A wavelet-based super-resolution method for multi-slice MRI

Rafiqul Islam, Andrew J. Lambert, Mark R. Pickering, Jennie M. Scarvell, Paul N. Smith

School of Engineering and Information Technology (SEIT), University of New South Wales, Canberra, Australia.
The Trauma and Orthopaedic Research Unit, The Canberra Hospital, Canberra, Australia.

DOI: 10.4236/jbise.2012.512A109                

Abstract

In multi-slice magnetic resonance imaging (MRI), the resolution in the slice direction is usually reduced to allow faster acquisition times and to reduce the amount of noise in each 2D slice. To address this issue, a number of super resolution (SR) methods have been proposed to improve the resolution of 3D MRI volumes. Most of the methods involve the use of prior models of the MRI data as regularization terms in an ill-conditioned inverse problem. The use of user-defined parameters produces better results for these approaches but an inappropriate choice may reduce the overall performance of the algorithm. In this paper, we present a wavelet domain SR method which uses a Gaussian scale mixture (GSM) model in a sparseness constraint to regularize the ill-posed SR inverse problem. The proposed approach also makes use of an extension of the Dual Tree Complex Wavelet Transform to provide the ability to analyze the wavelet coefficients with sub-level precision. Our results show that the 3D MRI volumes reconstructed using this approach have quality superior to volumes produced by the best previously proposed approaches.

Keywords

Magnetic Resonance Imaging; Super Resolution; Gaussian Scale Mixture Model; Wavelet Regularization

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Huppert, B.J., Brandt, K.R., Ramin, K.D. and King, B.F. (1999) Single-shot fast spin-echo MR imaging of the Fetus: A pictorial essay. Radiographics, 19, 215-227. http: //radiographics.rsna.org/content/19/suppl 1/S215
[2]	Vignaux, O.B., et al. (2001) Comparison of single-shot fast spin-echo and conventional spin-echo sequences for MR imaging of the heart: Initial experience. Radiology, 219, 545-550. http://radiology.rsna.org/content/219/2/545
[3]	Gholipour, A., Estroff, J. and Warfield, S. (2010) Robust super-resolution volume reconstruction from slice acquisitions: Application to fetal brain MRI. IEEE Transactions on Medical Imaging, 29, 1739-1758. doi:10.1109/TMI.2010.2051680
[4]	Greenspan, H. (2009) Super-resolution in medical imaging. The Computer Journal, 52, 43-63 doi:10.1093/comjnl/bxm075
[5]	Plenge, E., et al. (2012) Super-resolution methods in MRI: Can they improve the trade-off between resolution, sig- nal-to-noise ratio, and acquisition time? Magnetic Resonance in Medicine, 68, 1983-1993. doi:10.1002/mrm.24187
[6]	Park, S.C., Park, M.K. and Kang M.G. (2003) Superresolution image reconstruction: A technical overview. IEEE Signal Processing Magazine, 20, 21-36. doi:10.1109/MSP.2003.1203207
[7]	Peled, S. and Yeshurun, Y. (2001) Super resolution in MRI: Application to human white matter fiber tract vis- ualization by diffusion tensor imaging. Magnetic Resonance in Medicine, 45, 29-35. doi:10.1002/1522-2594(200101)45:1<29::AID-MRM1005>3.0.CO;2-Z
[8]	Greenspan, H., Peled, S., Oz, G. and Kiryati N. (2001) MRI inter-slice reconstruction using super-resolution. Pr- ceedings of Medical Image Computing and Computer- Assisted Intervention MICCAI 2001, Lecture Notes in Computer Science, 2208, 1204-1206.
[9]	Irani, M. and Peleg, S. (1991) Improving resolution by image registration. CVGIP: Graphical Models and Image Processing, 53, 231-239. doi:10.1016/1049-9652(91)90045-L
[10]	Scheffler, K. (2002) Superresolution in MRI? Magnetic Resonance in Medicine, 48, 408-408. doi:10.1002/mrm.10203
[11]	Kramer, D., et al. (1990) Applications of voxel shifting in magnetic resonance imaging. Investigative Radiology, 25, 1305-1310. doi:10.1097/00004424-199012000-00006
[12]	Greenspan, H., Oz, G., Kiryati, N. and Peled, S. (2002) Super-resolution in MRI. Proceedings of the IEEE Inter- national Symposium on Biomedical Imaging, Washington DC, 7-10 July 2002, 943-946. doi:10.1109/ISBI.2002.1029417
[13]	Yan, Z. and Lu, Y. (2009) Super resolution of MRI using improved IBP. Proceedings International Conference on Computational Intelligence and Security, Beijing, 11-14 December, 643-647.
[14]	Peeters, R.R., et al. (2004) The use of super-resolution techniques to reduce slice thickness in functional MRI. International Journal of Imaging Systems and Techn- ology, 14, 131-138. doi:10.1002/ima.20016
[15]	Joshi, S., et al. (2009) MRI resolution enhancement using total variation regularization. Proceedings IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Boston, 28 June - 1 July 2009, 161-164.
[16]	Ben-Ezra, A., Greenspan, H. and Rubner Y. (2009) Re- gularized super-resolution of brain MRI. Proceedings IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Boston, 28 June - 1 July 2009, 254-257.
[17]	Shilling, R., et al. (2009) A super-resolution framework for 3-D high-resolution and high-contrast imaging using 2-D multi-slice MRI. IEEE Transactions on Medical Imaging, 28, 633-644. doi:10.1109/TMI.2008.2007348
[18]	Islam, R., Lambert, A.J. and Pickering, M.R. (2012) Su- per resolution of 3D MRI images using a Gaussian scale mixture model constraint. Proceedings IEEE International Conference on Acoustics, Speech and Signal Processing, Kyoto, 25-30 March 2012, 849-852.
[19]	Kingsbury, N. (2001) Complex wavelets for shift invariant analysis and filtering of signals. Applied and Computational Harmonic Analysis, 10, 234-253. doi:10.1006/acha.2000.0343
[20]	Bertero, M. and Boccacci, P. (1998) Introduction to in- verse problems in imaging. Taylor & Francis, Bristol. doi:10.1887/0750304359
[21]	Landweber, L. (1951) An iteration formula for fredholm integral equations of the first kind. American Journal of Mathematics, 73, 615-624. doi:10.2307/2372313
[22]	Daubechies, I., Defrise, M. and De Mol, C. (2004) An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications on Pure and Applied Mathematics, 57, 1413-1457. doi:10.1002/cpa.20042
[23]	Vonesch, C. and Unser, M. (2008) A fast thresholded landweber algorithm for wavelet-regularized multidimensional deonvolution. IEEE Transactions on Image Processing, 17, 539-549. doi:10.1109/TIP.2008.917103
[24]	Zhang, Y. and Kingsbury, N. (2009) Image deconvolu- tion using a Gaussian Scale Mixtures model to approximate the wavelet sparseness constraint. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, Taipei, 19-24 April 2009, 681-684. doi:10.1109/ICASSP.2009.4959675
[25]	Sendur, L. and Selesnick, I. (2002) Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Transactions on Signal Pro- cessing, 50, 2744-2756. doi:10.1109/TSP.2002.804091
[26]	Andrews, D.F. and Mallows, C.L. (1974) Scale mixtures of normal distributions. Journal of the Royal Statistical Society. Series B (Methodological), 36, 99-102. http://www.jstor.org/stable/2984774
[27]	Wainwright, M.J. and Simoncelli, E.P. (2000) Scale mixtures of Gaussians and the statistics of natural images. Advanced Neural Information Processing Systems, 12, 855-861.
[28]	Collins, D., et al. (1998) Design and construction of a realistic digital brain phantom. IEEE Transactions on Medical Imaging, 17, 463-468. doi:10.1109/42.712135
[29]	Baker, S. and Matthews, I. (2004) Lucas-Kanade 20 years on: A unifying framework. International Journal of Computer Vision, 56, 221-255. doi:10.1023/B:VISI.0000011205.11775.fd
[30]	Pickering, M.R. (2011) A new similarity measure for multi-modal image registration. Proceedings of IEEE International Conference on Image Processing, Brussels, 11-14 September, 2011, 2273-2276.