Optimal sampling and reconstruction of MRI signals resulting from sinusoidal gradients

The optimum continuous time filter and its various discrete time implementations for free induction delay signals resulting from sinusoidal gradients of magnetic resonance imaging (MRI) are formulated. It is found that the estimation error associated with implementation based on linear temporal sampling, or, equivalently, nonlinear spatial frequency sampling, is smaller than that of nonlinear temporal sampling. It is shown that the optimal maximum likelihood estimator for sinusoidal gradients has higher error variance than that of constant gradients. Experimental results verifying the theoretical predictions are presented