Fast iterative magnetic resonance (MR) image reconstruction
with compensation for magnetic field (B0) inhomogeneities
Different tissue types have different magnetic susceptabilities,
and this causes local perturbations
of the magnetic field
in an MR scanner,
particularly near the boundaries between air and soft tissue.
This causes significant local changes in the resonant frequency
of hydrogen spins.
(Rightmost column of images below.)
If ignored,
these field nonuniformities cause distortions
in MR images that are reconstructed
by conventional algorithms
from the raw MR measurements,
particularly
in the brain regions near the nasal cavities.
(Left column of images below.)
There are conventional non-iterative methods
for reconstructing MR images
with partial compensation
for field inhomogeneities,
but they work poorly
in many cases.
(Second column of images below.)
We have developed an iterative algorithm
for reconstructing MR images
that corrects for field inhomogeneities.
(Third column of images below.)
Considerations in the design of this algorithm include
- A statistical model for the noise in MR measurements
- A physical model for the MR measurements.
that includes the effects of field inhomogeneities.
- A cost function that characterizes the image
that "best fits" the data
according to the statistical model.
- An iterative algorithm for minimizing that cost function.
Each iteration of the algorithm
would be very expensive if implemented naively,
since it would require a 2D discrete-space Fourier transform
with nonuniform frequency locations,
since the images below
were acquired with a spiral k-space trajectory.
To reduce computation,
we have developed a nonuniform FFT (NUFFT) method
that is optimal in the minmax sense
of minimizing the worst-case interpolation error.
This gives us very fast computation,
while preserving image accuracy.
First slice
Second slice
Notice the big dark "hole" in the top center
of the head
in the left images,
corresponding
to a region of the head that is a bit higher
than the nasal sinus cavity.
This hole is only partially corrected
by the conventional "conjugate phase" reconstruction method
in the second column.
The third column
is the images formed by PhD student Brad Sutton,
co-advised by Jeff Fessler and Doug Noll,
using a iterative reconstruction method.
This method is described in a paper by Brad Sutton
that has been accepted for publication
in the IEEE Transactions on Medical Imaging.
A
preprint is available here.
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