I am currently working on a problem that may be interpreted as recovering an unknown function from its Radon transform. 


Unfortunately I don't have any background in Radon transform, but need to quickly get what I need for solving my problem.


The questions are: 


* are there properties (e.g. degree of smoothness) of the Radon transform that are related to the corresponding properties of the original function?
* is it possible to incorporate restrictions into the reconstruction of a function from its Radon transform? An example for such a restriction would knowledge about the geometry and absorbation properties of bones in computer tomography (that knowledge would amount knowing, how much energy of an x-ray is absorbed in a known interval)?
* does incorporating known restrictions into the recovery of the function improve the quality of the numerical reconstruction of that function?


I would also appreciate pointers to good "hands on" material on the Radon transform; preferably online articles and free software.



Basic Questions about Radon Transforms
to follow up on my comment with a few more pointers: 


Even if you will not be using the ready-to-use [MATLAB toolbox](http://www.mathworks.nl/help/images/the-inverse-radon-transformation.html) for Radon transform inversion, you will likely want to use MATLAB as a platform for the development and experimentation with your own codes. (It makes little sense to write all the visualisation and data management code yourself, in particular if, as you write, you are in a hurry.)


Various numerical techniques were discussed by Kunyansky in 2012, [here](http://omega.uta.edu/~aktosun/cbms2012/links.html) you can find his lecture notes and numerical algorithms with examples.


A tutorial on the use of MATLAB to invert Radon transforms can be found [here](http://www.math.upenn.edu/~cle/m584/matlab/ws2.html).


If you insist on open-source software, you can try [freemat](http://freemat.sourceforge.net/) with this inversion [toolbox](http://web.eecs.umich.edu/~fessler/code/index.html).


