Compressed Sensing MRSI (CS-MRSI) offers the ability to accelerate MRSI sequences while suffering minimal artifacts compared to conventional fast MRSI techniques. CS-MRSI exploits the inherent sparsity of MRSI images and incoherent artifacts of pseudo-random sub-Nyquist sampling of k-space combined with non-linear reconstruction to produces MRSI images. CS-MRSI can be used as an acceleration tool to decrease the scan time while maintaining acceptable spatial definition or to enable the acquisition of higher resolution scans while minimizing the associated time penalty. In this work we adopt the compressed sensing technique to accelerate a clinically relevant 2-D point resolved spectroscopy sequence. However, the process of weighing the cost and benefit of applying such a fast imaging technique is complicated due to the unique non-linear nature of the reconstruction process and has largely relied on qualitative assessments. Moreover, pseudo-random sub-Nyquist sampling of k-space can have unwanted effects on the modulation transfer function. In this work we set out to quantify the loss in image quality associated with CS-MRSI. We used simulations of a phantom based method to investigate the MTF behaviour of CS-MRSI with regard to different k-space sampling patterns. As expected, the k-space sampling patterns tested were found to have a direct effect on the MTFs. Moreover, limiting the deviation of the resulting k-space sampling pattern from the prescribed probability distribution function had a positive effect on the MTF overall. Not only was low-resolution response improved, but we also noticed an improvement of ∼ 26% in resolution at 0.1 MTF.