<p>Parallel MRI, in which k-space is regularly or irregularly undersampled, is critical for imaging speed acceleration. In this thesis, we show how to optimize a regular undersampling pattern for three-dimensional Cartesian imaging in order to achieve faster data acquisition and/or higher signal to noise ratio (SNR) by using nonlinear optimization. A new sensitivity profiling approach is proposed to produce better sensitivity maps, required for the sampling optimization. This design approach is easily adapted to calculate sensitivities for arbitrary planes and volumes. The use of a semi-definite, linearly constrained model to optimize a parallel MRI undersampling pattern is novel. To solve this problem, an iterative trust-region is applied. When tested on real coil data, the optimal solution presents a significant theoretical improvement in accelerating data acquisition speed and eliminating noise.</p> / Master of Applied Science (MASc)