New Algorithms for Parallel MRI S. Anzengruber 1 , F. Bauer 2 , A. Leit˜ ao 3 and R. Ramlau 1 1 RICAM, Austrian Academy of Sciences, Altenbergerstraße 69, 4040 Linz, Austria 2 Fuzzy Logic Laboratorium Linz-Hagenberg, Johannes Kepler University of Linz, Softwarepark 21, 4232 Hagenberg, Austria 3 Department of Mathematics, Federal University of St. Catarina, P.O. Box 476, 88040-900 Florian´opolis,Brazil E-mail: stephan.anzengruber@oeaw.ac.at, frank.bauer@jku.at, aleitao@mtm.ufsc.br, ronny.ramlau@oeaw.ac.at Abstract. Magnetic Resonance Imaging with parallel data acquisition requires algorithms for reconstructing the patient’s image from a small number of measured lines of the Fourier domain (k-space). In contrast to well-known algorithms like SENSE and GRAPPA and its flavors we consider the problem as a non-linear inverse problem. However, in order to avoid cost intensive derivatives we will use Landweber-Kaczmarz iteration and in order to improve the overall results some additional sparsity constraints. 1. Introduction The Magnetic Resonance Imaging, also known as MR imaging or simply MRI, is one of the most popular and powerful medical imaging techniques. Using strong magnetic fields the atoms (mostly hydrogen) in a specified slice of the body are turned into small radio stations emitting signals with a specific frequency. These signals can be detected simultaneously with multiple antenna coils placed around the body (therefore “Parallel MRI”). As a result we get the 2D Fourier transform of the water distribution of this particular slice. In one pass one can read one line of this 2D Fourier transform; the acquiring time of this line is due to medical and technical constraints already at the lower possible limit. Hence a speed up of the method can just be achieved by measuring less data, ie. less lines in the Fourier domain. As all antenna coils have different spatial characteristics (i.e. they illuminate different parts of the image) even now from the theoretical point of view all necessary information to get a high resolution image are hidden in the data. We want to retrieve these information from the parallel measurements by appropriate mathematical algorithms. These have to cope with two problems, on the one hand side they have to keep the noise at a reasonable level and on the other hand need to keep undersampling (i.e. in the spatial domain overfolding) artifacts as low as possible. An additional complication is posed by the problem that the sensitivity characteristics of the antenna coils is not very well known and may change from patient to patient. This problem has been largely investigated and a number of one pass methods have been developed, e.g. SMASH [1], SENSE [2], GRAPPA [3] and SPACE-RIP [4]. 2 Author for correspondence 6th International Conference on Inverse Problems in Engineering: Theory and Practice IOP Publishing Journal of Physics: Conference Series 135 (2008) 012009 doi:10.1088/1742-6596/135/1/012009 c  2008 IOP Publishing Ltd 1