A fast algorithm for denoising magnitude diffusion-weighted images with rank and edge constraints.
OBJECTIVE
To accelerate denoising of magnitude diffusion-weighted images subject to joint rank and edge constraints.


METHODS
We extend a previously proposed majorize-minimize method for statistical estimation that involves noncentral χ distributions to incorporate joint rank and edge constraints. A new algorithm is derived which decomposes the constrained noncentral χ denoising problem into a series of constrained Gaussian denoising problems each of which is then solved using an efficient alternating minimization scheme.


RESULTS
The performance of the proposed algorithm has been evaluated using both simulated and experimental data. Results from simulations based on ex vivo data show that the new algorithm achieves about a factor of 10 speed up over the original Quasi-Newton-based algorithm. This improvement in computational efficiency enabled denoising of large datasets containing many diffusion-encoding directions. The denoising performance of the new efficient algorithm is found to be comparable to or even better than that of the original slow algorithm. For an in vivo high-resolution Q-ball acquisition, comparison of fiber tracking results around hippocampus region before and after denoising will also be shown to demonstrate the denoising effects of the new algorithm.


CONCLUSIONS
The optimization problem associated with denoising noncentral χ distributed diffusion-weighted images subject to joint rank and edge constraints can be solved efficiently using a majorize-minimize-based algorithm.
Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA.|Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA.
Fan
F
Lam
Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA.|Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA.
Ding
D
Liu
Center for Vital Longevity, University of Texas at Dallas, Dallas, Texas, USA.
Zhuang
Z
Song
Department of Radiology and Biomedical Imaging, University of California, San Francisco, California, USA.|Department of Veterans Affairs Medical Center, Center for Imaging of Neurodegenerative Diseases, San Francisco, California, USA.
Norbert
N
Schuff
Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA.|Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA.
Zhi-Pei
ZP
Liang
D000465:Algorithms; D000818:Animals; D016477:Artifacts; D001921:Brain / Q000033:anatomy & histology*; D003198:Computer Simulation; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods; D021621:Imaging, Three-Dimensional / Q000379:methods*; D066298:In Vitro Techniques; D015233:Models, Statistical; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D059629:Signal-To-Noise Ratio; D013552:Swine
diffusion imaging; edge constraint; magnitude image denoising; majorize-minimize algorithm; noncentral χ distribution; rank constraint