MRI Reconstruction Using Discrete Fourier Transform: A tutorial
The use of Inverse Discrete Fourier Transform (IDFT) implemented in the form of Inverse Fourier Transform (IFFT) is one of the standard method of reconstructing Magnetic Resonance Imaging (MRI) from uniformly sampled K-space data. In this tutorial, three of the major problems associated with the use of IFFT in MRI reconstruction are highlighted. The tutorial also gives brief introduction to MRI physics; MRI system from instrumentation point of view; K-space signal and the process of IDFT and IFFT for One and two dimensional (1D and 2D) data.
[1] Z. P. Liang and P. C. Lauterbur, "Principles of Magnetic Resonance
Imaging, A signal processing perspective", IEEE Press, New York, 2000.
[2] D. G. Nishimura, "Principles of Magnetic Resonance Imaging", April
1996.
[3] E. M. Haacle and Z. P. Liang, "Challenges of Imaging Stucture and
Function with MRI", IEEE Transactions on Medicine and Biology, Vol.
19, pp 55 - 62, 2000.
[4] "MRI Basics: MRI Basics". Accessed September 21, 2007, from Website:
http://www.cis.rit.edu/htbooks/mri/inside.htm
[5] "MRI Physics: MRI Physics". Accessed May 11, 2008, from Website:
http://www.mri-physics.com/
[6] M. R. Smith, S. T. Nichols, R. M. Henkelman and M. L. Wood,
"Application of Autoregressive Moving Average Parametric Modeling
in Magnetic Resonance Image Reconstruction", IEEE Transactions on
Medical Imaging, Vol. M1-5:3, pp 257 - 261, 1986.
[7] F. J. Harris,"On the Use of Windows for Harmonic Analysis with the
Discrete Fourier Transform", Proceedings of the IEEE. Vol. 66, January
1978.
[8] M. R. Smith, S. T. Nichols, R. Constable and R. Henkelman, "A
quantitative comparison of the TERA modeling and DFT magnetic
resonance image reconstruction techniques", Magn. Reson. Med., Vol.
19 pp. 1-19, 1991.
[9] Z. P. Liang, F. E. Boada, R. T. Constable, E. M. Haacke, P. C.
Lauterbur, and M. R. Smith, "Constrained Reconstruction Methods in
MR Imaging", Reviews of MRM, vol. 4, pp.67 - 185, 1992.
[10] "MRI Scanner: MRI Scanner, www.magnet.fsu.edu/images/mriscanner.
jpg"
[11] Z. Hongmei, "Medical Image Processing Overview ", Lecture note,
University of Calgary.
[12] J. Hening, "Review- article: K-space sampling strategies", Eur. Radiol,
vol. 9, pp.1020 - 1031, 1999.
[13] E. J. Blink, " MRI: Physics", Online PDF file, 2004.
[14] R. C. Gonzales, Richard E. Woods, "Digital Image Processing ", second
edition,. Prentice Hall, 2002.
[15] M.L Wood and R. M. Henkelman, "Truncation artifacts in magnetic
Resonace Imaging ", J. Magn. Res. Med. Vol. 2, 1985.
[16] E. Hackle and Z. Liang, "Superresolution Reconstruction Through
Object Modeling and Estimation", IEEE transactions in A.S.S.P, 37:
592 - 595, 1989.
[17] R. Palaniappan, "Towards Optimal Model Order Selection for Autoregressive
Spectral Analysis of Mental Tasks Using Genetic Algorithm",
IJCSNS International Journal of Computer Science and Network Security,
Vol. 6 No. 1A, January 2006.
[18] H. Yan and J. Mao, "Data Truncation Artifact Reduction in MR Imaging
Using a Multilayer Neural Network" IEEE Trans. Med. Imaging ,
V01.12, No. 1,pp.73-77, 1993.
[19] Y. Hui and M. R. Smith, "Comment on Data Truncalion Artifact
Reduction in MR imaging Using a Multilayer Neural Networks ", IEEE
Trans. on Med. Imaging, June 1995.
[20] Y. Hui and M. R. Smith, "MRI Reconstruction From Truncated Data
Using A Complex Domain Backpropagation Neural Network", IEEE
Trans. on Med. Imaging, June 1997.
[21] Z. Wang, A. C. Bovik, and L. Lu, "Why is image quality assessment
so difficult", Proc. IEEE Int. Conf. Acoustics, Speech, and Signal
Processing, vol.4, Orlando, FL, pp. 3313-3316, May, 2002.
[22] T. Mathews Jr. and M. R. Smith, "Objective Image Quality Measures
for Evaluating Advanced MRI Reconstruction Method", Proc. of IEEE
CCECE, pp. 396 - 361, 1996.
[23] Z. Wang and A. Bovik, "A Universal quality index", IEEE Signal
Processing Letters, vol. 9, no. 3, pp. 8 1-84, March 2002.
[24] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image
quality assessment:From error measurement to structural similarity",
IEEE Transactions on Image Processing, accepted for publication April
2003.
[25] H. Akaike, "Power Spectrum Estimation through Autoregression Model
Fitting", Annals of the Institute of Statistical Mathematics, vol. 21, pp.
407-419, 1969.
[26] H. Akaike, "A New Look at the Statistical Model Identification", IEEE
Trans. Autom. Control, vol. AC-19, pp. 716-723, 1974.
[27] J. Rissanen, "Modelling by shortest data description", Automatica,
vol.14, pp.465-471, 1978.
[28] M.J. Salami, A. R. Najeeb, O. Khalifa and K. Arrifin, "MR Reconsturction
with Autoregressive Moving Average", International Conference
on Biotechnology Engineering, Kuala Lumpur, pp 676 - 704, May,
2007.
[29] G. P. Mulopulos, A. A. Hernandez and L. S. Gasztonyi "Peak Signal
to Noise Ratio Performance Comparison of JPEG and JPEG 2000 for
Various Medical Image Modalities" , Symposium on Computer June,
2003.
[30] B. Shrestha, C.G. O-Hara and N. H. Younan, "JPEG2000: IMAGE
QUALITY METRICS", ASPRS 2005 Annual Conference, Baltimore,
Maryland March 7-11, 2005.
[31] A. M, Eskicioglu and P. S. Fisher, P. S, "Image quality measures and
their performance", IEEE Transaction on Communications, 43(12): 2959
- 2965, 1995.
[1] Z. P. Liang and P. C. Lauterbur, "Principles of Magnetic Resonance
Imaging, A signal processing perspective", IEEE Press, New York, 2000.
[2] D. G. Nishimura, "Principles of Magnetic Resonance Imaging", April
1996.
[3] E. M. Haacle and Z. P. Liang, "Challenges of Imaging Stucture and
Function with MRI", IEEE Transactions on Medicine and Biology, Vol.
19, pp 55 - 62, 2000.
[4] "MRI Basics: MRI Basics". Accessed September 21, 2007, from Website:
http://www.cis.rit.edu/htbooks/mri/inside.htm
[5] "MRI Physics: MRI Physics". Accessed May 11, 2008, from Website:
http://www.mri-physics.com/
[6] M. R. Smith, S. T. Nichols, R. M. Henkelman and M. L. Wood,
"Application of Autoregressive Moving Average Parametric Modeling
in Magnetic Resonance Image Reconstruction", IEEE Transactions on
Medical Imaging, Vol. M1-5:3, pp 257 - 261, 1986.
[7] F. J. Harris,"On the Use of Windows for Harmonic Analysis with the
Discrete Fourier Transform", Proceedings of the IEEE. Vol. 66, January
1978.
[8] M. R. Smith, S. T. Nichols, R. Constable and R. Henkelman, "A
quantitative comparison of the TERA modeling and DFT magnetic
resonance image reconstruction techniques", Magn. Reson. Med., Vol.
19 pp. 1-19, 1991.
[9] Z. P. Liang, F. E. Boada, R. T. Constable, E. M. Haacke, P. C.
Lauterbur, and M. R. Smith, "Constrained Reconstruction Methods in
MR Imaging", Reviews of MRM, vol. 4, pp.67 - 185, 1992.
[10] "MRI Scanner: MRI Scanner, www.magnet.fsu.edu/images/mriscanner.
jpg"
[11] Z. Hongmei, "Medical Image Processing Overview ", Lecture note,
University of Calgary.
[12] J. Hening, "Review- article: K-space sampling strategies", Eur. Radiol,
vol. 9, pp.1020 - 1031, 1999.
[13] E. J. Blink, " MRI: Physics", Online PDF file, 2004.
[14] R. C. Gonzales, Richard E. Woods, "Digital Image Processing ", second
edition,. Prentice Hall, 2002.
[15] M.L Wood and R. M. Henkelman, "Truncation artifacts in magnetic
Resonace Imaging ", J. Magn. Res. Med. Vol. 2, 1985.
[16] E. Hackle and Z. Liang, "Superresolution Reconstruction Through
Object Modeling and Estimation", IEEE transactions in A.S.S.P, 37:
592 - 595, 1989.
[17] R. Palaniappan, "Towards Optimal Model Order Selection for Autoregressive
Spectral Analysis of Mental Tasks Using Genetic Algorithm",
IJCSNS International Journal of Computer Science and Network Security,
Vol. 6 No. 1A, January 2006.
[18] H. Yan and J. Mao, "Data Truncation Artifact Reduction in MR Imaging
Using a Multilayer Neural Network" IEEE Trans. Med. Imaging ,
V01.12, No. 1,pp.73-77, 1993.
[19] Y. Hui and M. R. Smith, "Comment on Data Truncalion Artifact
Reduction in MR imaging Using a Multilayer Neural Networks ", IEEE
Trans. on Med. Imaging, June 1995.
[20] Y. Hui and M. R. Smith, "MRI Reconstruction From Truncated Data
Using A Complex Domain Backpropagation Neural Network", IEEE
Trans. on Med. Imaging, June 1997.
[21] Z. Wang, A. C. Bovik, and L. Lu, "Why is image quality assessment
so difficult", Proc. IEEE Int. Conf. Acoustics, Speech, and Signal
Processing, vol.4, Orlando, FL, pp. 3313-3316, May, 2002.
[22] T. Mathews Jr. and M. R. Smith, "Objective Image Quality Measures
for Evaluating Advanced MRI Reconstruction Method", Proc. of IEEE
CCECE, pp. 396 - 361, 1996.
[23] Z. Wang and A. Bovik, "A Universal quality index", IEEE Signal
Processing Letters, vol. 9, no. 3, pp. 8 1-84, March 2002.
[24] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image
quality assessment:From error measurement to structural similarity",
IEEE Transactions on Image Processing, accepted for publication April
2003.
[25] H. Akaike, "Power Spectrum Estimation through Autoregression Model
Fitting", Annals of the Institute of Statistical Mathematics, vol. 21, pp.
407-419, 1969.
[26] H. Akaike, "A New Look at the Statistical Model Identification", IEEE
Trans. Autom. Control, vol. AC-19, pp. 716-723, 1974.
[27] J. Rissanen, "Modelling by shortest data description", Automatica,
vol.14, pp.465-471, 1978.
[28] M.J. Salami, A. R. Najeeb, O. Khalifa and K. Arrifin, "MR Reconsturction
with Autoregressive Moving Average", International Conference
on Biotechnology Engineering, Kuala Lumpur, pp 676 - 704, May,
2007.
[29] G. P. Mulopulos, A. A. Hernandez and L. S. Gasztonyi "Peak Signal
to Noise Ratio Performance Comparison of JPEG and JPEG 2000 for
Various Medical Image Modalities" , Symposium on Computer June,
2003.
[30] B. Shrestha, C.G. O-Hara and N. H. Younan, "JPEG2000: IMAGE
QUALITY METRICS", ASPRS 2005 Annual Conference, Baltimore,
Maryland March 7-11, 2005.
[31] A. M, Eskicioglu and P. S. Fisher, P. S, "Image quality measures and
their performance", IEEE Transaction on Communications, 43(12): 2959
- 2965, 1995.
@article{"International Journal of Information, Control and Computer Sciences:62767", author = "Abiodun M. Aibinu and Momoh J. E. Salami and Amir A. Shafie and Athaur Rahman Najeeb", title = "MRI Reconstruction Using Discrete Fourier Transform: A tutorial", abstract = "The use of Inverse Discrete Fourier Transform (IDFT) implemented in the form of Inverse Fourier Transform (IFFT) is one of the standard method of reconstructing Magnetic Resonance Imaging (MRI) from uniformly sampled K-space data. In this tutorial, three of the major problems associated with the use of IFFT in MRI reconstruction are highlighted. The tutorial also gives brief introduction to MRI physics; MRI system from instrumentation point of view; K-space signal and the process of IDFT and IFFT for One and two dimensional (1D and 2D) data.
", keywords = "Discrete Fourier Transform (DFT), K-space Data,Magnetic Resonance (MR), Spin, Windows.", volume = "2", number = "6", pages = "2181-7", }
