Plots showing the median relative error as a function of SNR from the Monte Carlo simulations with a brain image. In all cases, the relative error decreases as the amount of acquired data increases. FE1 encoding was generally superior in cases with very limited data or with high levels of noise. However, for moderate noise and sufficient data acquisition, random encoding performed better than the other two schemes, and FE2 outperforms FE1. For fully-encoded data, the SNR efficiency of the Fourier schemes allows them to dominate the random encoding scheme.