Patch-based Nonlocal Denoising for MRI and Ultrasound Images

1. Patch-based Nonlocal Denoising for MRI and Ultrasound Images Xin Li Lane Dept. of CSEE West Virginia University

2. 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

3. Computational Physical Big Picture: Computational Imaging Quality Examples: SMASH/SENSE for fast MRI Super-resolution in PET imaging High-dynamic-range (HDR) imaging Cost

4. Motivation: Modeling Human-related Prior Bilateral symmetry Shape boundary regularity

5. 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-based vs. Parametric: wavelet-based

6. Nonlocal Dependency translational symmetry reflective symmetry Beyond the reach of any localized models (MRF, wavelet-based, PDE-based)

7. Redundant Representation by Geometric Resampling x fliplr(x) flipud(x) flipud(fliplr(x)) Collection of P-by-P patches

8. Exploiting Manifold Constraint RPP B1 B3 B2 B0 B4 t Sparsifying transform Artificial third dimension t records the location information Nonlinear Dimensionality Reduction By Locally Linear Embedding (LLE) Roweis and Saul, Science’2000

9. Nonlocal Sparse Representation (NSR) Optimal sparsifying transform (KLT) Approximated solution (3D FFT/DCT) B0 B1 Bk … Pack into 3D Array D 3D-FFT Thresholding ^ ^ ^ B0 B1 Bk … Pack into 3D Array D 3D-IFFT

10. NSR Image Denoising Algorithm

11. 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)

12. Denoising Procedure Illustration by Toy Example Noisy 3D array Search similar patches Noisy image LLT Thresholding denoised 3D array Denoised image denoised patches

13. Benefit of Resampling Translation and 3 reflections Translation and 2 reflections noisy original Translation and 1 reflection Translation only GSM (ISNR=13.3dB) NSR (ISNR=17.5dB) GSM: Gaussian Scalar Mixture in Wavelet space (state-of-the-art denoising scheme)

14. MRI Image Denoising Noisy (Rician, =30) original NSR scheme PDE scheme

15. Ultrasound Despeckling SBF(local) Field-II Simulation NSR (nonlocal) Ultrasound Despeckling Assessment Index (USDSAI)* *Tay, P.C.; Acton, S.T.; Hossack, J.A., “A stochastic approach to ultrasound Despeckling,”ISBI’2006

16. Other (Non-medical) Applications of Nonlocal Sparse Representation original Randomly -sampled (20% data) RUP Scheme* griddata scheme EM+NSR scheme *Candes, E.J.; Romberg, J.; Tao, T., “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency Information,” IEEE Trans. onInfor. Theory, pp. 489- 509, Feb. 2006

17. 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)