The fields of inverse problems and imaging are new and flourishing
branches of both pure and applied mathematics. In particular, these
areas are concerned with recovering information about an object from
indirect, incomplete or noisy observations and have become one of
the most important and topical fields of modern applied mathematics.
The modern study of inverse problems and imaging applies a wide
range of geometric and analytic methods which in turn creates new
connections to various fields of mathematics, ranging from geometry,
microlocal analysis and control theory to mathematical physics,
stochastics and numerical analysis. Research in inverse problems
has shown that many results of pure mathematics are in fact crucial
components of practical algorithms. For example,a theoretical
understanding of the structures that ideal measurements should
reveal, or of the non-uniqueness of solutions,can lead to a dramatic
increase in the quality of imaging applications. On the other
hand,inverse problems have also raised many new mathematical
problems. For example, the invention of the inverse spectral method
to solve the Korteweg-de Vries equation gave rise to the field of
integrable systems and the mathematical theory of solitons.
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