Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30069
MRI Reconstruction Using Discrete Fourier Transform: A tutorial

Authors: Abiodun M. Aibinu, Momoh J. E. Salami, Amir A. Shafie, Athaur Rahman Najeeb


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.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF


[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:
[5] "MRI Physics: MRI Physics". Accessed May 11, 2008, from Website:
[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, 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.