This document proposes an adaptive noise driven total variation filtering method for denoising magnitude MR images corrupted by Rician noise. It begins with an introduction to MR imaging and Rician noise in magnitude MR images. Existing denoising methods like Gaussian, wavelet and total variation filtering are discussed. The proposed method estimates the noise level using local variances and adapts the regularization parameter in total variation filtering accordingly. Experimental results show the proposed method achieves better denoising performance than non-local means, bilateral and multiscale LMMSE filtering based on mean opinion scores and metrics like MSE and SSIM.

1. Adaptive Noise Driven Total Variation
Filtering for Magnitude MR Image Denosing
Nivitha Varghees. V, M. Sabarimalai Manikandan & Rolant Gini

2. Outline

Introduction
MR
Image Denoising Methods
Proposed
Rician
Total Variation Filtering
Noise Estimation Scheme
Experimental
Conclusion
Results

3. Magnetic Resonance (MR)Imaging
non-invasive medical test that widely used by physicians
to diagnose and treat pathologic conditions
 provide clear and detailed structures of internal organs
and tissues of human body
 MRI to examine the brain, spine, cardiac, abdomen, pelvis,
breast, joints (e.g., knee, wrist, shoulder, and ankle), blood
vessels and other body parts
 MRI scanner uses powerful magnets and radio waves to
create pictures of the body
 The main source of noise in MRI images is the thermal
noise in the patient’s body [Now99].


4. Rician Noise in Magnitude MR Images
The raw MR data generated from a MRI machine are
corrupted by zero-mean Gaussian distributed noise with
equal variance
 In MR reconstruction, the spatial-domain complex MR
data are obtained from the frequency-domain raw MR
data by taking an inverse Fourier transform (IFT)
 For clinical diagnosis and analysis, the magnitude MR
data is constructed by taking the square root of the sum of
the square of the two real and imaginary data.
 The construction of the magnitude MR data transforms
the distribution of Gaussian noise into a Rician
distributed noise


5. Existing Image Denoising Methods
 Linear
models (e.g. Gaussian filter)
 Nonlinear
 DCT
models (e.g. Median filter)
and SVD filters
 Neighborhood
filters
 Non-Local
filters
 Multiscale
LMMSE
 Bilateral
filters
 Wavelet
transforms
 Total
variation (TV) filter

6. Performance of Existing Methods
 Gaussian
filter performs well in the flat regions of
images but do not well preserve the image edges.
 Transform based methods fail to reproduce image
details and often introduce artifacts
 Neighborhood filters may distort fine edges and local
geometries.
 Non-local estimation method over smooth out image
edges.
 Wavelet based hard thresholding scheme introduce
Gibbs oscillation near discontinuities.

7. Formulation of Total Variation Filtering
 Good
edge preserving capability
simultaneously removing noise
E(u) =






2
uz
2
while
 R(u )
: norm of a vector,
z : observed noisy data,
u: desired unknown image to be restored,
λ: regularization parameter,
R (u) : regularization functionals

8. Performance of TV Filtering for
Fixed Value of ʎ
Performance of the total variation filter for different values of regularization parameter
. (a) Original MRI image, (b) Image with Rician noise with σ= 10), (c) Restored image
with ʎ= 10, (d) Restored image with ʎ = 15, (e) Restored image with ʎ = 25, (f)
Restored image with ʎ= 40.

9. Proposed Total Variation Filtering
Noisy Image
Restored Image
ʎ
(a) Traditional TV Filtering Approach
Noisy Image
(ʎ)
Restored Image
(b) Propose Noise Level Driven TV Filtering Approach

10. Rician Distribution of Noisy MRI Data
The Rician probability density function (PDF) of the corrupted
magnitude MR image intensity m is given as
m2  A2  Am 
p(m A,  )  2 e
I 0  2  u (m),
2

2
 
m
where, Io denotes the 0th order modified Bessel
function of the first kind,
 σ2 is the noise variance in the MRI image,
 A is the signal amplitude of the clean image,
 m denotes the MR magnitude variable,
 u (.) is the unit step Heaviside function.


11. Noise Models for Rician Noise Estimation
 For
magnitude MR images with large
background, the Rician distribution is reduced to
a Rayleigh distribution with the probability
density function (PDF):
m2
p(m A,  )  2 e
u (m)
2

2
m


In the bright regions of the MR image where the
SNR is assumed to be large, the Rician
distribution can be approximated using a
Gaussian PDF:

12. Rician Noise Estimation Using Local
Variances

Variance of noise in magnitude MR image is
computed as
 the regularization parameter of TV is adapted based on
the estimated noise standard deviation for a given image

13. Performance of Rician Noise Estimator
36
34
32
estimated noise standard deviation, 
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
noise standnard deviation, n
Estimation of standard deviation of noise using the mode
of the locally estimated variance. • corresponds to the average of the
estimated standard deviations obtained for all test images for each noise
standard deviation.

14. Performance of Rician Noise Estimator

15. Performance of MRI Denoising Methods
(a) Original MR image. (b) MR image with Rician noise with standard
deviation σ= 20. (c) Restored image using proposed adaptive TV filtering
approach. (d) Restored image using the multi-scale LMMSE approach. (e)
Restored image using the non-local filtering approach. (f) Restored image
using the bilateral filtering approach.

16. Performance of MR Image Denoising Methods
σ=10
σ=15
MSE
σ=20
SSIM MOS
MOS
MSE
SSIM
MOS
MSE
SSIM
Noisy
4.3
130.3
0.506
2.3
303.8 0.37
1.3
551.7 0.29
1
874.4
0.24
NLM
4.8
79.6
0.639
4.3
180.1 0.55
3.7
326.9 0.49
3
522.7
0.45
Bilateral
filter
Multiscale
LMMSE
Proposed
Method
4.7
89.98
0.617
3.7
205.4 0.51
2.8
369.1 0.49
2.3
579.4
0.38
5
81.6
0.636
4.7
186.4 0.55
3.2
337.3 0.50
2.2
536.3
0.46
5
80.4
0.639
4.6
180.4 0.55
4.2
324.6 0.49
3.4
513.3
0.44
SSIM: Structural Similarity Measure
MSE: Mean Squared Error
MOS: Mean Opinion Score
MSE
σ=25
SSIM MOS

17. Conclusion





In this work, we studied the effect of regularization parameter
on TV denoising
Here, the regularization parameter is adapted based on the
noise level in magnitude MR images
The noise level is computed using local variances of image
The performance of different denoising algorithms such as
NLM, bilateral, multiscale LMMSE approach, and proposed
method is evaluated in terms subjective test and objective
mertics
Experiments showed that the proposed method provides
significantly better quality of denoised images as compared to
that of the existing methods

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