A good book on inverse problems for engineers

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.

I have found that Vogel's Computational Methods for Inverse Problems is a spectacular reference.

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