Numerical methods and software for functional magnetic resonance images reconstruction (Q2718066)

This paper is devoted to the problem on functional magnetic resonance imaging (fMRI) reconstruction and its application in the medical area. The mathematical aspect of this problem is the computing of the values of a time varying function if its Fourier 2D transformation values (in the frequency-phase space) at some instant are given. The inverse discrete Fourier transform produces images of low quality (Gibbs artifact). Therefore, different reconstruction methods are considered: the keyhole method and the RIGR method with one or two reference images. The regularization algorithms are used by solving the ill-posed problems. Some results obtained with the MRITool (Matlab software package produced by authors of this article) are given as examples, three plates are in color.