Statistical and Computational Inverse Problems

This book covers the statistical mechanics approach to computational solution of inverse problems, an innovative area of current research with very promising numerical results. The techniques are applied to a number of real world applications such as limited angle tomography, image deblurring, electical impedance tomography, and biomagnetic inverse problems. Contains detailed examples throughout and includes a chapter on case studies where such methods have been implemented in biomedical engineering.

From the reviews: "The book is devoted to the development of the statistical approach to inverse problems … . The content is written clearly and without citations in the main text. Every chapter has a section called ‘Notes and comments’ where the citations and further reading, as well as brief comments on more advanced topics, are provided. The book is aimed at postgraduate students … . The book also will be of interest for many researchers and scientists working in the area of image processing." (Tzvetan Semerdjiev, Zentralblatt MATH, Vol. 1068, 2005) "Inverse problems are usually ill-posed in the sense that a solution need not exist, need not be unique, and depends in a discontinuous way on the data … . there have been two quite separate communities dealing with such problems, one basing their methods mainly on functional analysis, the other one on statistics. … several attempts have been made to bridge the gap between these two groups. The book under review … is a further, quite successful attempt in this direction." (Heinz W. Engel, SIAM Review, Vol. 48 (1), 2006)