Adaptive Noise Driven Total Variation Filtering for Magnitude MR Image Denosing

Nivitha Varghees. V, M. Sabarimalai Manikandan & Rolant Gini

Outline

Introduction

MR Image Denoising Methods

Proposed Total Variation Filtering

Rician Noise Estimation Scheme

Experimental Results

Conclusion

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].

Magnetic Resonance (MR)Imaging

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

Rician Noise in Magnitude MR Images

Linear models (e.g. Gaussian filter)

Nonlinear models (e.g. Median filter)

DCT and SVD filters

Neighborhood filters

Non-Local filters

Multiscale LMMSE

Bilateral filters

Wavelet transforms

Total variation (TV) filter

Existing Image Denoising 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.

Performance of Existing Methods

2E(u) = ( )

2u z R u

: norm of a vector,

z : observed noisy data,

u: desired unknown image to be restored,

λ: regularization parameter,

R (u) : regularization functionals

Formulation of Total Variation Filtering

Good edge preserving capability while simultaneously removing noise

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.

Performance of TV Filtering for Fixed Value of ʎ

Proposed Total Variation Filtering

Noisy Image Restored Image (ʎ)

Noisy Image Restored Image

ʎ

(a) Traditional TV Filtering Approach

(b) Propose Noise Level Driven TV Filtering Approach

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.

Rician Distribution of Noisy MRI Data

The Rician probability density function (PDF) of the corrupted magnitude MR image intensity m is given as

2 2

02 2 2( , ) ( ),

2

m m A Amp m A e I u m

For magnitude MR images with large background, the Rician distribution is reduced to a Rayleigh distribution with the probability density function (PDF):

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:

2

2 2( , ) ( )

2

m mp m A e u m

Noise Models for Rician Noise Estimation

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

Rician Noise Estimation Using Local Variances

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 360

2

4

6

8

10

12

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18

20

22

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26

28

30

32

34

36

noise standnard deviation, n

est

ima

ted

no

ise

sta

nd

ard

de

via

tion

,

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.

Performance of Rician Noise Estimator

Performance of Rician Noise Estimator

(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.

Performance of MRI Denoising Methods

σ=10 σ=15 σ=20 σ=25

MOS MSE SSIM MOS MSE SSIM 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

4.7 89.98 0.617 3.7 205.4 0.51 2.8 369.1 0.49 2.3 579.4 0.38

Multiscale LMMSE

5 81.6 0.636 4.7 186.4 0.55 3.2 337.3 0.50 2.2 536.3 0.46

Proposed Method

5 80.4 0.639 4.6 180.4 0.55 4.2 324.6 0.49 3.4 513.3 0.44

Performance of MR Image Denoising Methods

SSIM: Structural Similarity Measure

MSE: Mean Squared Error

MOS: Mean Opinion Score

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

Conclusion

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References

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References