Quaternion Fourier Transforms for Signal and Image Processing

This book presents the state of the art, together with the most recent research results, in the use of Quaternion Fourier Transforms (QFT) for the processing of color images and complex valued signals. It is based on the work of the authors in this area since the 1990s and presents the mathematical concepts, computational issues and applications on images and signals. The book, together with the MATLAB toolbox developed by two of the authors (QTFM), allows the reader to make use of the presented concepts and experiment with them in practice through the examples provided in the book.
Following the introduction, Chapter 1 introduces the quaternion algebra H and presents some properties which will be of use in the subsequent chapters. Chapter 2 gives an overview of the geometric transformations which can be represented using quaternions. Chapter 3 provides the definition and properties of QFT. The signals and images considered are those with vector-valued samples/pixels.
The fourth and final chapter is dedicated to the illustration of the use of QFT to process color images and complex improper signals. The concepts presented in this chapter are illustrated on simulated and real images and signals.