Spatially regularized T(1) estimation from variable flip angles MRI.

PURPOSE: To develop efficient algorithms for fast voxel-by-voxel quantification of tissue longitudinal relaxation time (T(1)) from variable flip angles magnetic resonance images (MRI) to reduce voxel-level noise without blurring tissue edges.
METHODS: T(1) estimations regularized by total variation (TV) and quadratic penalty are developed to measure T(1) from fast variable flip angles MRI and to reduce voxel-level noise without decreasing the accuracy of the estimates. First, a quadratic surrogate for a log likelihood cost function of T(1) estimation is derived based upon the majorization principle, and then the TV-regularized surrogate function is optimized by the fast iterative shrinkage thresholding algorithm. A fast optimization algorithm for the quadratically regularized T(1) estimation is also presented. The proposed methods are evaluated by the simulated and experimental MR data.
RESULTS: The means of the T(1) values in the simulated brain data estimated by the conventional, TV-regularized, and quadratically regularized methods have less than 3% error from the true T(1) in both GM and WM tissues with image noise up to 9%. The relative standard deviations (SDs) of the T(1) values estimated by the conventional method are more than 12% and 15% when the images have 7% and 9% noise, respectively. In comparison, the TV-regularized and quadratically regularized methods are able to suppress the relative SDs of the estimated T(1) to be less than 2% and 3%, respectively, regardless of the image noise level. However, the quadratically regularized method tends to overblur the edges compared to the TV-regularized method.
CONCLUSIONS: The spatially regularized methods improve quality of T(1) estimation from multiflip angles MRI. Quantification of dynamic contrast-enhanced MRI can benefit from the high quality measurement of native T(1).