GPU implementation of Levenberg-Marquardt optimization for Ti mapping

T1 mapping is an emerging MRI research tool to characterize diseased myocardial tissue. The Ti map is generated by fitting an exponential relaxation curve to the acquired image data. Levenberg-Marquardt algorithm is a standard way to solve this nonlinear curve fitting problem. However, the execution on the standard CPU can be time-consuming and incompatible with clinical routine. In this paper, a GPU implementation is performed to reduce the computation time of the standard T1 mapping. In addition, a new vectorized approach is proposed to include spatial regularization in the curve fitting process to improve the robustness. The GPU implementation is validated on NVIDIA K42000 GPU using cardiac T1 data from 16 volunteers. The computation time shows significant decrease in both pixel-wise and vectorized curve fitting. The pixel-wise curve fitting is accelerated by a factor of 30+ compared to the standard sequential C code and the vectorized curve fitting is improved by a factor of 47 and 38 for 3-parameter and 2-parameter curve fitting compared to the Matlab code.