Applications of Filtering Concepts Applied to Other MRI Methods

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There are other kinds of filtering that go on that you can model the effects of, and that might be useful
One to obviously keep in mind is filtering due to signal decay, find that using a FWHM definition of resolution have for a SE, for example, that

$\displaystyle \mbox{FWHM}_{SE}$ $\textstyle =$ $\displaystyle \mbox{FWHM}_{SE,T_{2}} + \mbox{FWHM}_{SE,T_{2}'}$

$\textstyle =$ $\displaystyle \frac{\sqrt{3}}{\pi}\Delta x\left(\frac{T_s}{T_2}\right)+ \frac{\Delta x}{\pi}\left(\frac{T_s}{T_2^\prime}\right)$ (13.16)
Also have a section in the book where we use filter concepts to describe the effect of zero-padded interpolation.
- Saw that Gibbs looks better at larger matrix sizes, even without filtering
- This is true, even if don't have any data, but only reconstruct at a larger matrix size.
- get prettier images, even though no gain in real resolution is obtained.
- Also show that this is equivalent to -space shifting data with linear phase to get -space shifted intermediate pixels.
Can also consider partial Fourier imaging from a filtering standpoint.
- What is reconstructed image when less than all of data is sampled, or data is sampled asymmetrically.

Next: MID-TERM NOTES Up: Gibbs Ringing and Filters Previous: Gibbs Ringing and Filters Contents

Michael Thompson 2003-11-21

$\displaystyle \mbox{FWHM}_{SE}$	$\textstyle =$	$\displaystyle \mbox{FWHM}_{SE,T_{2}} + \mbox{FWHM}_{SE,T_{2}'}$
	$\textstyle =$	$\displaystyle \frac{\sqrt{3}}{\pi}\Delta x\left(\frac{T_s}{T_2}\right)+ \frac{\Delta x}{\pi}\left(\frac{T_s}{T_2^\prime}\right)$	(13.16)