Dedicated to Nicole DeLaittre
The inverse problems studied in this book take its roots in medical imaging such as electrical impedance tomography (EIT) and similar methods from geophysics with applications to the oil & gas production industry. It was motivated by needs of non-destructive and non-intrusive methods for study of hidden objects such as internal human organs or Earth's natural resources.
The inverse problems in this book are formulated as the mathematical problems of recovering the coefficients of functional and differential systems of equations from data about their solutions. These problems are opposite in some sense to the forward problems of evaluating functions. The inverse problems are well suited for computer simulations and many classical and current mathematical problems can be restated with ease as discrete or continuous inverse problems.
The tools of study and solutions of the inverse problems considered in this book allow one to "see inside" the objects using data about the electro-magnetic fields and sound waves observed at the boundary or outside the object.
Copyright © 2012 by David V. Ingerman
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