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February  2007, 1(1): i-iii. doi: 10.3934/ipi.2007.1.1i

Editorial

Lassi Päivärinta 1, , Matti Lassas 1, and  Jackie (Jianhong) Shen 2,

1. 

Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 FI-00014
2. 

Attorney at CBS Corporation, San Francisco CA, United States

Published  January 2007

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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Citation: Lassi Päivärinta, Matti Lassas, Jackie (Jianhong) Shen. Editorial. Inverse Problems & Imaging, 2007, 1 (1) : i-iii. doi: 10.3934/ipi.2007.1.1i
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