Solving an inverse diffusion problem for magnetic resonance dosimetry by afast regularization method

An inverse diffusion problem that appears in Magnetic Resonance dosimetry i s studied. The problem is shown to be equivalent to a deconvolution problem with a known kernel. To cope with the singularity of the kernel, nonlinear regularization functionals are considered which can provide regular soluti ons, reproduce steep gradients and impose positivity constraints. A fast de terministic algorithm for solving the involved non-convex minimization prob lem is used. Accurate restorations on real 256 x 256 images are obtained by the algorithm in a few minutes on a 266-MHz PC that allow to precisely qua ntitate the relative absorbed dose. (C) 2001 Academic Press.