

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

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

24. max at  x No correction, with correction shifts in pixels

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

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

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 ‘  ’