In December 2001, I obtained my PhD degree in Computational Mathematics, with a minor in Computer Science, from North Carolina State University in the United States. From September 2001 until August 2003, I was a postdoctoral fellow at the Symbolic Computation Group, in the School of Computer Science, University of Waterloo, Canada. Afterwards, I was sponsored by INRIA, the French National Institute for Research in Computer Science and Control, for a one-year research visit to the project team GALAAD (Geometry, Algebra, Algorithms) in Sophia Antipolis, France.
In January 2005, I moved to Belgium and became a member of the research group of Computational Mathematics (CMA) at University of Antwerp.
In May 2018, I joined the Division of Computing Science and Mathematics at University of Stirling in Scotland UK as a Lecturer in Mathematics.
The topic of my PhD research belongs to the domain of symbolic computation and computer algebra. During my PhD study and early postdoc years, my focus had been on the representation and manipulation of polynomials, with a focus on efficiency. Polynomials are one of the fundamental objects in computer algebra, as well as computational mathematics in general. Being able to represent and manipulate them efficiently can have dramatic effects on the cost of many algorithms. At the end of this period, I started to investigate symbolic-numeric computing with polynomials and rational functions.
In January 2005, I joined the research group of Computational Mathematics (CMA) at the University of Antwerp in Belgium. The CMA research group at Antwerp has a lot of expertise in scientific computing, besides the background in approximation theory. This collaboration has led to some very interesting results and has become a valuable learning experience that expanded the spectrum and the depth of my research.
Bringing together tools from exponential analysis, Padé approximation, and sparse interpolation from computer algebra, our results allow to break the Nyquist sampling rate in signal processing. This achievement has led to a series of patent applications and a spin-off project. At the same time, we have been actively exploring applications in sciences and engineering, which include direction of arrival (DOA), sonar, radar, motor fault diagnosis, power system transient detection, magnetic resonance spectroscopy (MRS), fluorescence lifetime imaging (FLIM), music signal models, and bioelectrical signals such as the electroencephalogram (EEG), etc.
In May 2018, I joined the Division of Computing Science and Mathematics at University of Stirling. I continue to seek opportunities for multidisciplinary collaboration, departing from an interesting practical application.
Advancing exponential analysis: high-resolution information from sparse and regularly sampled data
PI: Dr Wen-shin Lee
Funded by: The Carnegie Trust
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Women in Mathematics Day
PI: Dr Anna Kirpichnikova
Funded by: London Mathematical Society
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Other
Exponential Analysis: Theoretical Progress and Technological Innovation
Cuyt A, Lee W, Plonka-Hoch G & Knaepkens F (2022) Exponential Analysis: Theoretical Progress and Technological Innovation. Dagstuhl Seminar 22221, Wadern, Germany Dagstuhl Reports, 12 (5), pp. 170-187. https://doi.org/10.4230/DagRep.12.5.170
Article
Validated analysis of modulated signals: From de Prony to Padé and beyond
Cuyt A, Hou Y & Lee W (2022) Validated analysis of modulated signals: From de Prony to Padé and beyond. Journal of Computational and Applied Mathematics, 413, Art. No.: 114346. https://doi.org/10.1016/j.cam.2022.114346
Article
Antenna Position Estimation Through Subsampled Exponential Analysis of Signals in the Near Field
Louw R, Knaepkens F, Cuyt A, Lee W, Wijnholds SJ, de Villiers DIL & Weideman R (2021) Antenna Position Estimation Through Subsampled Exponential Analysis of Signals in the Near Field. URSI Radio Science Letters, 3. https://doi.org/10.46620/21-0062
Conference Proceeding
Louw R, Knaepkens F, Cuyt A, Lee W, Wijnholds SJ, de Villiers DIL & Weideman R (2021) Antenna position estimation through sub-sampled exponential analysis of harmonically related input signals. In: Proceedings of XXXIV General Assembly and Scientific Symposium (GASS) of the International Union of Radio Science (Union Radio Scientifique International - URSI). XXXIV General Assembly and Scientific Symposium (GASS) of the International Union of Radio Science (Union Radio Scientifique International - URSI), Rome, Italy, 28.08.2021-04.09.2021. Piscataway, NJ, USA: IEEE. https://doi.org/10.23919/URSIGASS51995.2021.9560519
Conference Proceeding
Decomposing Textures Using Exponential Analysis
Hou Y, Cuyt A, Lee W & Bhowmik D (2021) Decomposing Textures Using Exponential Analysis. In: ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE International Conference on Acoustics, Speech and Signal Processing, Toronto, Ontario, Canada, 06.06.2021-11.06.2021. Piscataway: IEEE. https://doi.org/10.1109/ICASSP39728.2021.9413909
Article
VEXPA: Validated EXPonential Analysis through regular sub-sampling
Briani M, Cuyt A, Knaepkens F & Lee W (2020) VEXPA: Validated EXPonential Analysis through regular sub-sampling. Signal Processing, 177, Art. No.: 107722. https://doi.org/10.1016/j.sigpro.2020.107722
Article
Sparse multidimensional exponential analysis with an application to radar imaging
Cuyt A, Hou Y, Knaepkens F & Lee W (2020) Sparse multidimensional exponential analysis with an application to radar imaging. SIAM Journal on Scientific Computing, 42 (3), p. B675–B695. https://doi.org/10.1137/19M1278004
Article
How to get high resolution results from sparse and coarsely sampled data
Cuyt A & Lee W (2020) How to get high resolution results from sparse and coarsely sampled data. Applied and Computational Harmonic Analysis, 48 (3), pp. 1066-1087. https://doi.org/10.1016/j.acha.2018.10.001
Article
Regular sparse array direction of arrival estimation in one dimension
Knaepkens F, Cuyt A, Lee W & de Villiers DIL (2020) Regular sparse array direction of arrival estimation in one dimension. IEEE Transactions on Antennas and Propagation, 68 (5), pp. 3997-4006. https://doi.org/10.1109/TAP.2019.2963618
Article
High accuracy trigonometric approximations of the real Bessel functions of the first kind
Cuyt A, Lee W & Wu M (2020) High accuracy trigonometric approximations of the real Bessel functions of the first kind. Computational Mathematics and Mathematical Physics, 60 (1), pp. 119-127. https://doi.org/10.1134/S0965542520010078
Conference Proceeding
Practical Performance of Regular Sparse Array Direction of Arrival Estimation in 1-D
De Villiers DIL, Louw R, Weideman R, Cuyt A, Knaepkens F & Lee W (2019) Practical Performance of Regular Sparse Array Direction of Arrival Estimation in 1-D. In: 9th IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications, APWC 2019. IEEE-APS Conference on Antennas and Propagation for Wireless Communications, Granada, Spain, 09.09.2019-13.09.2019. Piscataway, NJ: Institute of Electrical and Electronics Engineers Inc. pp. 112-112. https://doi.org/10.1109/APWC.2019.8870566
Conference Proceeding
From exponential analysis to Padé approximation and tensor decomposition, in one and more dimensions
Cuyt A, Knaepkens F & Lee W (2018) From exponential analysis to Padé approximation and tensor decomposition, in one and more dimensions. In: Gerdt V, Koepf W, Seiler W & Vorozhtsov E (eds.) Computer Algebra in Scientific Computing. CASC 2018. Lecture Notes in Computer Science (LNCS), 11077. Computer Algebra in Scientific Computing, Lille, France, 17.09.2018-21.09.2018. Cham, Switzerland: Springer International Publishing, pp. 116-130. https://doi.org/10.1007/978-3-319-99639-4_8
Article
Multivariate exponential analysis from the minimal number of samples
Cuyt A & Lee W (2018) Multivariate exponential analysis from the minimal number of samples. Advances in Computational Mathematics, 44 (4), pp. 987-1002. https://doi.org/10.1007/s10444-017-9570-8
Article
Faint and clustered components in exponential analysis
Cuyt A, Tsai M, Verhoye M & Lee W (2018) Faint and clustered components in exponential analysis. Applied Mathematics and Computation, 327, pp. 93-103. https://doi.org/10.1016/j.amc.2017.11.007
Conference Proceeding
Superresolution underwater acoustics
Cuyt A, Lee W, Tijskens E, Hong W, Wang J, Cools T & Geerts T (2018) Superresolution underwater acoustics. In: Proceedings of Euronoise 2018. Euronoise 2018, 27.05.2018-31.05.2018. Crete, Greece: Hellenic Institute of Acoustics, pp. 2845-2850. http://www.euronoise2018.eu/docs/papers/469_Euronoise2018.pdf
Article
Deterministic sparse FFT for M-sparse vectors
Plonka G, Wannenwetsch K, Cuyt A & Lee W (2018) Deterministic sparse FFT for M-sparse vectors. Numerical Algorithms, 78 (1), pp. 133-159. https://doi.org/10.1007/s11075-017-0370-5
Conference Proceeding
Sparse interpolation, the FFT algorithm and FIR filters
Briani M, Cuyt A & Lee W (2017) Sparse interpolation, the FFT algorithm and FIR filters. In: Gerdt V, Koepf W, Seiler W & Vorozhtsov E (eds.) Computer Algebra in Scientific Computing - 19th International Workshop, CASC 2017, Beijing, China, September 18-22, 2017, Proceedings. Lecture Notes in Computer Science (LNCS), 10490. 19th International Workshop on Computer Algebra in Scientific Computing, Beijing, China, 18.09.2017-22.09.2017. Cham, Switzerland: Springer International Publishing, pp. 27-39. https://doi.org/10.1007/978-3-319-66320-3
Conference Proceeding
Validated exponential analysis for harmonic sounds
Briani M, Cuyt A & Lee W (2017) Validated exponential analysis for harmonic sounds. In: Torin A, Hamilton B, Bilbao S & Newton M (eds.) Proceedings of the 20th International Conference on Digital Audio Effects (DAFx-17). DAFx proceedings series. 20th International Conference on Digital Audio Effects, Edinburgh, UK, 05.09.2017-09.09.2017. Hamburg, Germany: University of Edinburgh, pp. 222-227. http://www.dafx17.eca.ed.ac.uk/Proceedings.html
Other
Sparse Modelling and Multi-exponential Analysis
Cuyt A, Labahn G, Sidi A & Lee W (2016) Sparse Modelling and Multi-exponential Analysis. Dagstuhl Seminar 15251, Wadern, Germany Dagstuhl Reports, 6 (6), pp. 48-69. https://doi.org/10.4230/DagRep.5.6.48
Conference Proceeding
Sparse interpolation and rational approximation
Cuyt A & Lee W (2016) Sparse interpolation and rational approximation. In: Hardin D, Lubinsky D & Simanek B (eds.) Modern Trends in Constructive Function Theory. Contemporary Mathematics, 661. Constructive Functions 2014 - Conference in Honor of Ed Saff's 70th Birthday, Nashville, TN, USA, 26.05.2014-30.05.2014. Providence, RI, USA: American Mathematical Society, pp. 229-242. https://bookstore.ams.org/conm-661
Conference Proceeding
A short-time Prony method for the detection of transients
Cuyt A, Lee W & Tsai M (2016) A short-time Prony method for the detection of transients. In: Papadrakakis M, Papadopoulos V, Stefanou G & Plevris V (eds.) ECCOMAS Congress 2016 - VII European Congress on Computational Methods in Applied Sciences and Engineering Proceedings. VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016), Crete Island, Greece, 05.06.2016-10.06.2016. Athens, Greece: Institute of Structural Analysis and Antiseismic Research, National Technical University of Athens, pp. 4313-4321. https://www.eccomas2016.org/proceedings/pdf/7676.pdf
Article
On tensor decomposition, sparse interpolation and Padé approximation
Cuyt A, Lee W & Yang X (2016) On tensor decomposition, sparse interpolation and Padé approximation. Jaen Journal on Approximation, 8 (1), pp. 33-58. http://www.ujaen.es/revista/jja/pdf/pre/jja-0008-01-16-3.pdf
Article
Towards unsupervised fluorescence lifetime imaging using low dimensional variable projection
Zhang Y, Cuyt A, Lee W, Lo Bianco G, Wu G, Chen Y & Li DD (2016) Towards unsupervised fluorescence lifetime imaging using low dimensional variable projection. Optics Express, 24 (23), pp. 26777-26791. https://doi.org/10.1364/oe.24.026777
Article
Numerical reconstruction of convex polytopes from directional moments
Collowald M, Cuyt A, Hubert E, Lee W & Salazar Celis O (2015) Numerical reconstruction of convex polytopes from directional moments. Advances in Computational Mathematics, 41 (6), pp. 1079-1099. https://doi.org/10.1007/s10444-014-9401-0
Edited Book
Feng R, Lee W & Sato Y (eds.) (2014) Computer Mathematics -- 9th Asian Symposium (ASCM2009), Fukuoka, December 2009, 10th Asian Symposium (ASCM2012), Beijing, October 2012, Contributed Papers and Invited Talks. Berlin Heidelberg: Springer-Verlag. https://www.springer.com/gb/book/9783662437988; https://doi.org/10.1007/978-3-662-43799-5
Patent
Smart data sampling and data reconstruction
Cuyt A & Lee W (2014) Smart data sampling and data reconstruction. Issuing Office no. EP2745404B1.
Conference Proceeding
Sparse reconstruction of correlated multichannel activity
Peelman S, Van der Herten J, De Vos M, Lee W, Van Huffel S & Cuyt A (2013) Sparse reconstruction of correlated multichannel activity. In: 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC 2013), Osaka, Japan, 03.07.2013-07.07.2013. Piscataway, NJ, USA: IEEE, pp. 3897-3900. https://doi.org/10.1109/EMBC.2013.6610396
Patent
Smart data sampling and data reconstruction
Cuyt A & Lee W (2013) Smart data sampling and data reconstruction. Issuing Office no. US 9,690,749 B2.
Article
Symbolic-numeric sparse interpolation of multivariate polynomials
Giesbrecht M, Labahn G & Lee W (2009) Symbolic-numeric sparse interpolation of multivariate polynomials. Journal of Symbolic Computation, 44 (8), pp. 943-959. https://doi.org/10.1016/j.jsc.2008.11.003
Article
A new algorithm for sparse interpolation of multivariate polynomials
Cuyt A & Lee W (2008) A new algorithm for sparse interpolation of multivariate polynomials. Theoretical Computer Science, 409 (2), pp. 180-185. https://doi.org/10.1016/j.tcs.2008.09.002
Conference Proceeding
From quotient-difference to generalized eigenvalues and sparse polynomial interpolation
Lee W (2007) From quotient-difference to generalized eigenvalues and sparse polynomial interpolation. In: SNC '07 Proceedings of the 2007 international workshop on Symbolic-numeric computation. Symbolic-Numeric Computation 2007 (SNC 2007), London, Ontario, Canada, 25.07.2007-27.07.2007. New York: ACM, pp. 110-116. https://dl.acm.org/citation.cfm?id=1277518
