IJPAM: Volume 60, No. 4 (2010)
INTEGRAL EQUATION AND ITS RANDOM ANALOG
USING THE ``COLLAGE METHOD'' FOR FIXED POINTS





College of Physical and Engineering Science
University of Guelph
50, Stone Road East, Guelph, Ontario, N1G 2W1, CANADA



University of Milan
Milan, ITALY
e-mail: davide.latorre@unimi.it

University of Waterloo
Waterloo, Ontario, N2L 3G1, CANADA
e-mail: ervrscay@math.uwaterloo.ca
Abstract.Many inverse problems in applied mathematics can be formulated as the approximation of a target element in a complete metric space
by the fixed point
of an appropriate contraction mapping
.
The method of collage coding seeks to solve this problem by finding a contraction mapping
that minimizes the
so-called collage distance
. In this paper, we develop a collage coding framework for inverse problems
involving deterministic or random Hammerstein integral operators. Such operators are used to model image blurring. We
illustrate the method with examples.
Received: March 6, 2010
AMS Subject Classification: 45Q05, 45R05, 60H25
Key Words and Phrases: Hammerstein integral equations, inverse problems, fixed point equations, random fixed point equations, collage theorem
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 4