A good book on inverse problems for engineers 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.
 A: 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.
A: I have found that Vogel's Computational Methods for Inverse Problems is a spectacular reference.
A: 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
A: 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:


*

*Statistical and Computational Inverse Problems, Jari Kaipio and Erkki Somersalo, https://www.springer.com/de/book/9780387220734

*Linear and Nonlinear Inverse Problems with Practical Applications, Jennifer L. Mueller and Samuli Siltanen, https://epubs.siam.org/doi/book/10.1137/1.9781611972344
A light introduction (short, concise, a little more focused on math, but still with good applications) is


*

*A Taste of Inverse Problems: Basic Theory and Examples, Martin Hanke, https://epubs.siam.org/doi/book/10.1137/1.9781611974942
In a similar spirit, but older and a little longer, but also very well written is


*

*Inverse Problems in the Mathematical Sciences, Charles W. Groetsch, https://www.springer.com/la/book/9783322992048
A: 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.
A: 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.
