Rician Noise Removal in Diffusion Tensor MRI

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Rician Noise Removal in Diffusion Tensor MRI

• Saurav Basu, Tom Fletcher, Ross Whitaker
• School of Computing
• University of Utah

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Why DT-MRI filtering?

• DT-MRI plagued by low SNR
• Multiple scans needed to increase SNR
• Issues long acquisition time, patient comfort
  system throughput
• Noise in DT-MRI adversely affects tensor
  measurements used in clinical studies

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Rician noise in DT-MRI

• DW images are magnitudes of complex valued
  signals.
• If the real and imaginary components of the
  signal are assumed to have a Gaussian noise, the
  resulting magnitude image will have Rician
  distributed noise.

gaussian
magnitude
where is zero mean, stationary Gaussian
noise with standard deviation
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Rician Noise
A signal is said to be corrupted with Rician
noise if the pdf of the noisy signal has a Rice
distribution
Unlike the normal distribution the pdf is not
symmetric about the true signal value A
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p(x)
A
Rice Distribution
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How does Rician noise affect estimated tensors?
We performed Monte Carlo simulations with two
cases
Tensor splitting gradient direction
Tensor aligned with gradient direction
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Previous filtering approaches
2 categories
Tensor Space
DWI space
Anisotropic Diffusion Parker(2000)
Riemannian Space filtering Pennec (2004)
Bayesian regularization using Gaussian markov
random fields. Martin (2004)
Constrained Variational approach Wang, Vemuri
(2004)
Very effective techniques, but do not explicitly
handling Rician noise as part of the filtering
process.
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Rician Bias Correction Filter

• Based on maximum a posteriori (MAP) approach to
  image reconstruction
• In statistics MAP estimation is used to obtain a
  point estimate of an unobserved quantity based on
  empirical data

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• Given an initial noisy image u0 we want to
  estimate the clean image u.
• We know that p(u0u) has a Rician distribution.
• To estimate the clean value we want to maximize
  p(uu0)

From Bayes Rule
constant for a given noisy image u0
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maximize with gradient ascent
noise model (likelihood )
prior
posterior
prior what is pdf of the unobserved data
(clean image) which we are trying to estimate?
noise model (likelihood) what is the
conditional probability of the observed data(
noisy image) , given a particular value of the
unobserved data (clean image)?
posterior The probability of the unobserved
data (clean image) given the observed data (noisy
image)
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Rician likelihood term
Using the Rician pdf for the noise model we get
rician likelihood term
Taking derivative w.r.t. u,
Rician attachment Term
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Combining with the prior
The Rician attachment term can be combined with
any image prior. We use a Gibbs prior with
Perona Malik Energy functional.
edge preserving smoothing prior
Gibbs prior
Perona Malik energy
weighing factor
conductance
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Combining the Rician correction term with prior
we get the update equation for the filtered image
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Preliminary Results
We compared 4 different filtering methods on both
synthetic and real datasets
DWI Space
Tensor Space

• Anisotropic Diffusion without Rician attachment
• 2. Rician Bias Correction filter

1. Anisotropic Diffusion in Euclidean space
2. Anisotropic Diffusion on the Riemannian manifold

• Error Metrics
• RMS error in tensor components
• Fractional Anisotropy
• Trace

• Parameters optimized for RMS error in tensor
  components.
• For both synthetic and real data we used 7 images
  for each slice (6 gradient directions 1
  baseline)

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Synthetic Data Results

• 10x10x4 volume of tensors
• 2 tensor orientations (along gradient and
  splitting the gradient directions)
• Synthetic rician noise

Clean
Noisy (SNR15)
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DWI Space Filters
Rician DWI
Aniso DWI
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Tensor Space Filters
Riemannian
Euclidean
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Real Data Results
Issue No ground truth data available for DT-MRI
!
How do we evaluate filtering performance
quantitatively?
Solution

• we developed a method to estimate a ground truth
  data from repeated scans of the same object
• if xi is a set of intensities for the same
  voxel in N repeated scans we find the ML estimate
  of the true value A by maximizing the log
  likelihood function

p(xA) is the Rician pdf
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• Generated ground truth from 5 scans
• added known Rician noise (SNR10,15,20)
• compared errors as before

Clean Coronal Slice
Noisy Coronal Slice(SNR15)
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DWI Space
Rician DWI
Aniso DWI
Both Aniso-DWI and Rician DWI gave very good
results with Rician being marginally better
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Tensor Space
Riemannian Tensor
Euclidean Tensor
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