Matrix Regularization for SENSE Imaging

SENSE (SENSitivity Encoding) is a recent powerful parallel imaging technique that uses multiple RF receive coils to reduce the MRI scan time. The sensitivity of multiple coils allows the decoupling of the overlapping images formed as a result of reducing the field-of-view (FOV). This process requires the solution of a matrix equation of the form, I = SM + N, where I is the measured signal in each coil, M is the actual image, S is the sensitivity of each coil and N is the noise in each coil. The inversion of this equation is sensitive to perturbations that arise if the sensitivity S is ill-conditioned, which is the case for high time-reduction factors. Matrix regularization introduces additional criteria in order to single out stable solutions. We will present two regularization techniques, namely, linear regularization and Backus-Gilbert regularization, the latter not requiring certain prior knowledge of the object. Both are applied for higher (time) acceleration factors. We find relative weighting factors for which there are reasonable trade-offs between signal intensity and aliasing.