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I'm looking for a book on inverse problems which is suitable for engineers; both introduction and practical applications are required. Currently I'm looking to Parameter Estimation and Inverse Problems by Richard C. Aster, Brian Borchers and Clifford H. Thurber. I mostly look for applied problems, guides on the methods, requirements and constraints etc, that can be used to solve a particular problem.

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  • $\begingroup$ Have you seen this and this? $\endgroup$ – J. M. is a poor mathematician May 10 '12 at 14:21
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    $\begingroup$ tarantola's book (the second one of J.M.'s links) can be downloaded for free from his personal website $\endgroup$ – begeistzwerst May 10 '12 at 14:25
  • $\begingroup$ @J.M., it seems the first one is easier to start with, is it? $\endgroup$ – zeliboba May 10 '12 at 14:43
  • $\begingroup$ I liked both (and no, I'm not a specialist); they worked nicely for me, but you should look into them and draw your own conclusions. $\endgroup$ – J. M. is a poor mathematician May 10 '12 at 14:46
  • $\begingroup$ there is a book by A.G. Ramm called Inverse problems, mathematical and analytical techniques with applications to engineering which I used and found to be a pretty good introduction to the subject. $\endgroup$ – tibL May 10 '12 at 16:16
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P.C. Hansen, Discrete Inverse Problems: Insight and Algorithms, 2010, 213p
"for engineering grad students ... gentle introduction ... hands-on experience using the Matlab package Regularizaton Tools". PDFs for several of the chapters are here.

Added: teachers might like C.W. Groetsch, Inverse Problems: Activities for Undergraduates, 1999, 222p: many examples, some historical, from different fields.

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    $\begingroup$ Just for clarification, the PDFs you link to at www2.imm.dtu.dk/~pcha/DIP seem to be slides rather than the book chapters themselves. $\endgroup$ – J W Apr 24 '16 at 8:38
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I have found that Vogel's Computational Methods for Inverse Problems is a spectacular reference.

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    $\begingroup$ Some details about what makes Vogel a spectacular reference would be great, $\endgroup$ – J W Jun 19 '18 at 9:16
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I have just published an introductory book on inverse problems suitable for engineers, which may suit your needs. It presents easy to grasp fundamental ideas as well as applications, its pre-requisites are kept to a minimum, and includes step by step exercises.

http://www.springer.com/engineering/computational+intelligence+and+complexity/book/978-3-642-32556-4

https://link.springer.com/book/10.1007%2F978-3-642-32557-1

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There is a list of books on inverse problems. Unfortunately it is from 1998, but the author (who happens to be Brian Borchers, one of the coauthors of your book) indicated for every item how much math is needed. Perhaps you can find something suitable.

Personally, I have only looked into [EHN96] and a new 2010 edition of [Kir96], both of which are mainly dealing with the mathematical theory of inverse problems, so they probably are not what you are looking for.

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  • $\begingroup$ are there new findings/developments in the field of inverse modeling which would really encourage to search for recent books? $\endgroup$ – zeliboba May 10 '12 at 15:11
  • $\begingroup$ i am not a specialist either, so i don't know. but you are right, if you are new to the field, it should not matter whether you read a recent book or one from the 90s. still it would be nice having an up-to-date list. $\endgroup$ – begeistzwerst May 10 '12 at 15:18
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This is a copy of my answer to this question at matheducators.se which I add here for convenience.

Some more recent books on inverse problems that also stress applications are:

A light introduction (short, concise, a little more focused on math, but still with good applications) is

In a similar spirit, but older and a little longer, but also very well written is

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The book, An Introduction to Inverse Problems with Applications, mentioned in Francisco Moura Neto's answer certainly appears both applied and gentle as an introduction. The main prerequisite seems to be linear algebra, but some exposure to multivariable calculus, numerical methods and differential equations would be valuable too.

Another option is the course notes on inverse problems by Fox, Nicholls & Tan. These notes go somewhat faster than the abovementioned book and spend several chapters on nondeterministic methods.

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