Publications
Todd Ell's current list of publications:
2015
Connecting Spatial and Frequency Domains for the Quaternion Fourier Transform , Applied Mathematics and Computation, Volume 271, 15 November 2015, Pages 581-593, co-authored with H. De Bie, N. De Schepper, K. Rubrecht and S.J. Sangwine.
2014
Quaternion Fourier Transforms for Signal and Image Processing, FOCUS Digital signal and image processing series, Wiley-ISTE publisher, 160 pages, May 2014, ISBN: 978-1-84821-478-1, co-authored with S.J. Sangwine and Nicolas Le Bihan.
Instantaneous frequency and amplitude of orthocomplex modulated signals based on quaternion Fourier transform, Signal Processing, Elsevier, Volume 94, January 2014, Pages 308-318, Co-authored with S.J. Sangwine and Nicolas Le Bihan.
2013
Quaternion Fourier Transform: Re-tooling Image and Signal Processing Analysis, Applied Mathematics and Computation, Quaternion and Clifford Fourier Transforms and Wavelets, Trends in Mathematics, Springer Basel, 2013, Eckhard Hitzer and Stephen Sangwine (editors).
2012
Complex and Hypercomplex Discrete Fourier Transforms Based on Matrix Exponential Forms of Euler's Formula, Applied Mathematics and Computation, Elsevier, 2012, Co-authored with S.J. Sangwine.
Quaternion Wigner-Ville distribution, Applied geometric algebras in computer science and engineering, 5th conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE 2012), La Rochelle : France, 2012, Co-authored with Nicolas Le Bihan.
2011
Quaternion Fourier Transform: Re-Tooling Image & Signal Processing Analysis, presented at 9th International Conference on Clifford Algebras and Their Application in Mathematical Physics, Weimar Germany, July 15-20, 2011.
Fundamental Representations and Algebraic Properties of Biquaternions or Complexified Quaternions, Advances in Applied Clifford Algebras, September 2011, Volume 21, Issue 3, pp 607-636, co-authored with S.J. Sangwine and Nicolas Le Bihan.
2010
Hypercomplex models and processing of vector images, in: Christophe Collet, Jocelyn Chanussot and Kacem Chehdi (eds), Multivariate Image Processing, Digital Signal and Image Processing Series, ISTE/Wiley, 2010, Chapter 13, pp 407–436, ISBN 978-1-84821-139-1. Co-authored with S.J. Sangwine and N. Le Bihan.
Complex and Hypercomplex Discrete Fourier Transforms Based on Matrix Exponential Form of Euler’s Formula, e-print arXiv:1001.4379, 25 January 2010, available at http://arxiv.org/abs/arxiv:1001.4379. Co-authored with S.J. Sangwine.
Fundamental representations and algebraic properties of biquaternions or complexified quaternions, e-print arXiv:1001.0240, 1 January 2010, available at http://arxiv.org/abs/arxiv:1001.0240. Co-authored with S.J. Sangwine and N. Le Bihan.
2008
Projective-Space Colour Filters using Quaternion Algebra, 16th European Conference on Signal Processing (Eusipco), Lausanne, Switzerland, 25–29 August 2008, EURASIP 2008. Co-authored with S.J. Sangwine.
Theory of vector filters based on linear quaternion functions, 16th European Conference on Signal Processing (Eusipco), Lausanne, Switzerland, 25–29 August 2008, EURASIP 2008. Co-authored with S.J. Sangwine.
2007
Hypercomplex Fourier Transforms of Color Images, IEEE Transactions on Image Processing, 16, (1), January 2007, pages 22-35, Co-authored with S.J. Sangwine.
Quaternion Involutions and Anti-Involutions, Computers and Mathematics with Applications, 53, (1), January 2007, pages 137-143, Co-authored with S.J. Sangwine.
Hypercomplex Algebras in Digital signal Processing: Benefits and Drawbacks, Proceedings of EUSIPCO 2007, Fifteenth European Signal Processing Conference, Poznan, Poland, 3-7 September 2007, 1322–6, Co-authored with Daniel Alfsmann, Heinz Goeckler, and S.J. Sangwine.
Multi-Vector Color-Image Filters, IEEE International Conference on Image Processing (ICIP 2007), San Antonio, Texas, USA, 16-19 September 2007, V 245-248.
Hypercomplex Color Affine Filters, IEEE International Conference on Image Processing (ICIP 2007), San Antonio, Texas, USA, 16-19 September 2007, V 249-252.
On Systems of Linear Quaternion Functions, e-print arXiv:0702084, 4 February 2007, available at http://arxiv.org/abs/math.RA/0702084.
2006
Development of Testbed for MEMS-based Air-Data, Attitude & Heading Reference Systems, AIAA Guidance, Navigation, and Control Conference and Exhibit, 21-24 Aug 2006, Keystone Resort & Conference Center Keystone, Colorado, Co-authored with B. Rutkiewicz , R. Nielsen, K. Drutowski.
2004
Colour-Dependent Linear Vector Image Filtering, Proceedings of EUSIPCO 2004, Twelfth European Signal Processing Conference, Vienna, Austria, 6-10 September 2004, pp.585-588, Co-authored with S.J. Sangwine and B.N. Gatsheni.
Gray-Centered RGB Color Space, Second European Conference on Color in Graphics, Imaging and Vision (CGIV 2004), Technology Center AGIT, Germany, 5-8 April 2004, The Society for Imaging Science and Technology, pages 183-6, Co-authored with S.J. Sangwine.
2003
Vector Amplification for Color-Dependent Image Filtering, IEEE International Conference on Image Processing (ICIP 2003), Barcelona, Spain, 14-17 September 2003, II, pages 129-132. Co-authored with B.N. Gatsheni and S.J. Sangwine.
Hypercomplex Correlation Techniques for Vector Images, IEEE Transactions on Signal Processing, 51, (7), July 2003, pages 1941-1953. Co-authored with C.E. Moxey and S.J. Sangwine.
2002
Vector Zone Plates as Test Patterns for Linear Vector Filters, IEEE International Conference on Image Processing (ICIP 2002), Rochester, New York, USA, 22-25 September 2002, II, pages 361-364. Co-authored with S.J. Sangwine.
Color-Grayscale Image Registration Using Hypercomplex Phase-Correlation, IEEE International Conference on Image Processing (ICIP 2002), Rochester, New York, 22-25 September 2002, II, pages 385-388. Co-authored with C.E. Moxey and S.J. Sangwine.
Hypercomplex Operators and Vector Correlation, Proceedings of EUSIPCO 2002, Eleventh European Signal Processing Conference, Toulouse, France, 3-6 September 2002, III, pages 247-250. Co-authored with C.E. Moxey and S.J. Sangwine.
Linear Colour-Dependent Image Filtering based on Vector Decomposition, Proceedings of EUSIPCO 2002, Eleventh European Signal Processing Conference, Toulouse, France, 3-6 Sept. 2002, European Association for Signal Processing, II, pages 274-277. Co-authored with B.N. Gatsheni and S.J. Sangwine.
Vector Correlation of Color Images, First European Conference on Colour in Graphics, Imaging and Vision (CGIV 2002), University of Poitiers, France, 2-5 April 2002, The society for Image Science and Technology, pages 343-347. Co-authored with C.E. Moxey and S.J. Sangwine.
Mathematical Approaches to Linear Vector Filtering of Color Images, First European Conference on Colour in Graphics, Imaging and Vision (CGIV 2002), University of Poitiers, France, 2-5 April 2002, The society for Image Science and Technology, pages 348-351. Co-authored with S.J. Sangwine.
2001
Vector Phase Correlation, Electronic Letters, Vol. 37, No. 25, December 2001, pages 1513-1515. Co-authored with S.J. Sangwine and C.E. Moxey.
Hypercomplex Fourier Transforms of Color Images, IEEE International Conference on Image Processing (ICIP 2001), Thessaloniki, Greece, 7-10 Oct. 2001, Vol. 1, pages 137-140. Co-authored with S.J. Sangwine.
2000
Colour Image Filters based on Hypercomplex Convolution, IEE Proceedings—Vision, Image and Signal Processing, Vol. 147, No. 2, pages 89-93, April 2000. Co-authored with S.J. Sangwine.
Hypercomplex Color-Sensitive Smoothing Filters, 2000 Proceedings of International Conference on Image Processing, IEEE Signal Processing Society, Vol. 1, pages 541-544, Co-authored with C.J. Evans and S.J. Sangwine.
Hypercomplex Wiener-Khintchine Theorem with Application to Color Image Correlation, IEEE International Conference on Image Processing (ICIP 2000), Vancouver, Canada, 11-14 September 2000 Vol. II, pages 792-795. Co-authored with S.J. Sangwine.
Decomposition of 2D Hypercomplex Fourier Transforms into Pairs of Complex Fourier Transforms, Signal Processing X, Theories and Applications (Proceedings of EUSIPCO 2000, Tenth European Signal Processing Conference, Tampere, Finland), M. Gabbouj and P. Kuosmanen, Editors, 5-8 September 2000, Vol. II, Pages 1061-1064. Co-authored with S.J. Sangwine.
Colour-Sensitive Edge Detection using Hypercomplex Filters, in: Gabbouj, M. and Kuosmanen (eds), 'Signal Processing X, Theories and Applications', Proceedings of EUSIPCO 2000, Tenth European Signal Processing Conference, Tampere, Finland, 5-8 September 2000, I, 107-110. Co-authored with C.J. Evans and S.J. Sangwine.
The Discrete Fourier Transform of a Colour Image, Image Processing II: Mathematical Methods, Algorithms and Applications (Proceedings of Second IMA Conference on Image Processing, De Monfort University, Leicester, UK, September 1998), J. M. Blackledge and M. J. Turner, editors, pages 430-441, Chichester, 2000. Horwood Publishing for Institute of Mathematics and its Applications. Co-authored with S.J. Sangwine.
1999
Hypercomplex Auto- and Cross-Correlation of Color Images, IEEE International Conference on Image Processing (ICIP'99), Kobe, Japan, 24-28 October 1999, pages 319-322. Co-authored with S.J. Sangwine. [Poster size:320 Kb]
Pre-1999
Quaternion-Fourier Transforms for Analysis of Two-Dimensional Linear Time-Invariant Partial Differential Systems, 32nd IEEE Conference on Decision and Control, San Antonio, Texas, December 13-15, 1993.
Doctoral Thesis: Hypercomplex Spectral Transformations, University of Minnesota, University Microfilms International Number 9231031, June 1992.
Masters Thesis: Ultrasonic Continuous Wave Spirometer, University of North Dakota, May 1983.
Miscellaneous
Poster: Processing of Colour Images Using Hypercomplex Numbers, S.J. Sangwine,C.J. Evans and T.A. Ell [size: 1.2Mb]