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The homogeneity of the amplitude of one of the polarizations of the RF fleld B 1 is a crucial issue in Magnetic Resonance Imaging (MRI), and several methods have been proposed for enhancing this uniformity (\Shimming"). The existing approaches aim at controlling the homogeneity of B + 1 and limiting the Speciflc Absorption Rate (SAR) of the RF fleld by independently controlling magnitude and phase of individual excitation currents in MRI scanners, either birdcage or TEM coil system. A novel approach is presented here which allows a joint control of B + 1 uniformity, SAR, and purity of polarization of the total RF B 1 fleld. We propose a convex optimization procedure with convex constraints, and special attention has been devoted to the issue of convexity of the proposed functional. The method is applied to MRI brain imaging; numerical tests have been performed on a realistic head model at low, medium, and high RF fleld in order to assess the efiectiveness of the proposed method. We found that maintaining a speciflc polarization plays an important role also in maintaining the homogeneity of B + 1 amplitude.

FIELD SYNTHESIS IN INHOMOGENEOUS MEDIA: JOINT CONTROL OF POLARIZATION, UNIFORMITY AND SAR IN MRI B<sub>1</sub>-FIELD