THE ROLE OF APPLIED MATHEMATICS
in imaging has increased during the past ten yearsthanks to the increased performance
of computers and some decisive steps toward statistical image modeling. The
mathematical paradigm for representing an image is still unknown. However, recent
results, such as this one which connects the compression rate of a picture to its
"Sobolev index", illustrates well the use of mathematics to understand images.
Just as wavelets, imaging is a "scientific crossroad" where non linear differential
equations (work by J.L. Morel, P.L.Lions, L. Alvarez, S. Osher and L. Rudin) meet
Ising models of statistical physics (works by S.Geman and D. Geman). Finally, during
recent years, imaging became more and more a means of surveillance (radar, satellite),
reconnaissance (remote sensing and medical diagnosis). Applied mathematics (and physics)
can contribute to a better interpretation of data in these domains.
