The Mojette Transform
theory and applications
Publication Date: February 2009 Hardback 288 pp.
Applied sciences in the 20th century have developed and used unitary transforms for concentrating energy. Now, the challenge lies in the expression and use of redundancy to build redundant systems. The Mojette transform is a very simple transform using only additions but with strong properties that break this challenge.
The first part of the book gives the basics of the Mojette transform both mathematically and the corresponding optimal algorithms. The second part exemplifies its use through different fields: image representation, watermarking, medical imaging, distributed storage, information and cryptography.
This book about a discrete exact Radon transform explains how to usefully produce and cope with redundancy for solving 21st century problems
First Part. Mojette Theory
1. Discrete Geometry and Projections, David Coeurjolly, Nicolas Normand.
2. Discrete Versions of the Radon Transform, Imants Svalbe, Jeanpierre Guédon.
3. Direct Mojette Transform, Jeanpierre Guédon, Nicolas Normand.
4. Reconstructability with the Inverse Mojette Transform, Jeanpierre Guédon, Nicolas Normand.
5. Inverse Mojette Transfrom Algorithms, Nicolas Normand, Imants Svalbe, Pierre Evenou and Andrew Kingston.
6. Multiresolution Mojette Transform, Andrew Kingston, Florent Autrusseau, Benoît Parrein.
Second Part. Applications
7. Communication, Networks and Storage, Benoît Parrein, Fadi Boulos, Nicolas Normand and Pierre Evenou.
8. Mojette Discrete Tomography, Myriam Servières, Jeanpierre Guédon, Nicolas Normand and Yves Bizais.
9. Lossless Compression, Andrew Kingston, Florent Autrusseau.
10. Mojette-based Security, Andrew Kingston, Florent Autrusseau, Eric Grall, Thierry Hamon and Benoît Parrein.
About the Authors
Jeanpierre Guédon is a Professor at the University of Nantes, France. His fields of interest are centered on applying mathematics to medical imaging, information theory and imaging science.