June 19, 2008
I’m releasing part of the code developed during my PhD. Those are tools useful in the field of convex processing, and more precisely to solve a problem called convex feasbility problem.
This is based on Qt4, and released mostly under the GPL (with an added restriction : you must cite my work if you use this). Oh.. and there are unit tests, examples, and documentation, too.
caution : rest of the post is for those mathematically oriented people, and no more related to free software.
The convex feasbility problem is to find a point in the intersection of closed convex sets inside a Hilbert space. Believe it or not, quite some real-life problems can be formulated as such, for examples some image reconstruction problems in medical imaging, or also in the field of signal processing.
This code provides the necessary tools to play and test those algorithms. Besides all elementary methods on Euclidian/Hilbert Space, it provides a way to compute projections on different interesting convex sets. There are also the needed tools to experiment with tomography, which is one of the main application in my PhD. You can compute the radon transform of an image and use this as data in convex feasibility formulation.
This is of course mostly of interest for those working in convex optimization and/or tomography. I want to highligh the fact that sharing such kind of code is very rare in this community. I would have gained a lot of time at the beginning of my thesis if other people had provided such code.