Optimal sampling and reconstruction of NMR signals with time-varying gradients

Summary form only given. An optimal sampling and reconstruction scheme has been derived for free induction decay (FID) signals resulting from sinusoidal gradients that occur in nuclear magnetic resonance (NMR) imaging. The problem has been formulated as a linear parameter estimation problem by writing the observed signal, r(t), as the sum of the noise-free FID signal and a zero mean, white, Gaussian random process with intensity σ² . The noise-free FID signal is modeled to be a linear combination of the uniform samples of the object distribution, f(n ₁,n₂). The optimal maximum-likelihood (ML) estimate of f(n₁,n₂) is derived for the constant-gradient case and then generalized to arbitrary time varying gradients