Publications of E.R. Vrscay
Publications of E.R. Vrscay
2020

D. La Torre, J. Marcoux, F. Mendivil and E.R. Vrscay (2020),
Denoising of diffusion magnetic resonance images using a
modified and differentiable MongeKantorovich distance for
measurevalued functions, in
Commun. Nonlinear Sci. Numer. Simulat. 91, 105456.

D. Otero, D. La Torre, O. Michailovich and E.R. Vrscay (2020),
Optimization of structural similarity in mathematical imaging, in
Optimization and Engineering, https://doi.org/10.1007/s11081020095258.

T. Costa, V. Gaudet, E.R. Vrscay and Z. Wang (2020),
Perceptual Colour Difference Uniormity in high dynamic range
and wide colour gamut, in
Proceedings of ICIP 20 Conference.

T. Costa, V. Gaudet, E.R. Vrscay and Z. Wang (2020),
Variation of Perceived Colour Difference Under Different
Surround Luminance, in
Image Analysis and Recognition, ICIAR 2020, LNCS 12131,
5650 (Springer).

A.K. Cheeseman, H.R. Tizhoosh and E.R. Vrscay (2020),
Studying the Effect of Digital Stain Separation of Histopathology
Images on Image Search Performance, in
Image Analysis and Recognition, ICIAR 2020, LNCS 12132,
262273 (Springer).
2019

H. Kunze, D. La Torre, F. Mendivil and E.R. Vrscay (2019),
Selfsimilarity of solutions to integral and differential
equations with respect to a fractal measure, in
Fractals 27 (2), 1950014 (13 pages)

D. Li, D. La Torre and E.R. Vrscay (2019),
Existence, uniqueness and asymptotic behaviour of intensitybased
measures which conform to a generalized Weber's model
of perception, in
Image Analysis and Recognition, ICIAR 2019, LNCS 11662,
297308. (Springer).

A. Cheeseman, H. Tizhoosh and E.R. Vrscay (2019),
A compact representation of histopathology images using
digital stain separation and frequencybased encoded local
projections, in
Image Analysis and Recognition, ICIAR 2019, LNCS 11663,
147158. (Springer).
2018

W. Jiang, F. Ghasempour, F. Mendivil, S.D. Peterson and E.R. Vrscay (2018),
An algorithm to construct conformable tubular networks
that occupy arbitrary regions in $R3$,
Applied Mathematical Modelling 62, 194206.

D. La Torre, E. Maki, F. Mendivil and E.R. Vrscay (2018),
Iterated function systems with placedependent probabilities
and the inverse problem of measure approxmation using moments,
Fractals 26 (5), 1850076 (2018).
https://doi.org/10.1142/S0218348X18500767. (17 pages)

D. Li, D. La Torre and E.R. Vrscay (2018),
The use of intensitybased
measures to produce image function metrics which accommodate Weber's
models of perception, in
Image Analysis and Recognition, ICIAR 2018, LNCS 10882,
326335. (Springer).

H. Wang, R. Mann and E.R. Vrscay (2018),
A diffusionbased twodimensional Empirical Mode Decomposition (EMD)
algorithm for image analysis, in
Image Analysis and Recognition, ICIAR 2018, LNCS 10882,
295305. (Springer).

D. Otero, D. La Torre, O. Michailovich and E.R. Vrscay (2018),
Alternate direction method of multipliers for unconstrained
structural similaritybased optimization, in
Image Analysis and Recognition, ICIAR 2018, LNCS 10882,
2029. (Springer).
2017

D. Otero, D. La Torre, O. Michailovich and E.R. Vrscay,
On the theory of functionvalued mappings and its application to
the processing of hyperspectral images,
Signal Processing 134, 185196.

Book chapter:
D. Brunet, Z. Wang, E.R. Vrscay, S.S. Channappayya and
A.C. Bovik, "Optimizing image quality,"
Handbook of Convex Optimization Methods in Imaging Science,
V. Monga (Ed.), Springer International Publishing AG, pp. 1541.

H. Kunze, D. La Torre, F. Mendivil and E.R. Vrscay (2018),
Collage Theorembased approaches for solving inverse problems for
differential equations: A review of recent developments, in
Journal of Physics Conference Series 1047, 012004,
doi:10.1088/17426596/1047/1/012004.
Proceedings of the 9th International Conference on Inverse Problems in
Engineering (ICIPE 2017). 12 pages.

F. Ghasempour, W. Jiang, F. Mendivil, S.D. Peterson and E.R. Vrscay (2018),
Constructing tubular networks that occupy arbitrary regions
in $R3$, in
Journal of Physics Conference Series 1047, 012003,
doi:10.1088/17426596/1047/1/012003.
Proceedings of the 9th International Conference on Inverse Problems in
Engineering (ICIPE 2017). 13 pages.

D. La Torre, E. Maki, F. Mendivil and E.R. Vrscay,
"Inverse problems using iterated function systems with
placedependent probabilities," in
Springer Proceedings in Mathematics and Statistics 259,
115125. Proceedings of the 25th International Conference
on Applied Mathematics, Modeling and Computational Science, AMMCS 2017
(Waterloo, Ontario, Canada).
2016

D. La Torre, F. Mendivil and E.R. Vrscay (2016),
Iterated function systems on functions of bounded variation,
Fractals 24 (02), June 2016.
doi 10.1142.S0218348X16500195. (10 pages)

D. Otero, D. La Torre and E.R. Vrscay (2016),
Image denoising using EulerLagrange equations
for functionvalued mappings, in
Image Analysis and Recognition, ICIAR 2016, LNCS 9730, 110119.
(Springer).

A.K. Cheeseman, I.A. KowalikUrbaniak and E.R. Vrscay (2016),
Objective image quality measures of degradation in compressed
natural images and their comparison with subjective assessments, in
Image Analysis and Recognition, ICIAR 2016, LNCS 9730, 163172.
(Springer).

D. La Torre, F. Mendivil, O. Michailovich and E.R. Vrscay (2016),
Total variation minimization for measurevalued images with diffusion
spectrum imaging as motivation, in
Image Analysis and Recognition, ICIAR 2016, LNCS 9730, 131137 (Springer).

D. La Torre, F. Mendivil and E.R. Vrscay (2016),
Total variation denoising of probability measures using iterated
functions systems with probabilities in
Proceedings of ICNPAA Congress on Mathematical Problems in
Engineering, Aerospace and Science, ICNPAA 2016 (American Institute of Physics),
ISBN 9780735414648, pp. 0200911 to 0200915.
2015

D. Otero, D. La Torre, and E.R. Vrscay (2015),
"Structural similaritybased optimization problems with L1regularization:
Smoothing using mollifiers, in
Image Analysis and Recognition, ICIAR 2015,
LNCS 9164, 3342 (Springer).

I.A. KowalikUrbaniak, J. Castelli, N. Hemmati, D. Koff, E.R. Vrscay,
Z. Wang and J. Wang (2015),
"Modelling of subjective radiological assessments
with objective image quality measures for brain and body CT images, in
Image Analysis and Recognition, ICIAR 2015,
LNCS 9164, 313 (Springer).
2014

D. La Torre, H. Kunze, F. Mendivil and E.R. Vrscay (2014),
Continuous
evolution of equations and inclusions involving setvalued contraction
mappings with applications to Generalized Fractal Transforms,
Electronic J. Differential Equations 142, 117.

D. La Torre and E.R. Vrscay (2014),
Fourier transforms of measurevalued
images, selfsimilarity and the inverse problem,
Signal Processing 101, 1118.

E.R. Vrscay, D. Otero and D. La Torre (2014),
"A simple class of fractal
transforms for hyperspectral images, Applied Mathematics and
Computation 231, 435444.

V. Capasso, H. Kunze, D. La Torre and E.R. Vrscay (2014),
Solving
inverse problems for differential equations by a "generalized collage"
method and application to a mean field stochastic model,
Nonlinear Analysis: Real World Applications 15, 276289.

I.A. KowalikUrbaniak, D. La Torre, E.R. Vrscay and Z. Wang (2014),
Some 'Weberized' $L2$based Methods of Signal/Image Approximation, in
Image Analysis and Recognition, ICIAR 2014, LNCS 8814, 2029 (Springer).

P. Bendevis and E.R. Vrscay (2014),
"Structural SimilarityBased
Approximation Over Orthogonal Bases: Investigating the
Use of Individual Component Funcions $S$_{k}(x,y), in
Image Analysis and Recognition, ICIAR 2014, LNCS 8814, 5564 (Springer).

D. Otero, O.V. Michailovich and E.R. Vrscay (2014),
An Examination of Several Methods of Hyperspectral Image Denoising:
Over Channels, Spectral Functions and Both Domains, in
Image Analysis and Recognition, ICIAR 2014, LNCS 8814, 131140 (Springer).

D. Otero and E.R. Vrscay (2014),
Unconstrained
Structural SimilarityBased Optimization, in
Image Analysis and Recognition, ICIAR 2014, LNCS 8814, 167178 (Springer).

D. Otero and E.R. Vrscay (2014), "Solving Optimization Problems
Which Employ Structural Similarity as Fidelity Measure," in
Proceedings of IPCV'14, 474479. Available from
http://worldcompproceedings.com/proc/proc2014/ipcv.html, 474479.

I. KowalikUrbaniak, D. Brunet, J. Wang}, D. Koff,
N. SmolarskiKoff, E.R. Vrscay, B. Wallace and Z. Wang (2014),
The quest for 'diagnostically lossless'
medical image compression: A comparative
study of objective quality metrics for compressed medical images,
Proceedings SPIE 9037, Medical Imaging 2014, Available
from SPIE Digital Library doi: 10.1117/12:2043196 (15 pages).
2013

V. Capasso, H. Kunze, D. La Torre and E.R. Vrscay (2013),
Solving
inverse problems for biological models using the collage method
for differential equations, J. Mathematical Biology 67 (1),
2538.

H. Kunze, D. La Torre, F. Mendivil and E.R. Vrscay (2013),
Inverse problems for DEs and PDEs using the collage theorem: A
survey, Int. J. Applied Nonlinear Science 1 (1), 3051.

H. Kunze, D. La Torre and E.R. Vrscay (2013),
Collagebased
inverse problems for IFSM with entropy maximization and sparsity
constraints, Image Analysis and Stereology 32 (3), 183188.

E.R. Vrscay, D. Otero and D. La Torre (2013),
Hyperspectral images as functionvalued
mappings, their selfsimilarity and a class of fractal transforms, in
Image Analysis and Recognition, ICIAR 2013, LNCS 7950, 225234 (Springer).

I. C. Salgado Patarroyo, S. Dolui, O.V. Michailovich and E.R. Vrscay (2013),
Reconstruction of HARDI data using a split
Bregman optimization approach, in
Image Analysis and Recognition, ICIAR 2013, LNCS 7950, 589596 (Springer).

J. Ladan and E.R. Vrscay (2013),
The discrete orthonormal Stockwell transform
and variations, with applications to image compression, in
Image Analysis and Recognition, ICIAR 2013, LNCS 7950, 235244 (Springer).
2012

Book:
H.E. Kunze, D. La Torre, F. Mendivil and E.R. Vrscay (2012), Fractalbased
methods of analysis, 408 pp., Springer, New York. ISBN 9781461418900.

D. Brunet, E.R. Vrscay and Z. Wang (2012),
On the mathematical properties of the
structural similarity index, IEEE Transactions on Image Processing
21 (4), 14881499.

H. Kunze, D. La Torre and E.R. Vrscay (2012),
Solving inverse problems
for DEs using the collage theorem and entropy maximization,
Applied Math Letters 25 (12), 23062311.

H. Kunze, D. La Torre, F. Mendivil and E.R. Vrscay (2012),
Generalized
fractal transforms and selfsimilar objects in
cone metric spaces, Computers and Mathematics
with Applications 64, 17611769.

H. Kunze, D. La Torre, K. Levere and E.R. Vrscay (2012), "Solving inverse problems
for delay integral equations using the 'collage method' for fixed points,"
Int. J. Math. Stat. 11 (1), 111.

D. Glew and E.R. Vrscay (2012),
Selfsimilarity of images in the wavelet domain in
terms of $l2$ and structural similarity, in
Image Analysis and Recognition, ICIAR 2012, LNCS 7324, 131140 (Springer).

D. Glew and E.R. Vrscay (2012),
Max and min values of the structural similarity
function S(x,a) on the $L2$ sphere SR(a),
a in $RN$, in
Image Analysis and Recognition, ICIAR 2012, LNCS 7324, 6978 (Springer).

H. Yeganeh, Z. Wang and E.R. Vrscay (2012),
Adaptive windowing for
optimal visualization of medical images based
on a structural fidelity measure, in
Image Analysis and Recognition, ICIAR 2012, LNCS 7324, 321330 (Springer).

O. Michailovich, D. La Torre and E.R. Vrscay (2012),
Functionvalued mappings,
total variation and compressed sensing for diffusion MRI, in
Image Analysis and Recognition, ICIAR 2012, LNCS 7324, 286295 (Springer).

I. KowalikUrbaniak, E.R. Vrscay, Z. Wang, C. CavaroMenard, D. Koff,
B. Wallace and B. Obara (2012),
"The impact of skullbone intensity on the quality of compressed CT neuro
images," Proceedings of SPIE Conference on Medical Imaging 2012, Vol 8319, published
in Progress of Biomedical Optics and Imaging, 13 (35). 9 pages.

D. La Torre and E.R. Vrscay (2012),
"Fractalbased measure approximation with entropy maximization
and sparsity constraints,"
in Bayesian Inference and Maximum Entropy Methods in Science and
Engineering,
Proceedings of MaxEnt 2011, AIP Conference Proceedings, 1443, 6371 (American
Institute of Physics).
2011

D. La Torre and E.R. Vrscay (2011),
Generalized fractal transforms
and selfsimilarity: Recent results and applications,
Image Analysis and Stereology 30 (2), 6376 (2011).

N. Portman, U. Grenander and E.R. Vrscay (2011),
GRID macroscopic growth law and its application to image inference,
Quarterly in Applied Mathematics
69 (2), 227260, S0033569X(2011)011924.

N. Portman and E.R. Vrscay (2011),
Existence and uniqueness of solutions
to the GRID macroscopic growth equation,
Applied Mathematics and Computation
217 (21), 83188327.

D. La Torre and E.R. Vrscay (2011),
Random measurevalued image functions,
fractal transforms and selfsimilarity, Applied Mathematics Letters
24, 14051410.

D. Brunet, E.R. Vrscay and Z. Wang (2011)
A class of metrics based on the structural similarity index,
in Image Analysis and Recognition, ICIAR 2011,
LNCS 6753, 100110.
(Springer).

D. Brunet, E.R. Vrscay and Z. Wang (2011)
Structural similaritybased affine approximation and
selfsimilarity of images revisited,
in Image Analysis and Recognition, ICIAR 2011,
LNCS 6754, 264275.
(Springer).

A. Rehman, Z. Wang, D. Brunet and E.R. Vrscay (2011),
"SSIMinspired image denoising using sparse representations,"
ICASSP 2011, 11211124.
(Springer).
2010

H.E. Kunze, D. La Torre and E.R. Vrscay (2010),
Solving inverse problems
for variational equations using 'generalized collage methods' with
applications to boundary value problems, Nonlinear Analysis: Real
World Applications 11 (5), 37343743.

D. Brunet, E.R. Vrscay and Z. Wang (2010),
Structural similaritybased approximation of signals and images, in
Image Analysis and Recognition, ICIAR 2010},
Lecture Notes in Computer Science 6111, pp. 112.

A. Sanchez, C. Drapaca, S. Sivaloganathan and E.R. Vrscay (2010),
Elastography of biological tissue: Direct inversion methods that allow for local
shear modulus variations, in
Image Analysis and Recognition, ICIAR 2010, ibid., pp. 195206.
2009

J. Timko and E.R. Vrscay (2009),
SpinDependent Bohmian Electronic Trajectories for Helium,
Foundations of Physics 39, 10551071.

S.K. Alexander, P. Fieguth, M. Ioannidis and E.R. Vrscay (2009),
Hierarchical annealing for synthesis of binary porous media images,
Mathematical Geosciences 41 (4), 357378.

D. La Torre, E.R. Vrscay, M. Ebrahimi and M.F. Barnsley (2009),
Measurevalued images, associated fractal transforms and the selfsimilarity of images,
SIAM Journal of Imaging Sciences 2, 2, 470507.

H. Kunze, D. La Torre and E.R. Vrscay (2009),
A generalized collage method based upon the LaxMilgram functional for solving
boundary value inverse problems, Nonlinear Analysis; Theory, Methods and Applications
71, e13371343.

H. Kunze, D. La Torre and E.R. Vrscay (2009),
Inverse problems for random differential equations using the collage method for
random contraction mappings, J. Computational and Applied Mathematics
223, 2, 853861.

V. Capasso, H. Kunze, D. La Torre and E.R. Vrscay (2009),
Parametric estimation for deterministic and stochastic differential equations with
applications, Advances in Nonlinear Analysis:
Theory, Methods and Applications (S.Sivasundaram ed.), pp. 7184 (Cambridge Scientific).

D. Brunet, E.R. Vrscay and Z. Wang (2009),
The use of residuals in image denoising,
in Image Analysis and Recognition, ICIAR 2009,
Lecture Notes in Computer Science 5627, pp. 112
(Springer, BerlinHeidelberg).

N. Portman, U. Grenander and E.R. Vrscay (2009),
Direct estimation of biological growth properties from image data using the
'GRID' model,
in Image Analysis and Recognition, ICIAR 2009,
Lecture Notes in Computer Science 5627, pp. 832843
(Springer, BerlinHeidelberg).

M. Ebrahimi, E.R. Vrscay and A. Martel (2009),
Coupled multiframe superresolution
with diffusive motion model and total variation regularization,
Proceedings of the
2009 International Workshop on Local and Nonlocal
Approximation in Image Processing,
Tuusula, Finland, 1921 August 2009. 8 pp.

H. Kunze, D. La Torre and E.R. Vrscay (2009),
"On iterated multifunction systems,"
in Stereology and image analysis, Proceedings of the 10th
European Congress of ISS (V. Capasso et al. Editors), Societa'
Editrice Esculapio, Bologna, pp. 149155.

D. La Torre and E.R. Vrscay (2009),
"Generalized fractal transforms and selfsimilar images," in
in Stereology and image analysis, ibid., pp. 161167.

H. Kunze, D. La Torre and E.R. Vrscay (2009),
"Solving inverse problems for the Hammerstein integral operator," in
in Stereology and image analysis, ibid., pp. 168174.
2008

H. Kunze, D. La Torre and E.R.Vrscay (2008),
From Iterated Function Systems to
Iterated Multifunction Systems,
Communications on Applied Nonlinear Analysis
15 (4), 114.

M. Ebrahimi and E.R. Vrscay (2008),
Selfsimilarity in imaging, 20 years after 'Fractals Everywhere',
Proceedings of the 2008 International Workshop on Local and Nonlocal
Approximation in Image Processing, Lausanne, Switzerland, 2324 August 2008.

E.R. Vrscay (2008),
A simple model for affine selfsimilarity of images and its applications,
Proceedings of the 2008 International Workshop on Local and Nonlocal
Approximation in Image Processing, Lausanne, Switzerland, 2324 August 2008.

M. Ebrahimi and E.R. Vrscay (2008),
"Multiframe superresolution with no explicit motion estimation,"
Proceedings of the 2008 Interational Conference on Image Processing,
Computer Vision and Pattern Recognition,
IPCV 2008, Las Vegas, Nevada, 1417 July 2008.

S.K. Alexander and E.R. Vrscay (2008),
"IFS imaging beyond compression,"
Nonlinear Analysis: Theory, Methods and Applications 71, 12, e1215e1226.
(Proceedings of the World Conference on
Nonlinear Analysis, Orlando, Florida, 29 July 2008).

H. Kunze, D. La Torre and E.R. Vrscay (2008),
A generalized collage method based upon the LaxMilgram functional for solving
boundary value inverse problems,
Nonlinear Analysis: Theory, Methods and Applications 71, 12, e1337e1343.
(Proceedings of WCNA 2008).

G.S. Mayer and E.R. Vrscay (2008),
"Selfsimilarity of Fourier Domain Data",
Nonlinear Analysis: Theory, Methods and Applications 71, 12, e855e864.
(Proceedings of WCNA 2008).

D. La Torre and E.R. Vrscay (2008),
"Generalized fractal transforms for measurevalued images,"
Nonlinear Analysis: Theory, Methods and Applications 71, 12, e1598e1607.
(Proceedings of WCNA 2008).

S.K. Alexander, E.R. Vrscay and S. Tsurumi (2008),
A simple, general model for the affine selfsimilarity of images,
in Image Analysis and Recognition, ICIAR 2008,
Lecture Notes in Computer Science, 5112,
(Springer, BerlinHeidelberg) pp. 192203.

M. Ebrahimi and E.R. Vrscay (2008),
The role of scale in the context of the
nonlocalmeans filter,
in Image Analysis and Recognition, ICIAR 2008,
Lecture Notes in Computer Science, 5112,
(Springer, BerlinHeidelberg) pp. 170181.

G.S. Mayer, E.R. Vrscay, M.L. Lauzon, B.G. Goodyear and J.R. Mitchell (2008),
Selfsimilarity of images in the
Fourier domain, with applications to MRI,
in Image Analysis and Recognition, ICIAR 2008, ibid., pp. 4352.
2007

Book chapter:
D. La Torre, F. Mendivil and E.R. Vrscay (2007),
Iterated function systems on multifunctions, in
Math Everywhere, Deterministic and Stochastic Modelling in Biomedicine,
Economics and Industry, G. Aletti, M. Burger, A. Micheletti and D. Morale Eds., pp. 125138
(Springer Verlag, Berlin).

H.E. Kunze, D. La Torre and E.R. Vrscay (2007),
Random fixed point equations and inverse problems by collage theorem,
J. Math. Anal. Appl., 334, 11161129.

H.E. Kunze, D. La Torre and E.R. Vrscay (2007),
Contractive multifunctions, fixed point inclusions and iterated
multifunction systems, J. Math. Anal. Appl.,
330, 157173.

G.S. Mayer and E.R. Vrscay (2007),
Measuring information gain for frequencyencoded superresolution
MRI, Magnetic Resonance Imaging, 7, 10581069.

H.E. Kunze, D. La Torre and E.R. Vrscay (2007),
"Solving inverse problems for random equations and applications,"
Proceedings of the International Symposium on Inverse Problems, Design and Optimization,
Ed. G. Dulicravich et al., pp. 521527.

H.E. Kunze, D. La Torre and E.R. Vrscay (2007),
"Solving inverse problems for DEs by collage method and applications to
variational optimization,"
Proceedings of the International Symposium on Inverse Problems, Design and Optimization
(G. Dulicravich {\em et al.} Eds.), pp. 513520.

S.K. Alexander, E.R. Vrscay and S. Kovacic (2007),
"A simple model for image selfsimilarity with possible use of
mutual information," in Proceedings of EUSIPCO 07,
Poznan, Poland, September 2007, (5 pages).

G.S. Mayer and E.R. Vrscay (2007),
Iterated Fourier Transform Systems: A Method for Frequency
Extrapolation, in
Image Analysis and Recognition, ICIAR 2007, LNCS 4633,
728739. (Springer).

M. Ebrahimi and E.R. Vrscay (2007),
Solving the inverse problem of image zooming using 'Selfexamples',
Image Analysis and Recognition, ICIAR 2007, LNCS 4633,
117130. (Springer).

N. Portman, U. Grenander and E.R. Vrscay (2007),
New computational methods of construction of 'Darcyan' biological
coordinate systems, in
Image Analysis and Recognition, ICIAR 2007, LNCS 4633,
143156. (Springer).

M. Ebrahimi and E.R. Vrscay (2007),
"Nonlocalmeans singleframe image zooming,"
Proceedings of the 6th International Congress on Industrial and
Applied Mathematics (ICIAM), July 2007, Zurich, Switzerland.

M. Ebrahimi and E.R. Vrscay (2007),
"Regularization schemes involving selfsimilarity in imaging inverse
problems," Journal of Physics, Conference Series,
Proceedings of Applied Inverse Problems (AIP) 2007, June 2529, 2007,
University of British Columbia, Vancouver, Canada (15 pages).
2006

M. Ghazel, G. Freeman and E.R. Vrscay (2006),
Fractalwavelet image denoising revisited,
IEEE Transactions on Image Processing, 15, No. 9, 26692675.

G. Mayer and E.R. Vrscay (2006),
Mathematical analysis of "phase ramping" for superresolution
magnetic resonance imaging, in Image Analysis and Recognition, ICIAR 2006,
LNCS 4141, 8293. (Springer).

E.R. Vrscay (2006),
Continuous evolution of fractal transforms and nonlocal PDE imaging, in Image
Analysis and Recognition, ICIAR 2006, LNCS 4141, 446457. (Springer).

M. Ebrahimi and E.R. Vrscay (2006),
Fractal image coding as projections onto convex sets, in Image
Analysis and Recognition, ICIAR 2006, LNCS 4141, 493506. (Springer).

M. Ebrahimi and E.R. Vrscay (2006), "Regularized fractal image decoding," Proceedings of CCECE 2006, the
Canadian Conference on Electrical and Computer Engineering, Ottawa, Canada, pp. 19331938, IEEE Catalog Number 06CH37749C,
ISBN: 1424400384.

G.S. Mayer and E.R. Vrscay (2006), "Measures of information for superresolution MRI,"
Magnetic Resonance Materials in Biology, Physics and Medicine 19 (1), 6061 (2006).
2005

J. Bona and E.R. Vrscay (2005),
Continuous evolution of functions
and measures toward fixed points of
contraction mappings, in Fractals in Engineering: New Trends in Theory and Applications,
Ed. J. LevyVehel and E. Lutton (Springer Verlag, London), pp. 237253.

M. Ghazel, G. Freeman, E.R. Vrscay and R.K. Ward (2005),
Wavelet image denoising using
localized thresholding operators,
in Image Analysis and Recognition, ICIAR 2005,
LNCS 3656, 149158.
(Springer).

K. Wilkie and E.R. Vrscay (2005),
Mutual informationbased regionofinterest image coregistration,
in Image Analysis and Recognition, ICIAR 2005, LNCS 3656, 6372.

M. Ghazel, G. Freeman, E.R. Vrscay, R.K. Ward and R. Abugharbieh (2005), "Joint fractalwavelet image
denoising and interpolation," Proceedings of Canadian Conference on Electrical and Computer
Engineering, CCECE 2005, Saskatoon, Saskatchewan, May 14, 2005.
2004

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

C. Colijn and E.R. Vrscay (2004),
Quantum relaxation in hydrogen eigenstates
and twostate transitions Phys. Lett. A 327, 113122.

S.K. Alexander, P. Fieguth and E.R. Vrscay (2004), "Hierarchical annealing for scientific models,"
International Conference on Acoustics, Speech and Signal Processing (ICASSP 2004), Montreal,
PQ, 1721 May 2004. Proceedings, Volume 3, 3336 (Springer Verlag).
2003
2002

C.Colijn and E.R. Vrscay (2002)
Spindependent Bohm trajectories for hydrogen eigenstates
Physics Letters A 300 (45), 334340.
Erratum
Physics Letters A 316, 424 (2003).)

F. Mendivil and E.R Vrscay (2002),
"Fractal vector measures and vector calculus
on planar fractal domains," Chaos, Solitons and Fractals 14
(8), 12391254.

E.R. Vrscay (2002), "From Fractal Image Compression to FractalBased Methods
in Mathematics,"
in Fractals in Multimedia, IMA Volumes in Mathematics and Applications,
ed. M. Barnsley, D. Saupe
and E.R. Vrscay, Vol. 132 (Springer Verlag, New York) pp. 65106.

H. Kunze and E.R. Vrscay (2002), "Using the Picard Contraction Mapping to Solve
Inverse Problems in Ordinary Differential Equations," in Fractals
in Multimedia, ibid., pp. 157174.

F. Mendivil and E.R. Vrscay (2002),
"Self affine vector measures and calculus on
fractals," in Fractals in Multimedia, ibid., pp. 137156.
2001

Book chapter:
H. Hartenstein, M. Ruhl, D. Saupe and E.R. Vrscay (2001) "On the inverse
problem of fractal image compression," in Ergodic Theory, Analysis
and Efficient Simulation of Dynamical Systems, Ed. B. Fiedler
(Springer Verlag, Berlin Heidelberg), pp. 617647.
2000

M. Ghazel and E.R. Vrscay (2000), "An effective hybrid fractalwavelet
image coder using quadtree partitioning and pruning," Proceedings of the
Canadian Conference on Electrical and Computer Engineering, CCECE 2000,
Halifax, Nova Scotia, May, 2000, 5 pp.
1999

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

M. Ghazel, E.R. Vrscay and A.K. Khandani (1999), "An Interpolative
Scheme in Fractal Image Compression in the Wavelet Domain," in
Computer Analysis of Images and Patterns, Ljubljana, Slovenia, Aug. 1999
(Springer Verlag, Berlin), pp. 191200.

E.R. Vrscay and D. Saupe (1999), "Can one break the 'collage barrier'
in fractal image coding?" in Fractals: Theory and Applications
in Engineering, Ed. M. Dekking, J. LevyVehel, E. Lutton and C. Tricot
(Springer Verlag, London), pp. 307323.

B. Forte, F. Mendivil and E.R. Vrscay (1999),
"IFSType Operators on Integral Transforms," in
Fractals: Theory and Applications
in Engineering, Ed. M. Dekking, J. LevyVehel, E. Lutton and C. Tricot
(Springer Verlag, London), pp. 125138.
1998

E.R. Vrscay (1998)
A Generalized Class of FractalWavelet Transforms
for Image Representation and Compression of Images
Can. J. Elect. Comp. Eng. 23 (12), 6983.

B. Forte, F. Mendivil and E.R. Vrscay (1998),
"Chaos Games for Iterated Function Systems with Grey Level
Maps", SIAM J. Math. Anal. 29 (4), pp. 878890.

M.G.A. Crawford and E.R. Vrscay (1998),
Generalized coherent states for the PoschlTeller potential and a classical limit
Phys. Rev. A 57 (1) 106113.

R.D. Dony and E.R. Vrscay (1998), "IFS Coding Using an MPC Network Library,"
Canadian Conference on Electrical and Computer Engineering,
Waterloo, May 1998, 6164.

M. Ghazel, A.K. Khandani and E.R. Vrscay (1998), "Improving Fractal
Image Compression Schemes Through Quantization and Entropy Coding,"
Canadian Conference on Electrical and Computer Engineering,
Waterloo, May 1998, 661664.

Book chapter:
B. Forte and E.R. Vrscay (1998),
Theory of Generalized Fractal
Transforms, in Fractal Image Encoding and
Analysis, Ed. Y. Fisher (Springer Verlag, New York).
NATO Advanced Study Institute, Trondheim,
Norway, July 817, 1995.

Book chapter:
B. Forte and E.R. Vrscay (1998),
Inverse Problem
Methods for Generalized Fractal
Transforms, in Fractal Image Encoding and
Analysis, ibid..
1997

R.A. Wannamaker and E.R. Vrscay (1997),
"Fractal Wavelet Compression of Audio Signals"
J. Audio Eng. Soc. 45 (78), 540553

S.M. McRae and E.R. Vrscay (1997),
"Perturbation Theory and
the Classical Limit of Quantum Mechanics
J. Math. Phys. 38, 28992921.

F. Mendivil and E.R. Vrscay (1997),
"Correspondence between FractalWavelet Transforms and
Iterated Function Systems with GreyLevel Maps,"
in Fractals in Engineering, Ed. J. Levy Vehel, E. Lutton
and C. Tricot (Springer Verlag, New York).

F. Mendivil and E.R. Vrscay (1997), "FractalBased Techniques in Image Compression,"
Canadian Conference on Electrical and Computer Engineering,
St. John's, Newfoundland, May 1997, 486489.

E.R. Vrscay and F. Mendivil (1997), "Generalized FractalWavelet Transforms
for Image Representation and Compression,"
Canadian Conference on Electrical and Computer Engineering,
St. John's, Newfoundland, May 1997, 490495.
1996
1995
1994

B. Forte, M. LoSchiavo and E.R. Vrscay (1994), "Continuity
Properties of Attractors for Iterated Fuzzy Set Systems",
J. Australian Math. Soc. Ser. B 36, 175193.

B. Forte and E.R. Vrscay (1994) "Solving the Inverse Problem for
Function/Image Approximation Using Iterated Function Systems I.
Theoretical Basis", Fractals 2, 325334, as part of the
Proceedings of the conference "Fractals in Engineering,"
Montreal, June 14, 1994.

B. Forte and E.R. Vrscay (1994) "Solving the Inverse Problem for
Function/Image Approximation Using Iterated Function Systems II.
Algorithm and Computations", Fractals 2, 335346, as part of the
Proceedings of the conference "Fractals in Engineering,"
Montreal, June 14, 1994.

S.M. McRae and E.R. Vrscay (1994),
"ClassicalQuantum Correspondence in Time Dependent
Perturbation Theory," in
Coherent States: Past, Present and Future, edited by
D.H. Feng, J.R. Klauder and M.R. Strayer. (World Scientific,
New Jersey), pp. 315329.
1993

P. Centore and E.R. Vrscay (1993), "Continuity of Attractors and
Invariant Measures of Iterated Function Systems,"
Canadian Math. Bull. 37, 315329.

B.R. McQuarrie and E.R. Vrscay (1993),
RayleighSchrodinger
Perturbation Theory to Large Order for Radial KleinGordon
Equations Phys. Rev. A 47, 868878.

P.M. Benoit S.M. McRae and E.R. Vrscay (1993),
"ClassicalQuantum Correspondence
in Perturbation Theory," in
Quantum Dynamics of Chaotic Systems:
Proceedings of the Third Drexel
Symposium on Quantum Nonintegrability, May 2022, 1992 (Gordon and Breach,
Langhorne, PA).
1992
1991

E.R. Vrscay (1991), "Irregular Behaviour Arising From
Quasiperiodic Forcing of Simple Quantum Systems: Insight from
Perturbation Theory", J. Phys. A: Math. Gen 24, L463L468.

E.R. Vrscay and D. Weil (1991),
Missing Moment and Perturbative
Methods for Polynomial Iterated Function Systems Physica D
50, 478492.

C.C. Gerry, R. Grobe and E.R. Vrscay (1991),
Squeezed Vacuum
States in a Nonlinear Medium Modulated by Periodic Kicking
Phys. Rev. A 43, 361370.

Book chapter:
E.R. Vrscay (1991), "Iterated Function Systems: Theory, Application
and the Inverse Problem", NATO
Advanced Study Institute on Fractal
Geometry and Analysis, NATO ASI Series C 346, edited by J. Belair
and S. Dubuc, p. 405468 (Kluwer, Dordrecht, The Netherlands).
1990

T.C. Scott, R.A. Moore, G.J. Fee, M.B. Monagan and E.R. Vrscay (1990),
"Perturbative Solutions of Quantum Mechaical Problems by
Symbolic Computation", J. Comp. Phys. 87, 366395.

S. Arianatnam, W.C. Xie and E.R. Vrscay (1990), "Chaotic
Motion Under Parametric
Excitation", Dynamics and Stability of Systems 4, 111130.

E.R. Vrscay (1990), "Moment and Collage Methods for the Inverse
Problem of Fractal Construction with Iterated Function Systems",
in Fractals in the Fundamental and Applied Sciences,
H.O. Peitgen, J.M. Henriques and L.F. Penedo, Editors,
p. 443461 (North Holland).

C. Cabrelli, U. Molter and E.R. Vrscay (1990),
Recurrent Iterated Function
Systems: Invariant Measures, A Collage Theorem and Moment Relations
in Fractals in the Fundamental and Applied Sciences,
H.O. Peitgen, J.M. Henriques and L.F. Penedo, Editors,
p. 7180 (North Holland).
1989

E.R. Vrscay and C.J. Roehrig (1989),
Using Moments", in Computers and Mathematics, E. Kaltofen and S.M. Watt, Editors.

C.C. Gerry and E.R. Vrscay (1989),
Dynamics of pulsed SU(1,1) coherent states
Phys. Rev. A 39 (11), 57175724.

C.C. Gerry, P.K. Ma and E.R. Vrscay (1989),
Dynamics of SU(1,1) coherent states driven by a damped harmonic oscillator
Phys. Rev. A 39 (2), 668674.
1988
1986