Download Magnetic Resonance Imaging: Coil Sensitivity Estimation Michael

Magnetic Resonance Imaging:
Coil Sensitivity Estimation
Michael Allison
9/9/11
Fessler Medical Imaging Group
●
Focus on image reconstruction, registration, and some
analysis.
Magnetic Resonance
(MR)
Computed Tomography
(CT)
Positron Emission Tomography
(PET)
Security
*Source images from Wikipedia.org.
Fessler Medical Imaging Group
●
Focus on image reconstruction, registration, and some
analysis.
Magnetic Resonance
(MR)
Computed Tomography
(CT)
Positron Emission Tomography
(PET)
Security
*Source images from Wikipedia.org.
MRI Basics
●
●
Use strong magnetization to cause hydrogen atoms
(dipoles) to spin.
Spinning atoms induce a current in a wire coil – this is our
signal.
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Collect signal over time to get our data.
●
MR image is simply the inverse DFT of the data.
COIL
*Source images from Westbrook, MRI in Practice, 2005.
SIGNAL
MRI Coils
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Two types of receive coils:
Patient goes inside coil.
●Near uniform sensitivity.
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Placed onto patient.
●Spatially varying sensitivity.
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Why use surface coils?
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●
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Higher signal for nearby tissue (higher SNR).
Use multiple surface coils to accelerate MR
image acquisition (e.g., SENSE imaging [1]).
In both cases you require the coil sensitivity.
[1] Pruessmann et al., SENSE: sensitivity encoding for fast MRI, MRM, 1999.
Coil Sensitivity Estimation
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Reconstruct a body coil (y) and surface coil (z) image
using iFFT.
Model the images as:
sensitivity
●
magnetization
IID Gaussian errors
Ratio is the obvious estimate:
number of pixels
Coil Sensitivity Estimation
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Ratio estimate is corrupted:
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But, sensitivities are smooth.
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Use a statistical approach (e.g., [1,2]):
regularization parameter
diag{y} binary mask
finite
differencing
matrix
[1] Keeling et al., Appl. Math Comput., 159, 2004. [2] Huang et al., MRM, 53, 2005.
Coil Sensitivity Estimation
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Solving estimate is computationally difficult for
large images due to of size of R.
Use iterative methods:
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Conjugate gradient is also slow due to large
number of pixels.
We propose a new iterative method based on
augmented Lagrangian (AL) principles [1].
[1] Ramani et al., IEEE TMI, 30, 2011.
Augmented Lagrangian Estimate
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Introduce two new variables, u0,1, to get the equivalent:
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Resulting AL algorithm is:
Lagrange parameters
Lagrange multipliers
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Use alternating minimization to find estimate (see [1]).
[1] Allison et al., ISMRM, 2011.
Experiment
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Evaluate on breast phantom data (384x96 pixels):
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Resulting estimate (λ = 26, R is second order):
Convergence Plots
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Comparison of convergence speed versus CG
with diagonal preconditioner.
Thank You.