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

G.S. Mayer and E.R. Vrscay. Selfsimilarity of Fourier Domain Data. Nonlinear Analysis (in press).

G.S. Mayer, E.R. Vrscay, M.L. Lauzon, B.G. Goodyear and J.R. Mitchell. Selfsimilarity of images in the Fourier domain, with applications. ICIAR 2008, LCNS 5112, SpringerVerlag, Berlin Heidelberg, pages 43  52, 2008.

G.S. Mayer and E.R. Vrscay. Iterated Fourier Transform Systems: A Method for Frequency Extrapolation. ICIAR 2007, LNCS 4633, SpringerVerlag, Berlin Heidelberg, 2007.
 H.E. Kunze, D. La Torre and E.R. Vrscay,
Contractive multifunctions, fixedpont
inclusions and iterated multifunction systems, J. Math. Anal. Appl.330, 159173 (2007).

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, 11161129 (2007).

D. La Torre, F. Mendivil and E.R. Vrscay,
Iterated function systems on multifunctions, in
Math Everywhere (SpringerVerlag, Heidelberg, 2006).

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. 8293 (2006).

M. Ebrahimi and E.R. Vrscay,
Fractal image coding as projection onto
convex sets, in Image Analysis and Recognition, ICIAR 2006, ibid.,
pp. 493506 (2006).

M. Ghazel, G. Freeman and E.R. Vrscay,
"Fractalwavelet image denoising revisited, IEEE Trans. Image Proc. 15(9),
26692675 (2006).

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. LevyVehel and E. Lutton (Springer Verlag, London 2005), pp. 237253.

H. Kunze, J. Hicken and E.R. Vrscay,
Inverse problems for ODEs using contraction
maps: Suboptimality of the `Collage Method', Inverse Problems 20, 977991 (2004).

M. Ghazel, G. Freeman and E.R. Vrscay,
Fractal image denoising, IEEE Trans. Image Proc. 12(12),
15601578 (2003).

F. Mendivil and E.R Vrscay,
Fractal vector measures and vector calculus
on planar fractal domains, Chaos, Solitons and Fractals 14,
No. 8, 12391254 (2002).
 E.R. Vrscay,
From Fractal Image Compression to FractalBased Methods in Mathematics,
in Fractals in Multimedia, edited by M.F. Barnsley, D. Saupe and E.R. Vrscay
(SpringerVerlag, New York, 2002).
1990  2000

B. Forte, F. Mendivil and E.R. Vrscay (1999),
IFSType Operators on Integral Transforms, in
Fractals: Theory and Applications
in Engineering,
edited by M. Dekking, J. LevyVehel, E. Lutton and C. Tricot
(Springer Verlag, London),
pp. 125138 (1999).

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. LevyVehel, E. Lutton and C. Tricot,
(Springer Verlag, London) pp. 307323 (1999).

H.E. Kunze and E.R. Vrscay,
Solving Inverse Problems for ODEs Using the Picard Contraction Mapping ,
Inverse Problems 15, 745770 (1999).

B. Forte and F. Mendivil,
A classical ergodic property for IFS: A simple proof,
Ergodic Theory and Dynamical Systems 18, xxxx (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.)

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).

B. Forte and E.R. Vrscay,
Inverse Problem Methods for Generalized Fractal Transforms,
in Fractal Image Encoding and Analysis, ibid.

E.R. Vrscay,
A Generalized Class of FractalWavelet Transforms for Image Representation
and Compression, Canadian Journal of Electrical and Computer Engineering,
Vol. 23, Nos. 12, pp. 6983 (1998).

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).

R.A. Wannamaker and E.R. Vrscay,
Fractal Wavelet Compression of Audio Signals, J. Audio
Engineering Society, Vol. 45, Nos. 78, pp. 540553 (1997).

F. Mendivil and E.R. Vrscay,
Correspondence Between FractalWavelet Transforms and Iterated Function Systems
With GreyLevel Maps, in Fractals in Engineering: From Theory to
Industrial Applications,, edited by J. Levy Vehel, E. Lutton and C. Tricot
(Springer Verlag, London, 1997).

B. Forte and E.R. Vrscay,
Solving the inverse problem for measures using iterated function systems:
A new approach, Adv. Appl. Prob., 27, 800820 (1995).

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, 177231 (1995).

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, 79100 (1992).