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

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.

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.

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.

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).