The fractional Fourier transform and quadratic field magnetic resonance imaging

Computers and Mathematics with Applications

Volumn 62, Issue 3, 2011, Pages 1576-1590

  Irarrazaval, Pablo ^a,b   Lizama, Carlos ^c   Parot, Vicente ^a,b   Sing Long, Carlos ^a,b   Tejos, Cristian ^a,b  

^a PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

^b Biomedical Imaging Center   (Chile)

^c UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

Author keywords

Fractional Fourier transform; Magnetic resonance imaging; Periodic strongly continuous semigroups

Indexed keywords

ACQUISITION STRATEGIES; CONTINUOUS SEMIGROUPS; DYNAMIC INTERPRETATION; FOURIER; FRACTIONAL FOURIER TRANSFORMS; K-SPACE; NUMERICAL EXAMPLE; QUADRATIC FIELDS; RECONSTRUCTION FORMULAS; RECONSTRUCTION PROBLEMS; SEMI-GROUP THEORY; SEMIGROUPS; TIME EVOLUTIONS;

MAGNETIC RESONANCE IMAGING; RESONANCE;

FOURIER TRANSFORMS;

EID: 79960985582     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.03.027     Document Type: Article

References (29)

1. H. Kober Wurzeln aus der Hankel-, Fourier-und aus anderen stetigen transformationen Quarterly Journal of Mathematics os-10 1939 45 59
2. V. Namias The fractional order Fourier transform and its application to quantum mechanics IMA Journal of Applied Mathematics 25 1980 241 265
3. H.M. Ozaktas, Z. Zalevsky, and M.A. Kutay The Fractional Fourier Transform: With Applications in Optics and Signal Processing Wiley Series in Pure and Applied Optics 2001 Wiley
4. l 2 and applications to differential-equations Journal of Methematical Analysis and Applications 136 1988 404 418
5. T. Alieva, V. Lopez, F. Agullolopez, and L.B. Almeida The fractional Fourier transform in optical propagation problems Journal of Modern Optics 41 1994 1037 1044
6. D. Mendlovic, and H.M. Ozaktas Fractional Fourier transforms and their optical implementation: I Journal of the Optical Society of America A 10 1993 1875 1881
7. H.M. Ozaktas, and D. Mendlovic Fourier-transforms of fractional order and their optical interpretation Optics Communications 101 1993 163 169 (Pubitemid 23697344)
8. H.M. Ozaktas, and D. Mendlovic Fractional Fourier transforms and their optical implementation: II Journal of the Optical Society of America A 10 1993 2522 2531
9. A. Bultheel, and H. Martinez-Sulbaran Recent developments in the theory of the fractional Fourier and linear canonical transforms Bulletin of the Belgian Mathematical Society-Simon Stevin 13 2006 971 1005
10. S.T. Liu, J.D. Xu, Y. Zhang, L.X. Chen, and C.F. Li General optical implementations of fractional Fourier-transforms Optics Letters 20 1995 1053 1055
11. A. Sahin, H.M. Ozaktas, and D. Mendlovic Optical implementation of the 2-dimensional fractional Fourier-transform with different orders in the 2 dimensions Optics Communications 120 1995 134 138
12. D. Mendlovic, H.M. Ozaktas, and A.W. Lohmann Fractional correlation Applied Optics 34 1995 303 309
13. L.B. Almeida The fractional Fourier-transform and timefrequency representations IEEE Transactions on Signal Processing 42 1994 3084 3091
14. X. Guanlei, W. Xiaotong, and X. Xiaogang Generalized entropic uncertainty principle on fractional Fourier transform Signal Processing 89 2009 2692 2697
15. K.K. Sharma, and S.D. Joshi Uncertainty principle for real signals in the linear canonical transform domains IEEE Transactions on Signal Processing 56 2008 2677 2683
16. S. Shinde, and V.M. Gadre An uncertainty principle for real signals in the fractional Fourier transform domain IEEE Transactions on Signal Processing 49 2001 2545 2548 (Pubitemid 33048425)
17. L.B. Almeida Product and convolution theorems for the fractional Fourier transform IEEE Signal Processing Letters 4 1997 15 17 (Pubitemid 127554931)
18. K.K. Sharma, and S.D. Joshi Fractional Fourier transform of bandlimited periodic signals and its sampling theorems Optics Communications 256 2005 272 278 (Pubitemid 41617879)
19. X.G. Xia On bandlimited signals with fractional Fourier transform IEEE Signal Processing Letters 3 1996 72 74
20. B.P. Sutton, D.C. Noll, and J.A. Fessler Fast iterative reconstruction for MRI in the presence of field inhomogeneities IEEE Transactions Medical Imaging 22 2003 178 188
21. J.Y. Lee, and L. Greengard The type 3 nonuniform FFT and its applications Journal of Computational Physics 206 2005 1 5
22. J.A. Goldstein Semigroups of Linear Operators and Applications Oxford Mathematical Monographs 1985 Oxford University Press USA
23. K.N. Khan, W. Lamb, and A.C. McBride Fractional transformations of generalized functions Integral Transforms and Special Functions 20 2009 471 490
24. A.C. McBride, and F.H. Kerr On namias' fractional Fourier transforms IMA Journal of Applied Mathematics 39 1987 159 175
25. Z.-P. Liang, and P.C. Lauterbur Principles of Magnetic Resonance Imaging: A Signal Processing Perspective 1999 Wiley-IEEE Press
26. P. Irarrazabal, C.H. Meyer, D.G. Nishimura, and A. Macovski Inhomogeneity correction using an estimated linear field map Magnetic Resonance in Medicine 35 1996 278 282 (Pubitemid 26044397)
27. K.-J. Engel, and R. Nagel One-Parameter Semigroups for Linear Evolution Equations Graduate Texts in Mathematics vol. 194 2000 Springer
28. I.S. Gradshteyn, and I.M. Ryzhik Table of Integrals, Series and Products 2nd edition 1980 Academic Press
29. W. Feller An Introduction to Probability Theory and Its Applications 2nd ed. Wiley Series on Probability and Statistics vol. 2 1970 John Wiley & Sons