Dawit Assefa, Harald Keller, and David A. Jaffray


  1. [1] A.R. Padhani and K.A. Miles, Multiparametric imaging of tumor response to therapy, Radiology, 256 (2), 2010, 348–364.
  2. [2] K.M. McMillan, B.P. Rogers, C.G. Koay, A.R. Laird, R.R. Price, and M.E. Meyerand, An objective method for combining multi-parametric MRI datasets to characterize malignant tumors, Medical Physics, 34 (3), 2007, 1053–1061.
  3. [3] M.A. Jacobs, Z.G. Zhang, R.A. Knight, H. Soltanian-Zadeh, A.V. Goussev, D.J. Peck, and M. Chopp, A model for multi-parametric MRI tissue characterization in experimental cerebral ischemia with histological validation in rat, Part 1, Stroke, 32, 2001, 943–949.
  4. [4] A. Di Costanzo, T. Scarabino, F. Trojsi, et al., Multi-parametric 3T MR approach to the assessment of cerebral gliomas: tumor extent and malignancy, Neuroradiology, 48, 2006, 622–631.
  5. [5] H. Witjes, M. Rijpkema, M. van der Graaf, W. Melssen,A. Heerschap, and L. Buydens, Multispectral magnetic res-onance image analysis using principal component and lineardiscriminant analysis. Technical Note, Magnetic Resonanceand Imaging, 17, 2003, 261–269.
  6. [6] J.V. Manj´on, N.A. Thacker, J.J. Lull, G.G. Mart´ı, L.M. Bonmat´ı, and M. Robles, Multicomponent MR image denoising, International Journal of Biomedical Imaging, 2009 (18), 2009, 10 pages.
  7. [7] J. Ward, V. Magnotta, N.C. Andreasen, W. Ooteman, P.Nopoulos, and R. Pierson, Color enhancement of multispec-tral MR images: improving the visualization of subcorticalstructures, Journal of Computer Assisted Tomography, 25 (6), 2001, 942–949.
  8. [8] T.A. Ell, Quaternion-Fourier transforms for analysis of two-dimensional linear time-invariant partial differential systems, Proc. 32nd IEEE Conf. on Decision and Control , San Antonio, TX, 1993, 1830–1841.
  9. [9] S.J. Sangwine, The problem of defining the Fourier transform of a color image, Proc. IEEE Int. Conf. Image Proc. (ICIP 98), Chicago, IL, 1, 1998, 171–175.
  10. [10] E.M.S. Hitzer, Quaternion Fourier transform on quaternion fields and generalizations, Journal of Advances in Applied Cliford. Algebras, 17 (3), 2007, 497–517.
  11. [11] M. Felsberg, T. B¨ulow, and G. Sommer, Commutative hypercomplex Fourier transform of multidimensional signals, in Geometric computing with Clifford algebras: theoretical foundations and applications in computer vision and robotics (London: Springer, 2001) 209–229.
  12. [12] D. Assefa, H. Keller, and D.A. Jaffray, Multi-parametric MR image processing using higher dimensional vector algebra, ACTA Press, Proc. IASTED, ISPHT , May 2011, 24–31.
  13. [13] V. Labunets, Clifford Algebras as unified language for image processing and pattern recognition, in J. Byrnes andG. Ostheimer (eds.), NATO Sciences Series II Mathematics,Physics & Chemistry (Kluwer, vol. 136, 2003).
  14. [14] D. Assefa, L. Mansinha, K.F. Tiampo, H. Rasmussen, and K. Abdella, The trinion Fourier transform of color images, Signal Processing, 91 (8), 2011, 1887–1900.
  15. [15] W.R. Hamilton, Lectures on quaternions (Hodges and Smith, Dublin, 1853) [Online]. Available
  16. [16] T.A. Ell and S.J. Sangwine, Hypercomplex Fourier transforms of color images, IEEE Transactions on Image Processing, 16 (1), 2007, 22–35.
  17. [17] S.-C. Pei, J.H. Chang, and J.J. Ding, Commutative reduced biquaternions and their Fourier transform for signal and image processing applications, IEEE Transactions on Signal Processing, 52 (7), 2004, 2012–2031.
  18. [18] H. Gillow-Wiles and T. Dray, Finding 3 × 3 Hermitian matrices over the octonions with imaginary eigenvalues, Advances in Applied Clifford Algebra, 20 (2), 2010, 247–254.
  19. [19] G. Sommer (ed.), Geometric computing with Clifford algebras (Berlin: Springer-Verlag, 2001).
  20. [20] S.J. Sangwine and T.A. Ell, Colour image filters based on hypercomplex convolution, Proc. Institution of Electrical Engineering, Vision Image and Signal Process., 147 (2), 2000, 89–93.
  21. [21] C.E. Moxey, S.J. Sangwine, and T.A. Ell, Hypercomplexcorrelation techniques for vector images, IEEE Transactions on Signal Processing, 51 (7), 2003, 1941–1953.
  22. [22] D. Assefa, L. Mansinha, K.F. Tiampo, H. Rasmussen, and K. Abdella, Local quaternion Fourier transform and color image texture analysis, Signal Processing, 90 (6), 2010, 1825–1835.
  23. [23] R.M. Haralick, K. Shanmugam, and I. Dinstein, Textural features for image classification, IEEE Transactions on Systems, Man, and Cybernetics, SMC-3 (6), 1973, 610–621.
  24. [24] M.R. Ross, D.F. Schomer, P. Chappell, and D.R. Enzmann, MR imaging of head and neck tumors: Comparison of T1-weighted contrast-enhanced fat-suppressed images with conventional T2-weighted and fast spin-echo T2-weighted images, American Journal of Roentgenology, 163 (1), 1994, 173–178.
  25. [25] A. Constantin, R. Bajcsy, and S. Nelson, Unsupervised segmentation of brain tissue in multivariate MRI, ISB/IEEE, 2010, 89–92.
  26. [26] D. Assefa, H. Keller, C. M´enard, N. Laperriere, R.J. Ferrari, and I. Yeung, Robust texture features for response monitoring of glioblastoma multiforme on T1-weighted and T2-FLAIR MR images: a preliminary investigation in terms of identification and segmentation, Medical Physics, 37 (4), 2010, 1722–1736.

Important Links:

Go Back