Work
A form of the discrete Radon transform known as the Mojette transform was invented here by the professor of my team Jean-Pierre Guedon. This transform has been used in medical imaging (CT reconstruction), image processing (detecting straight lines, motion detection), and in robust packet data transmission and distributed storage.
The Mojette projections (as with Radon projections) project the 2D image to a 1D function, the same as X-rays can be used to project a 3D chest to a 2D chest X-ray image.
Transmission example: you can obtain 5 Mojette projections of the data (where any 3 of these is enough to reconstruct the original data) and transmit each of these as a packet on individual channels. If any 2 of these packets are lost or corrupted in transmission the data can still be recovered from the remaining three projections. This can be tuned to the transmission quality of service to have Y projections with any X sufficient for reconstruction.
Distributed storage example: same idea as transmission but instead of sending the projections, they are stored on 5 separate network nodes. To recover the file any 3 of the 5 projections must be retrieved. Therefore if some nodes are stolen, destroyed, off or busy, the file can still be retrieved.
The projection angle set (e.g. the angles from which we X-ray the chest) required to reconstruct the data can be selected almost arbitrarily, so if we chose projections that have a similar angle, the projections themselves are also very similar. If we remove this correlation between projections (in an invertible way) we compress the data.
The Mojette projections have been shown to be very sensitive, just a few errors in the data can cause the reconstruction to become nonsense. This makes encryption of Mojette projections quite simple.
Highlights? Well the project is for the Louvre museum image data base. Objective: to compress, encrypt and robustly store the images across the museums of France. I am working with massive images from the Louvre, up to 20,000 x 20,000 pixels. I haven't got to visit there yet though.
The people here are great, just like at Monash. It's a good experience to work with a new group of people, though, to get different perspectives and they have different strengths and weaknesses in the research. I have learnt a lot and hopefully helped a lot.
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