kspace Data Preprocessing 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.

pitch/frequency 660 Hz 523. 2 Hz pitch/frequency 392 Hz G E C temporal frequency time

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

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

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

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

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

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

convolution – “shift & sum”

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

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

convolution – properties Image Space Upsampling sinc inte rp

Image Space Upsampling image from a phase corrected Propeller blade with ETL=36 and readout length=320. sinc-interpolated up to 64 x 512.

Ringing near the edge of a disc. Solid line for k-space data sampled on 512 x 512; dashed for 128 x 128; dashed-dot on 64 x 64 grid. a p s k o p a ce on i t a diz Reprinted with permission from Handbook of MRI Pulse Sequences. Elsevier, 2004. Tukey window function in k-space PSF in image space.

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

Cartesian sampling suited to sinc-interpolation sinc inte rp

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

nc i j t c e perf l kerne v n o c “fast” l kerne 64 multiply image 256

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

Propeller – Phase Correct one blade CORRECTED RAW

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

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

Fourier Transform Properties shift image phase roll across data b is blade image, r is reference image

max at Dx No correction, with correction shifts in pixels

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

no correction correlation correction only motion correction only full corrections

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 fieldof-view (FOV), essentially stretching the imaging object.

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