Geophysical Data Analysis: Discrete Inverse Theory Volume 45

This is a really good book if you are in to high level data processing. It's not a book for people that are starting in the area of geophysics. The important aspect of this book it's that it has a very detailed explanation of the mathematics involved in data processing. Things like Fourier transforms, designing filters, tomography etc. The material of the book is extremely dens but it's really well explained as long as you remember your calculus and lineal algebra.

Incredible applications of linear algebra. This book covers the meat of inverse problems in data analysis. Very clear presentation with many examples. It is a very challenging read nonetheless, even if you have a lot of familiarity with linear algebra. It uses linear algebra in a much different way than what people get exposed to in math courses, focusing on how to solve non-invertible linear systems. Although the title has the word "geophyical" in it, there is no emphasis on the geophysical sciences, it would be useful to anyone doing discrete inverse problems. No prerequisites other than basic linear algebra (matrix arithmetic) and patience.