Optimal Model Order Selection for Transient Error Autoregressive Moving Average (TERA) MRI Reconstruction Method
An alternative approach to the use of Discrete Fourier
Transform (DFT) for Magnetic Resonance Imaging (MRI) reconstruction
is the use of parametric modeling technique. This method
is suitable for problems in which the image can be modeled by
explicit known source functions with a few adjustable parameters.
Despite the success reported in the use of modeling technique as an
alternative MRI reconstruction technique, two important problems
constitutes challenges to the applicability of this method, these are
estimation of Model order and model coefficient determination. In
this paper, five of the suggested method of evaluating the model
order have been evaluated, these are: The Final Prediction Error
(FPE), Akaike Information Criterion (AIC), Residual Variance (RV),
Minimum Description Length (MDL) and Hannan and Quinn (HNQ)
criterion. These criteria were evaluated on MRI data sets based on the
method of Transient Error Reconstruction Algorithm (TERA). The
result for each criterion is compared to result obtained by the use of a
fixed order technique and three measures of similarity were evaluated.
Result obtained shows that the use of MDL gives the highest measure
of similarity to that use by a fixed order technique.
[1] Z. P. Liang, 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] "MRI Basics: MRI Basics". Accessed September 21, 2007, from Website:
http://www.cis.rit.edu/htbooks/mri/inside.htm
[4] 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.
[5] F. J. Harris,"On the Use of Windows for Harmonic Analysis with the
Discrete Fourier Transform", Proceedings of the IEEE. Vol. 66, January
1978.
[6] 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.
[7] R. C. Puetter, T. R. Gosnell, and A. Yahil "Digital image reconstruction:
Deblurring and Denoising", Annu. Rev. Astron. Astrophys., pp 43:139,
2005.
[8] 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.
[9] E. Hackle and Z. Liang, "Superresolution Reconstruction Through
Object Modeling and Estimation", IEEE transactions in A.S.S.P, 37:
592 - 595, 1989.
[10] R. Palaniappan, "Towards Optimal Model Oreder 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.
[11] 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.
[12] 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.
[13] Z. Wang, A. Bovik, "A Universal quality index", IEEE Signal Processing
Letters, vol. 9, no. 3, pp. 8 1-84, March 2002.
[14] 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.
[15] H. Akaike, "Power Spectrum Estimation through Autoregression Model
Fitting", Annals of the Institute of Statistical Mathematics, vol. 21, pp.
407-419, 1969.
[16] H. Akaike, "A New Look at the Statistical Model Identification", IEEE
Trans. Autom. Control, vol. AC-19, pp. 716-723, 1974.
[17] J. Rissanen, "Modelling by shortest data description", Automatica,
vol.14, pp.465-471, 1978.
[18] M.J.E Salami, A. R. Najeeb, O. Khalifa, K. Arrifin, "MR Reconsturction
with Autoregressive Moving Average", International Conference on
Biotechnology Engineering, Kuala Lumpur, pp 676 - 704, May, 2007.
[19] 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.
[20] B. Shrestha, C.G. O-Hara and N. H. Younan, "JPEG2000: IMAGE
QUALITY METRICS", ASPRS 2005 Annual Conference, Baltimore,
Maryland March 7-11, 2005.
[1] Z. P. Liang, 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] "MRI Basics: MRI Basics". Accessed September 21, 2007, from Website:
http://www.cis.rit.edu/htbooks/mri/inside.htm
[4] 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.
[5] F. J. Harris,"On the Use of Windows for Harmonic Analysis with the
Discrete Fourier Transform", Proceedings of the IEEE. Vol. 66, January
1978.
[6] 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.
[7] R. C. Puetter, T. R. Gosnell, and A. Yahil "Digital image reconstruction:
Deblurring and Denoising", Annu. Rev. Astron. Astrophys., pp 43:139,
2005.
[8] 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.
[9] E. Hackle and Z. Liang, "Superresolution Reconstruction Through
Object Modeling and Estimation", IEEE transactions in A.S.S.P, 37:
592 - 595, 1989.
[10] R. Palaniappan, "Towards Optimal Model Oreder 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.
[11] 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.
[12] 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.
[13] Z. Wang, A. Bovik, "A Universal quality index", IEEE Signal Processing
Letters, vol. 9, no. 3, pp. 8 1-84, March 2002.
[14] 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.
[15] H. Akaike, "Power Spectrum Estimation through Autoregression Model
Fitting", Annals of the Institute of Statistical Mathematics, vol. 21, pp.
407-419, 1969.
[16] H. Akaike, "A New Look at the Statistical Model Identification", IEEE
Trans. Autom. Control, vol. AC-19, pp. 716-723, 1974.
[17] J. Rissanen, "Modelling by shortest data description", Automatica,
vol.14, pp.465-471, 1978.
[18] M.J.E Salami, A. R. Najeeb, O. Khalifa, K. Arrifin, "MR Reconsturction
with Autoregressive Moving Average", International Conference on
Biotechnology Engineering, Kuala Lumpur, pp 676 - 704, May, 2007.
[19] 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.
[20] B. Shrestha, C.G. O-Hara and N. H. Younan, "JPEG2000: IMAGE
QUALITY METRICS", ASPRS 2005 Annual Conference, Baltimore,
Maryland March 7-11, 2005.
@article{"International Journal of Information, Control and Computer Sciences:59764", author = "Abiodun M. Aibinu and Athaur Rahman Najeeb and Momoh J. E. Salami and Amir A. Shafie", title = "Optimal Model Order Selection for Transient Error Autoregressive Moving Average (TERA) MRI Reconstruction Method", abstract = "An alternative approach to the use of Discrete Fourier
Transform (DFT) for Magnetic Resonance Imaging (MRI) reconstruction
is the use of parametric modeling technique. This method
is suitable for problems in which the image can be modeled by
explicit known source functions with a few adjustable parameters.
Despite the success reported in the use of modeling technique as an
alternative MRI reconstruction technique, two important problems
constitutes challenges to the applicability of this method, these are
estimation of Model order and model coefficient determination. In
this paper, five of the suggested method of evaluating the model
order have been evaluated, these are: The Final Prediction Error
(FPE), Akaike Information Criterion (AIC), Residual Variance (RV),
Minimum Description Length (MDL) and Hannan and Quinn (HNQ)
criterion. These criteria were evaluated on MRI data sets based on the
method of Transient Error Reconstruction Algorithm (TERA). The
result for each criterion is compared to result obtained by the use of a
fixed order technique and three measures of similarity were evaluated.
Result obtained shows that the use of MDL gives the highest measure
of similarity to that use by a fixed order technique.", keywords = "Autoregressive Moving Average (ARMA), MagneticResonance Imaging (MRI), Parametric modeling, Transient Error.", volume = "2", number = "6", pages = "2101-5", }
