SENSE Coefficient Calculation using Adaptive Regularization

Introduction The SENSE method for accelerated MR imaging [1] is based on a least squares inverse solution that is frequently ill-conditioned, which results in a loss in SNR due to variance inflation. The SNR loss factor due to ill-conditioning, relative to phased array combining [2] for optimum SNR without acceleration, is referred to as the G-factor. Ill-conditioning of the inverse solution is caused by the lack of independence of the coil sensitivity profiles, a condition also referred to as collinearity. Ill-conditioning also increases the sensitivity to errors in the complex B1-maps. A technique known as regularization [3] or conditioning may be used to increase the tolerance to error and reduce the mean squared error. One such method for regularization is diagonal loading, also known in statistical literature as ridge regression [4]. This method is used in adaptive antenna array processing [5,6], and has been used for both SMASH [7] and SENSE [8,9] parallel MR methods. The method of diagonal loading may be used to tradeoff artifact suppression for a reduction in SNR loss (improved G-factor). In the TSENSE method [9], the increased artifact suppression achieved by temporal filtering permits a more flexible tradeoff of SENSE artifact rejection for SNR. In this paper, a method for computing the SENSE coefficients using adaptive regularization is described. It is desirable to suppress the alias artifact to a specified level below either the desired signal or noise, in order that the SNR of the resultant image is not further degraded by artifact. Since the desired and aliased image intensities vary spatially, the desired or minimum required artifact suppression varies correspondingly. In most applications of diagonal loading, a fixed value of loading is used [7,8]. Using a fixed value of the regularization parameter results in artifact suppression that is spatially varying. However, in general there will be regions with artifact suppression that exceeds the minimum required suppression. In these regions, an increased value of diagonal loading may be used to reduce the SNR loss due to illconditioning. A method is described which adaptively adjusts the regularization parameter, based on an estimate of the desired artifact suppression, in order to meet a fixed signal-to-artifact ratio. Alternatively, given an estimate of the SNR, the adaptive regularization may be adjusted for a fixed artifact-to-noise ratio. When the diagonal loading is zero, the least squares SENSE solution optimizes the SNR subject to the constraint of perfectly nulling the aliased component. As the diagonal loading becomes large, there is no suppression and the solution becomes the same as phased array combining for optimum SNR [8]. Thus, by using adaptive regularization, regions where the artifact is small relative to the desired image intensity achieve nearly optimum SNR (i.e., G 1).