Tian Liu1,2, Weiyu Xu3, Amir Salman Avestimehr3, Yi Wang1,2
1Biomedical Engineering, Cornell University, Ithaca, NY, United States; 2Radiology, Weill Cornell Medical College, New York, NY, United States; 3School of Electrical & Computer Engineering, Cornell University, Ithaca, NY, United States
The inverse problem from magnetic field to susceptibility source is ill-posed. Even in a noise-free senario, there are infinite number of solutions fulfilling the observation, and a little error in the input data will result in severe noise propagation in the final outcome. In this abstract, we provide a detailed analytical and numerical analysis to demonstrate that the Morphology Enabled Dipole Inversion (MEDI) approah provides a unique and accurate solution under ideal conditions, and the error of the reconstruction is tightly bounded by the error in the gradient echo image in the presence of Gaussian noise.