Author Description
The factorization method is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. Aimed at students and researchers in Applied Mathematics, Physics and Engineering, this text introduces the reader to this promising approach for solving important classes of inverse problems. The wide applicability of this method is discussed by choosing typical examples, such as inverse scattering problems for the scalar Helmholtz equation, a scattering problem for Maxwell's equation, and a problem in impedance and optical tomography. The last section of the book compares the Factorization Method to established sampling methods (the Linear Sampling Method, the Singular Source Method, and the Probe Method).
Menrva's Summary
THE THESIS
This text investigates the mathematical framework and practical application of the factorization method for solving inverse scattering and tomography problems. Authors Andreas Kirsch and Natalia Grinberg provide a structured introduction to this technique, drawing upon their expertise in applied mathematics to explain how the method identifies unknown shapes or objects from scattered wave data. The book serves as a technical resource for students and researchers who require a rigorous approach to solving inverse problems in physics and engineering.
THE SCOPE MAP
What You Will Find
- Mathematical derivations for inverse scattering problems involving the scalar Helmholtz equation.
- Analysis of scattering problems related to Maxwell's equations.
- Applications in impedance and optical tomography.
- Comparative analysis of the factorization method against the Linear Sampling Method, the Singular Source Method, and the Probe Method.
Scope Limits
- The text focuses primarily on the mathematical theory and specific inverse scattering applications rather than broad, general-purpose inverse problem solving.
- It assumes a foundational background in mathematics and physics, omitting introductory material for non-specialists.
THE AUTHORITY PERSPECTIVE
Experts and researchers in the field of inverse problems recognize this work as a specialized, high-level reference for understanding the factorization method. Readers frequently note the technical density of the prose, which is tailored specifically for an audience of graduate-level mathematicians and engineers.
Page Count:
207
Publication Date:
2007-01-01
Publisher:
OUP Oxford
ISBN-10:
019152669X
ISBN-13:
9780191526695
Scattering Theory
Mathematics Statistics
Engineering
Tomography
Physics
Applied Mathematics
Mathematics - General
Mathematics