Second order total generalized variation (TGV) for MRI

Magnetic Resonance in Medicine

Volumn 65, Issue 2, 2011, Pages 480-491

  Knoll, Florian ^a   Bredies, Kristian ^b   Pock, Thomas ^a   Stollberger, Rudolf ^a  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF GRAZ   (Austria)

Author keywords

accelerated imaging; constrained reconstruction; denoising; radial sampling; total generalized variation

Indexed keywords

IMAGE ENHANCEMENT; IMAGE RECONSTRUCTION; MAGNETIC RESONANCE IMAGING; MAGNETISM; RESONANCE;

CONSTRAINED RECONSTRUCTION; DE-NOISING; GENERALIZED VARIATION; IN-VIVO MEASUREMENT; MATHEMATICAL FRAMEWORKS; PIECE-WISE CONSTANTS; RADIAL SAMPLING; TOTAL VARIATION;

IMAGE DENOISING;

CONTRAST MEDIUM;

ARTICLE; ARTIFACT; BRAIN; CONTROLLED STUDY; HUMAN; IMAGE DENOISING; IMAGE PROCESSING; IMAGE QUALITY; IMAGE RECONSTRUCTION; IN VIVO STUDY; MALE; MATHEMATICS; NORMAL HUMAN; NUCLEAR MAGNETIC RESONANCE IMAGING; PROSTATE; RETROSPECTIVE STUDY; SIGNAL NOISE RATIO; SIMULATION; TOTAL GENERALIZED VARIATION; TOTAL VARIATION;

EID: 79251548920     PISSN: 07403194     EISSN: 15222594     Source Type: Journal    
DOI: 10.1002/mrm.22595     Document Type: Article

References (25)

1. Rudin LI, Osher S, Fatemi E,. Nonlinear total variation based noise removal algorithms. Phys D 1992; 60: 259-268.
2. Liu B, King K, Steckner M, Xie J, Sheng J, Ying L,. Regularized sensitivity encoding (SENSE) reconstruction using Bregman iterations. Magn Reson Med 2009; 61: 145-152.
3. Wald MJ, Adluru G, Song HK, Wehrli FW,. Accelerated high-resolution imaging of trabecular bone using total variation constrained reconstruction. In: Proceedings of the 17th Scientific Meeting and Exhibition of ISMRM, Honolulu, HI. 2009.
4. Block KT, Uecker M, Frahm J,. Suppression of MRI truncation artifacts using total variation constrained data extrapolation. In: Proceedings of the 16th Scientific Meeting and Exhibition of ISMRM, Toronto, Canada. 2008.
5. Huang F, Chen Y, Duensing GR, Akao J, Rubin A, Saylor C,. Application of partial differential equation-based inpainting on sensitivity maps. Magn Reson Med 2005; 53: 388-397.
6. Lustig M, Donoho D, Pauly JM,. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn Reson Med 2007; 58: 1182-1195.
7. Block KT, Uecker M, Frahm J,. Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint. Magn Reson Med 2007; 57: 1086-1098.
8. Block T,. Advanced methods for radial data sampling in MRI. Ph.D. thesis, Georg-August-Universitaet Goettingen, 2008.
9. Bredies K, Kunisch K, Pock T,. Total generalized variation. SIAM J Imaging Sci 2010; 3: 492-526.
10. Candes EJ, Romberg J, Tao T,. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inform Theory 2006; 52: 489-509.
11. Donoho DL,. Compressed sensing. IEEE Trans Inform Theory 2006; 52: 1289-1306.
12. Lustig M, Donoho DL, Santos JM, Pauly JM,. Compressed sensing MRI. IEEE Signal Process Magazine 2008; 25: 72-82.
13. Nesterov Y,. Smooth minimization of nonsmooth functions. Math Programming Series A 2005; 103: 127-152.
14. Nemirovski, A., Prox-method with rate of convergence O(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM J Optim 2004; 15: 229-251.
15. Pock T, Cremers D, Bischof H, Chambolle A,. An Algorithm for Minimizing the Mumford-Shah Functional. In: International Conference on Computer Vision (ICCV), Kyoto, Japan; 2009.
16. Chambolle A, Pock T,. A first-order primal-dual algorithm for convex problems with applications to imaging. Technical report, Institute for Computer Graphics and Vision, Graz University of Technology, 2010.
17. Merwa R, Reishofer G, Feiweier T, Kapp K, Ebner F, Stollberger R,. Improved quantification of pharmacokinetic parameters at 3 Tesla considering B1 inhomogeneities. In: Proceedings of the 17th Scientific Meeting and Exhibition of ISMRM, Honolulu, HI. 2009; p 4363.
18. Pruessmann KP, Weiger M, Börnert P, Boesiger P,. Advances in sensitivity encoding with arbitrary k-space trajectories. Magn Reson Med 2001; 46: 638-651.
19. Bernstein MA, King KF, Zhou XJ,. Handbook of MRI Pulse Sequences. Academic Press; 2004.
20. Fessler JA, Sutton BP,. Nonuniform fast Fourier transforms using min-max interpolation. IEEE Trans Signal Process 2003; 51: 560-574.
21. NVIDIA. NVIDIA CUDA Programming Guide 2.0. NVIDIA Cooperation; 2008.
22. Engl HW, Hanke M, Neubauer A,. Regularization of inverse problems, Vol. 375: Mathematics and its applications, Dordrecht: Kluwer Academic Publishers Group; 1996.
23. Morozov VA,. On the solution of functional equations by the method of regularization. Soviet Math Dokl 1966; 7: 414-417.
24. Knoll F, Unger M, Diwoky C, Clason C, Pock T, Stollberger R,. Fast reduction of undersampling artifacts in radial MR angiography with 3D total variation on graphics hardware. MAGMA 2010; 23: 103-114.
25. Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A,. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med 2002; 47: 1202-1210.