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