This application-oriented textbook on Fourier techniques in imaging methods is largely written from the perspective of an engineer. The main goal of the author is to present a consistent mathematical description of linear imaging systems, where images are defined as bivariate functions or matrices. The contents of this book can be grouped into 5 parts. The first part (with Chapters 1‒5) starts with a short introduction of the main topic and presents some basic facts on linear algebra. The second part (with Chapters 6‒13) introduces some special functions and describes the main properties of continuous transforms (such as Fourier, Hankel and Radon transforms). The third part (with Chapters 14‒15) discusses results of sampling theory and discrete/fast Fourier transforms. In the fourth part (with Chapters 16‒20), the imaging systems are described as linear filters, including the inverse, matched, Wiener and Wiener‒Helstrom filters. The last part (with Chapters 21‒23) specifies some applications to model optical imaging systems, including holography. Numerous graphical examples illustrate the concepts. Many exercises are included at the end of each chapter. Software programs used to create the examples are available online. This comprehensive textbook represents a practical review of Fourier techniques in imaging methods. It will be very useful for graduate students (in engineering, science, computer science, and applied mathematics) as well as engineers interested in linear imaging systems.
Manfred Tasche (Rostock)