We present a method for tissue quantification at a resolution that would not be possible for either conventional Dixon method or MR spectroscopy. Our objective is to design a steady-state free precession (SSFP) pulse-sequence which maximizes the contrast to noise ratio in tissue segmentation by solving a nonlinear, nonconvex semi-definite optimization problem. To solve the problem a grid search is used to get a good starting point, and then a sequential, semi-definite trust-region method is developed. The subproblems in our algorithm contain only linear, second order, and semi-definite constraints. Our method can easily be adapted to other pulse sequence types, and it can handle any numbers of tissues and images. As an illustration, we show how the pulse sequences designed numerically could be applied to the problem of quantifying intraluminal lipid deposits in the carotid artery.
We also consider the case where the main magnetic field is not homogeneous, for which we first present a heuristic by adjusting RF pulse phase cycling to correct for the field inhomogeneity. Then we construct a total variation regularization based model, from which we extract two subproblems -field inhomogeneity estimation and tissue density estimation that can be interleaved iteratively. The computational and numerical results show that the model yields a good estimate of both field inhomogeneity and tissue density.