Preface

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

E

Y

is a canonical example of an inverse problem. Typically inverse problems are ill-

posed.

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

is

an important branch of

Image Science

and deals with image analysis in medical

applications.

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

j

survey papers to provide an overview and perspectives

vii