| Review: |
Inverse problems are mathematical problems that arise when ones goal is to recover ‘interior’ or ‘hidden’ information from ‘outside’, or otherwise available, noisy data. When we solve an inverse problem, we compute the source that gives rise to some observed data, using a mathematical model for the relation between the source and data. This textbook covers the basic subjects, focusing on the computational aspects. It aims to give the reader sufficient background in mathematics and numerical methods to understand the basic difficulties associated with linear inverse problems, to analyse the influence of measurement and approximation errors, and to design practical algorithms for computing regularized/stabilized solutions to these problems. There are chapters on: The Fredholm integral equation of the first kind; Discretizations of linear inverse problems; Regularization methods; Choosing the regularization parameter; Iterative regularization; Solving real problems; and The use of discrete smoothing norms. |