Clare Poynton1,2, William Wells III1,3
1Computer Science & Artificial Intelligence Lab (CSAIL), MIT, Cambridge, MA, United States; 2Harvard-MIT Division of HST, MIT, Cambridge, MA, United States; 3Brigham & Women's Hospital, Harvard Medical School, Boston, MA, United States
In MRI, measurements of the magnetic field contain useful information about the underlying spatial susceptibility distribution, but estimating susceptibility by direct inversion of the field is ill-posed. In addition, bias fields from mis-set shims and non-local susceptibility sources obscure the subtle susceptibility differences of interest. We describe a variational method for susceptibility estimation that is based on the Laplacian operator. Using the Laplacian of the field and the L1 norm, confounding field artifacts are effectively eliminated and sparse solutions that agree well with true susceptibility values are obtained.