A B-spline parametric model for high resolution dynamic magnetic resonance imaging

In this paper we propose a numerical method for the reconstruction of dynamic magnetic resonance images from limited data in the Fourier space. In some medical dynamic applications, temporal sequences of magnetic resonance data of the same slice of the body are acquired. In order to hasten the acquisition process, only the low frequencies are acquired for all the data sets, with the exception of the first one which is completely acquired. Then, it is not possible to use a Fourier technique to obtain high resolution images from limited data. In the proposed method, the images of the sequence are represented via a B-spline parametric model using a priori information from the first image. The use of B-splines is due to their computational efficiency and their good behaviour in image fitting and representation. The use of this parametric model allows to obtain high resolution images of good quality and zoom regions of interest without loosing important details. Mathematical and numerical aspects of the method are investigated and an outline of the algorithm is given. Reconstructions from simulated and experimental data are presented and analyzed.