Mojette Transform

The Mojette Transform is an application of discrete geometry. More specifically, it is a discrete and exact version of the Radon transform, thus a projection operator. The IRCCyN laboratory - UMR CNRS 6597 in Nantes, France has been developing it since 1994. The first characteristic of the Mojette Transform is using only additions and subtractions. The second characteristic is that the Mojette Transform is redundant, spreading the initial geometrical information into several projections. This transform uses discrete geometry in order to dispatch information onto a discrete geometrical support. This support is then projected by the Mojette operator along discrete directions. When enough projections are available, the initial information can be reconstructed. The Mojette transform has been already used in numerous applications domains: Medical tomography Network packet transfer Distributed storage on disks or networks Image fingerprinting and image cryptography schemes After one year of research, the first communication introducing the Mojette Transform was held in May 1995 in the first edition of CORESA National Congress CCITT Rennes. Many others will follow it for 18 years of existence. In 2011, the book The Mojette Transform: Theory and Applications at ISTE-Wiley was well received by the scientific community. All this support has encouraged the IRCCyN research team to continue the research on this topic. Jeanpierre Guédon, professor and inventor of the transform called it: "Mojette Transform". The word "Mojette" comes from the name of white beans in Vendee, originally written "Moghette" or "Mojhette". In many countries, bean is a basic educational tool representing an exact unit that teaches visually additions and subtractions. Therefore, the choice of the name "Mojette" serves to emphasize the fact that the transform uses only exact unit in additions and subtractions. The original purpose of the Mojette Transform was to create a discrete tool to divide the Fourier plane into angular and radial sectors.