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

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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.
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pitch/frequency
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log of k-space magnitude data.
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Heisenberg, Riemann Lebesgue
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Cartesian sampling reconstruct directly with
Fast Fourier Transform (FFT)
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non-Cartesian sampling requires gridding ?
additional errors
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CT vs. MRI
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high-order interp overshoots
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convolution shift sum


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convolution properties
Avoid Aliasing Artifacts

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Avoid Aliasing Artifacts Propeller k-space data
interpolated onto 4x fine grid
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convolution properties
Image Space Upsampling


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Image Space Upsampling
sinc-interpolated up to 64x512.
image from a phase corrected Propeller blade with
ETL36 and readout length320.
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Ringing near the edge of a disc. Solid line for
k-space data sampled on 512x512 dashed for
128x128 dashed-dot on 64x64 grid.
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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
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Cartesian sampling suited to sinc-interpolation
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Radial sampling (PR, spiral, Propeller) suited
to jinc-interpolation
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perfect jinc kernel
fast conv kernel
64
256
multiply image
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Propeller Phase Correct
Redundant data must agree, remove phase from each
blade image
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Propeller Phase Correct one blade

RAW
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Propeller - Motion Correct
2 scans sans motion

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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
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Fourier Transform Properties
shift image ?? phase roll across data


b is blade image, r is reference image
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max at Dx
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Fourier Transform Properties
rotate image?rotate data
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no correction
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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.
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Backup Slides
Propeller blades sample at points denoted with
o and are upsampled via sinc interpolation to
the points denoted with ?