Patch-based Nonlocal Denoising for MRI and Ultrasound Images
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Transcript of Patch-based Nonlocal Denoising for MRI and Ultrasound Images
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Patch-based Nonlocal Denoising for MRI and Ultrasound Images
Xin Li
Lane Dept. of CSEE
West Virginia University
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Outline• I come to see and be seen• Motivation: nonlocal (symmetry-related) dependency in
medical images• Technical Approach
– Patch-based image modeling and geometric resampling – From locally linear embedding (LLE) to locally linear transform
(LLT) – Nonlocal denoising algorithm
• Experimental results– Synthetic images, Gaussian noise– MRI images, Rician noise– Ultrasound images, speckle noise
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Big Picture: Computational ImagingQuality
Cost
Physical
Examples: SMASH/SENSE for fast MRISuper-resolution in PET imaging
High-dynamic-range (HDR) imaging
Computational
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Motivation: Modeling Human-related Prior
Bilateral symmetry Shape boundary regularity
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Patch-based Image Modeling • To overcome the curse of
dimensionality, we have to work at the middle ground between pixel-level and image-level
• An old concept with renewing interest– Vector quantization is
patch-based, JPEG used 8-by-8 patches (SP community)
– Patch-based recognition (CV community)
– Nonlinear dimensionality reduction (ML community)
P
P
Nonparametric: patch-basedvs.
Parametric: wavelet-based
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Nonlocal Dependency
reflective symmetry translational symmetry
Beyond the reach of any localized models (MRF, wavelet-based, PDE-based)
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Redundant Representation by Geometric Resampling
fliplr(x)x flipud(x) flipud(fliplr(x))
Collection of P-by-P patches
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Exploiting Manifold Constraint
B4
B2
B3
B0
B1
RPP
k
tttw
10 BB
Nonlinear Dimensionality ReductionBy Locally Linear Embedding (LLE) Roweis and Saul, Science’2000
0WD
},...,,1{ 1 kwwdiag W],...,,[ 10 kBBBD
Sparsifying transform
t
Artificial third dimension t records the location information
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Nonlocal Sparse Representation (NSR)
0FD
Approximated solution(3D FFT/DCT)
0WD
Optimal sparsifyingtransform (KLT)
B0 BkB1 Pack into3D Array D 3D-FFT
Thresholding
…
3D-IFFTPack into
3D Array D
B0 BkB1 …^ ^ ^
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NSR Image Denoising Algorithm
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Experimental Results on NSR• Computer-generated toy images, additive
White Gaussian noise– Illustrate the algorithm procedure and verify the
benefit of resampling
• MRI images, Rician noise– Benchmark: PDE-based scheme (total-variation
denoising)
• Ultrasound images, speckle noise– Benchmark: local schemes (SRAD, SBF, PDE)
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Denoising Procedure Illustration by Toy Example
Noisy image Search similar patchesNoisy 3D array
LLT Thresholding
denoised 3D arrayDenoised image denoised patches
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Benefit of Resampling
Translation only
Translation and 1 reflection
Translation and 2 reflections
Translation and 3 reflections
original noisy
NSR (ISNR=17.5dB)GSM (ISNR=13.3dB)
GSM: Gaussian Scalar Mixture in Wavelet space (state-of-the-art denoising scheme)
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MRI Image Denoising
original Noisy (Rician, =30)
PDE scheme NSR scheme
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Ultrasound Despeckling
Field-IISimulation
SBF(local)
11.2ˆ Q
40.2ˆ Q02.2ˆ Q
NSR (nonlocal) 2
ˆˆˆ NSRSBF xxx
Q̂ Ultrasound Despeckling Assessment Index (USDSAI)**Tay, P.C.; Acton, S.T.; Hossack, J.A., “A stochastic approach to ultrasound Despeckling,”ISBI’2006
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Other (Non-medical) Applications of Nonlocal Sparse Representation
original Randomly-sampled(20% data)
RUPScheme*
griddatascheme
EM+NSRscheme
*Candes, E.J.; Romberg, J.; Tao, T., “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency Information,” IEEE Trans. on Infor. Theory, pp. 489- 509, Feb. 2006
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Concluding Remarks
• Symmetry – an important piece of prior information about human subjects
• Patch-based models enable us to better distinguish signal (pattern of interest) from noise using the tool of nonlocal sparsity
• Our experiments have shown the effectiveness of such models in a variety of imaging modalities and noise conditions
• Interest in NIH RFP: Innovations in Biomedical Computational Science and Technology (R01)