This volume contains the refereed proceedings of the Special Session on In-
teraction of Inverse Problems and Image Analysis held at the annual meeting of
the American Mathematical Society which took place in New Orleans, Louisiana,
January 10-13, 2001.
The volume contains 15 papers, 14 of which are authored or coauthored by a
participant at the Session. One paper is by an invited speaker who was not able to
participate at the meeting.
Inverse Problems
deal with determining for a given input-output system an
input that produces an observed output, or of determining an input that produces
a desired output. In terms of an operator T acting between say two normed spaces
X and Y, the problem of solving the equation T(x)
y for given data y
is a canonical example of an inverse problem. Typically inverse problems are ill-
Important examples of ill-posed inverse problems include integral equations
of the first kind, tomography, and inverse scattering.
Signal Analysis/Processing
deals with digital representations of signals and their analog reconstructions from
digital representations.
Image Analysis
deals with problems such as image recov-
ery, enhancement, feature extraction, and motion detection.
Medical Imaging
an important branch of
Image Science
and deals with image analysis in medical
The common thread among the areas of Inverse Problems, Signal Analysis, and
Image Analysis is a canonical problem of recovery of an object (function, signal,
picture) from partial or indirect information about the object (often contaminated
by noise). Both Inverse Problems and Imaging Science have emerged in recent
years as interdisciplinary research fields with profound applications in many areas
of Science, Engineering, Technology, and Medicine. Research in Inverse Problems
and Image Processing has rich interactions with several areas of Mathematics, and
strong links to Signal Processing, Variational Problems, Applied Harmonic Analysis
and Computational Mathematics.
The goal of the Special Session on Interaction of Inverse Problems and Image
Analysis was to gather a group of mathematicians and a few scientists and engineers
from universities and research centers to report on recent research advances and to
provide motivation for mathematicians interested in learning about the interaction
of these two fields. For the latter goal, a couple of the invited 20-minute talks
provided overview presentations in the two areas. This facilitated understanding of
other invited talks and encouraged non-experts to attend the session. The spirit of
some of the expository presentations is conveyed in several papers in this volume.
The volume contains carefully refereed and edited original research papers and
a few high-level expository
survey papers to provide an overview and perspectives
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