Adaptive noise driven total variation filtering for magnitude mr image denosing
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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.
![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].
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Adaptive noise driven total variation filtering for magnitude mr image denosing
- 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 uz 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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