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 systems of differential/difference equations from 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 fundamental mathematical problems can be naturally restated as inverse problems.
The techniques of study and solutions of the inverse problems considered in this book allow one to "see inside" a body, using the sound waves or electro-magnetic fields data at the boundary or outside the body.