1. Institute of Medical Engineering 1 20th Annual International Conference on Magnetic Resonance Angiography Graz, 15-18.10.2008 Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware F. Knoll 1, M. Unger 2, F. Ebner 3, R. Stollberger 1 1 Institute of Medical Engineering, TU Graz, Austria 2 Institute for Computer Graphics and Vision, TU Graz, Austria, 3 Department of Radiology, Medical University Graz

2. 2 MRA - Club 08 Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware Introduction Total Variation constrained reconstruction methods effectively reduce streaking artifacts from undersampled radial data sets [1]. Iteratively solve a constrained optimization problem. Main Drawback: Computationally expensive → not suitable for daily clinical practice. [1] Block et al., MRM 57: 1086-1098 (2007)

3. 3 MRA - Club 08 Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware GPU Computing Make use of the massive parallelism of GPU architectures! Nvidia GForce GTX 280 240 Processor Cores CUDA (Compute Unified Device Architecture): C type programming access to GPU → Cheap, pocket sized supercomputer How to solve TV optimization problems?

4. 4 MRA - Club 08 Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware Total Variation [2] u…Reconstructed Images f…Original images with artifacts λ...Regularization parameter Ω…Image Domain [2] Rudin et al. Phys. D, 60(1-4) 259-268, 1992 → A parallelized formulation is needed for efficient GPU implementation.

5. 5 MRA - Club 08 Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware GPU Implementation Solve the associated dual Euler Lagrange Equations for each pixel in the 3D data set (Chambolle’s Algorithm) [3]. Parallization: A PDE for each pixel. Start an individual thread on the GPU for each calculation. [3] Pock et al., CVGPU Workshop CVPR 2008

6. 6 MRA - Club 08 Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware Results: 80 projections TR=3.74ms TE=1.48ms FA=20° Matrix size (x,y,z) = 448x352x40 Retrospective subsampling in x-y- plane 80 radial projections Δt = 12s CE dataset of the carotid arteries: a)Conventional Regridding Reconstruction b)Reconstruction with TV constraint

7. 7 MRA - Club 08 Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware Results: 40 projections TR=3.74ms TE=1.48ms FA=20° Matrix size (x,y,z) = 448x352x40 Retrospective subsampling in x-y- plane 40 radial projections Δt = 6s CE dataset of the carotid arteries: a)Conventional Regridding Reconstruction b)Reconstruction with TV constraint

8. 8 MRA - Club 08 Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware Reconstruction Time Implementation typeReconstruction time: 448x352x40 Dataset Performance (Iterations/s) CPU version9 min0.18 CUDA, Nvidia GTX 2800.24 s414 Speedup of 2300! GPU reconstruction times allow real time imaging.

9. 9 MRA - Club 08 Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware Conclusion Radial undersampling provides data sets with high temporal resolution. 3D ROF Total Variation efficiently removes streaking artifacts, while preserving blood vessels in MRA. The GPU implementation facilitates image reconstruction times that are far below the corresponding acquisition times. We believe that this may pave the way for these reconstruction strategies, currently promising research topics, to become powerful tools in daily clinical practice. www.gpu4vision.org Data fidelity term in image space limits the algorithm to special applications. k-space data fidelity term is WIP.

10. 10 MRA - Club 08 Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware Demonstration Acknowledgements: This work was funded by Austrian Science Fund (FWF) project F32 SFB : „Mathematical Optimization and Applications in Biomedical Sciences”