Divergence-free wavelet frames

IEEE Signal Processing Letters

Volumn 22, Issue 8, 2015, Pages 1142-1146

  Bostan, Emrah ^a   Unser, Michael ^a   Ward, John Paul ^a  

^a EPFL   (Switzerland)

Author keywords

Denoising; divergence free wavelets; flow MRI; phase contrast MRI; soft thresholding; tight wavelet frames; vector fields; vector wavelets; wavelet denoising

Indexed keywords

DECAY (ORGANIC); FAST FOURIER TRANSFORMS;

DE-NOISING; DIVERGENCE FREE WAVELETS; PHASE CONTRAST MRI; SOFT THRESHOLDING; TIGHT WAVELET FRAMES; VECTOR FIELDS; WAVELET DENOISING;

WAVELET ANALYSIS;

EID: 84921497868     PISSN: 10709908     EISSN: None     Source Type: Journal    
DOI: 10.1109/LSP.2015.2388794     Document Type: Article

References (20)

1. X. Zhou and Y. He, "Using divergence free wavelets for the numerical solution of the 2-D stationary Navier-Stokes equations," Appl. Math. Comput., vol. 163, no. 2, pp. 593-607, 2005.
2. K. Urban, Wavelets in Numerical Simulation: Problem Adapted Construction and Applications. Berlin, Germany: Springer, 2002, vol. 22.
3. M. Markl, A. Frydrychowicz, S. Kozerke, M. Hope, and O. Wieben, "4D flow MRI," J. Magn. Reson. Imag., vol. 36, no. 5, pp. 1015-1036, Nov. 2012.
4. E. Bostan, O. Vardoulis, D. Piccini, P. D. Tafti, N. Stergiopulos, and M. Unser, "Spatio-temporal regularization of flow-fields," in Proc. IEEE Int. Symp. Biomed. Imaging, Apr. 7-11, 2013, pp. 836-839.
5. F. Ong, M. Uecker, U. Tariq, A. Hsiao, M. T. Alley, S. S. Vasanawala, and M. Lustig, "Robust 4D flow denoising using divergence-free wavelet transform," Magn. Reson. Med., 2014, to be published.
6. D. Schiavazzi, F. Coletti, G. Iaccarino, and J. K. Eaton, "A matching pursuit approach to solenoidal filtering of three-dimensional velocity measurements," J. Comput. Phys., vol. 263, pp. 206-221, 2014.
7. G. Battle and P. Federbush, "Divergence-free vector wavelets," Michigan Math. J., vol. 40, no. 1, pp. 181-195, 1993.
8. P. G. Lemarie-Rieusset, "Analysesmulti-résolutions non orthogonales, commutation entre projecteurs et dérivation et ondelettes vecteurs á divergence nulle," Rev. Mat. Iberoamer., vol. 8, no. 2, pp. 221-237, 1992.
9. E. Deriaz and V. Perrier, "Divergence-free and curl-free wavelets in two dimensions and three dimensions: Application to turbulent flows," J. Turbulence, vol. 7, no. 3, pp. 1-37, 2006.
10. R. Stevenson, "Divergence-free wavelet bases on the hypercube: Freeslip boundary conditions, and applications for solving the instationary Stokes equations," Math. Comput., vol. 80, no. 275, pp. 1499-1523, 2011.
11. S. Kadri-Harouna and V. Perrier, "Effective construction of divergence- free wavelets on the square," J. Comput. Appl. Math., vol. 240, pp. 74-86, 2013.
12. K. Urban, "On divergence-free wavelets," Adv. Comput. Math., vol. 4, no. 1, pp. 51-81, 1995.
13. A. J. Majda and A. L. Bertozzi, Vorticity and Incompressible Flow. Cambridge, U.K.: Cambridge Univ. Press, 2002, vol. 27.
14. O. Christensen, An Introduction to Frames and Riesz Bases. Boston, MA, USA: Birkhäuser, 2003.
15. J. P.Ward, K. N. Chaudhury, andM. Unser, "Decay properties of Riesz transforms and steerable wavelets," SIAM J. Imag. Sci., vol. 6, no. 2, pp. 984-998, 2013.
16. J. P. Ward and M. Unser, "Harmonic singular integrals and steerable wavelets in ," Appl. Comput. Harmon. Anal., vol. 36, no. 2, pp. 183-197, 2014.
17. S. Held, M. Storath, P. Massopust, and B. Forster, "Steerable wavelet frames based on the Riesz transform," IEEE Trans. Image Process., vol. 19, no. 3, pp. 653-667, 2010.
18. M. Unser, N. Chenouard, and D. V. D. Ville, "Steerable pyramids and tight wavelet frames in ," IEEE Trans. Image Process., vol. 20, no. 10, p. 2705, Oct. 2011.
19. D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation by wavelet shrinkage," Biometrika, vol. 81, no. 3, pp. 425-455, 1994.
20. J. Ahrens, B. Geveci, and C. Law, "Paraview: An end-user tool for largedata visualization," The VisualizationHandbook, pp. 717-732, 2005.