List of Publications (Waterloo Group Only)
This page is still under construction, but below is a list of some of our publications (not meant to be a complete list, yet) from the research group at the University of Waterloo only. For a list of publications from members of our group at other institutions, please visit their respective web pages, listed here.
2001 - Current
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G.S. Mayer and E.R. Vrscay. Self-similarity of Fourier Domain Data. Nonlinear Analysis (in press).
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G.S. Mayer, E.R. Vrscay, M.L. Lauzon, B.G. Goodyear and J.R. Mitchell. Self-similarity of images in the Fourier domain, with applications. ICIAR 2008, LCNS 5112, Springer-Verlag, Berlin Heidelberg, pages 43 - 52, 2008.
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G.S. Mayer and E.R. Vrscay. Iterated Fourier Transform Systems: A Method for Frequency Extrapolation. ICIAR 2007, LNCS 4633, Springer-Verlag, Berlin Heidelberg, 2007.
- H.E. Kunze, D. La Torre and E.R. Vrscay,
Contractive multifunctions, fixed-pont
inclusions and iterated multifunction systems, J. Math. Anal. Appl.330, 159-173 (2007).
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H.E. Kunze, D. La Torre and E.R. Vrscay,
Random fixed point equations and inverse problems by collage theorem,
J. Math. Anal. Appl. 334, 1116-1129 (2007).
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D. La Torre, F. Mendivil and E.R. Vrscay,
Iterated function systems on multifunctions, in
Math Everywhere (Springer-Verlag, Heidelberg, 2006).
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E.R. Vrscay,
Continuous evolution of fractal transforms and nonlocal PDE imaging,
in Image Analysis and Recognition, ICIAR 2006, Lecture Notes in Computer
Science, Vol. 4141, pp. 82-93 (2006).
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M. Ebrahimi and E.R. Vrscay,
Fractal image coding as projection onto
convex sets, in Image Analysis and Recognition, ICIAR 2006, ibid.,
pp. 493-506 (2006).
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M. Ghazel, G. Freeman and E.R. Vrscay,
"Fractal-wavelet image denoising revisited, IEEE Trans. Image Proc. 15(9),
2669-2675 (2006).
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J. Bona and E.R. Vrscay,
Continuous evolution of functions and measures toward fixed points of
contraction mappings, in Fractals in Engineering: New Trends in Theory and Applications,
edited by J. Levy-Vehel and E. Lutton (Springer Verlag, London 2005), pp. 237-253.
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H. Kunze, J. Hicken and E.R. Vrscay,
Inverse problems for ODEs using contraction
maps: Suboptimality of the `Collage Method', Inverse Problems 20, 977-991 (2004).
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M. Ghazel, G. Freeman and E.R. Vrscay,
Fractal image denoising, IEEE Trans. Image Proc. 12(12),
1560-1578 (2003).
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F. Mendivil and E.R Vrscay,
Fractal vector measures and vector calculus
on planar fractal domains, Chaos, Solitons and Fractals 14,
No. 8, 1239-1254 (2002).
- E.R. Vrscay,
From Fractal Image Compression to Fractal-Based Methods in Mathematics,
in Fractals in Multimedia, edited by M.F. Barnsley, D. Saupe and E.R. Vrscay
(Springer-Verlag, New York, 2002).
1990 - 2000
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B. Forte, F. Mendivil and E.R. Vrscay (1999),
IFS-Type Operators on Integral Transforms, in
Fractals: Theory and Applications
in Engineering,
edited by M. Dekking, J. Levy-Vehel, E. Lutton and C. Tricot
(Springer Verlag, London),
pp. 125-138 (1999).
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E.R. Vrscay and D. Saupe
Can One Break the "Collage Barrier" in Fractal Image Coding?"
in Fractals: Theory and Applications in Engineering,
edited by M. Dekking, J. Levy-Vehel, E. Lutton and C. Tricot,
(Springer Verlag, London) pp. 307-323 (1999).
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H.E. Kunze and E.R. Vrscay,
Solving Inverse Problems for ODEs Using the Picard Contraction Mapping ,
Inverse Problems 15, 745-770 (1999).
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B. Forte and F. Mendivil,
A classical ergodic property for IFS: A simple proof,
Ergodic Theory and Dynamical Systems 18, xx-xx (1998).
(Note: This is the original manuscript. The year "2000" appears
in it because the file was regenerated from the original source file that year.)
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B. Forte and E.R. Vrscay,
Theory of Generalized Fractal Transforms, in Fractal Image Encoding and Analysis, edited by Y. Fisher (Springer Verlag, Heidelberg, 1998).
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B. Forte and E.R. Vrscay,
Inverse Problem Methods for Generalized Fractal Transforms,
in Fractal Image Encoding and Analysis, ibid.
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E.R. Vrscay,
A Generalized Class of Fractal-Wavelet Transforms for Image Representation
and Compression, Canadian Journal of Electrical and Computer Engineering,
Vol. 23, Nos. 1-2, pp. 69-83 (1998).
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B. Forte and E.R. Vrscay, Theory of Generalized Fractal Transforms, in Fractal Image Encoding and Analysis, edited by Y. Fisher (Springer Verlag, Heidelberg, 1998).
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R.A. Wannamaker and E.R. Vrscay,
Fractal Wavelet Compression of Audio Signals, J. Audio
Engineering Society, Vol. 45, Nos. 7-8, pp. 540-553 (1997).
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F. Mendivil and E.R. Vrscay,
Correspondence Between Fractal-Wavelet Transforms and Iterated Function Systems
With Grey-Level Maps, in Fractals in Engineering: From Theory to
Industrial Applications,, edited by J. Levy Vehel, E. Lutton and C. Tricot
(Springer Verlag, London, 1997).
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B. Forte and E.R. Vrscay,
Solving the inverse problem for measures using iterated function systems:
A new approach, Adv. Appl. Prob., 27, 800-820 (1995).
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B. Forte and E.R. Vrscay,
Solving the inverse problem for function and image approximation
using iterated function systems
Dyn. Cont. Disc. Imp. Sys. 1, 177-231 (1995).
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C.A. Cabrelli, B. Forte, U.M. Molter and E.R. Vrscay,
Iterated Fuzzy Set Systems: A New Approach to the Inverse
Problem for Fractals and Other Sets,
J. Math. Anal. Appl. 171, 79-100 (1992).