Recons.zip

Regularized reconstruction algorithms

Hello,
Just to be helpful and to obtain some quick preliminary results, I load 3 reconstruction algorithms and a processor script to call on the forward operator and each algorithm, i.e. CGNE, Tikhonov reconstruction and Lagged Diffusivity Fixed Point Iteration.
I just would like to get some feedback from anyone uses the codes. References where more information can be found are available within the codes. Any copyright or licence are not meant to be required as this is not a complete professional toolbox, and not much should be expected as results, but I still need to fill in some boxes to complete this load. Let me brief what's not present in the algorithms here; Algorithms do not really deal with the noise since this must be defined per problem by the users. Regularization parameter choice for the lagged diffusivity algorithm is in our privacy since it is a result of some mathematics.
Furthermore, boundary conditions are to be defined per problem. Attached picture is a result of lagged diffusivity algorithm after applying the code to tomo.m file provided by Per Christian Hansen. I also tested the same code on Emission Tomography of which the forward operator and the measurement are provided by John Bardsley, and I obtained a result with relative error value 0.33. Some graphical results are also available in the folder. You will see very smooth reconstruction of the cartoon images. It was obtained when pseudo inverse was given as initial guess.
I also acknowledge John Bardsley's help for teaching me how to use his complete toolbox. I attended Inverse Problem-3 class by professor Thorsten Hohage at the University of Goettingen, where I'm still phd. Thanks to that class, we learnt how to design regularization algorithms as a combination of CG iteration. For further questions, feel free to contact me per e-mail and as mentioned above every criticism is more than welcomed.