Optimal gradient waveform design for projection imaging and projection reconstruction echoplanar spectroscopic imaging

The use of modulated B0 projection gradient waveforms is proposed for magnetic resonance imaging (MRI) and magnetic resonance spectroscopic imaging (MRSI) to shape the k-space sampling density function to match the profile of an applied reconstruction window function. This allows for a time-efficient means of maximizing the signal-to-noise ratio when, for example, a low-pass spatial filter, designed to reduce k-space truncation artifacts and corresponding point-spread function sidelobe energies, is implemented. Both the two-dimensional (2D) and 3D cases are investigated. To create the projection gradient waveforms, a design method is developed that uses nonlinear constrained optimization (NLCO) to minimize the variance of the reconstruction noise. The design is subject to both equality and inequality constraints, which include the maximum gradient magnitude and slew rate. It is shown that NLCO can also be applied to twisting the projection trajectories for purposes of reducing the data acquisition time while still maintaining the desired sampling density. Applications to 1H MRSI are investigated via simulations. Advantages and limitations of the new sampling schemes are discussed.