Separation of water from fat tissues in magnetic resonance imaging is important for many applications because signals from fat tissues often interfere with diagnoses that are usually based on water signal characteristics. Water and fat can be separated with images acquired at different echo time shifts. The three-point method solves for the unknown off-resonance frequency together with the water and fat densities. Noise performance of the method, quantified by the effective number of signals averaged (NSA), is an important metric of the water and fat images. The authors use error propagation theory and Monte Carlo simulation to investigate two common reconstructive approaches: an analytic-solution based estimation and a least-squares estimation. Two water-fat chemical shift (CS) encoding strategies, the symmetric (-theta, 0, theta) and the shifted (0, theta, 2theta) schemes are studied and compared. Results show that NSAs of water and fat can be different and they are dependent on the ratio of intensities of the two species and each of the echo time shifts. The NSA is particularly poor for the symmetric (-theta, 0, theta) CS encoding when the water and fat signals are comparable. This anomaly with equal amounts of water and fat is analyzed in a more intuitive geometric illustration. Theoretical prediction of NSA matches well with simulation results at high signal-to-noise ratio (SNR), while deviation arises at low SNR, which suggests that Monte Carlo simulation may be more appropriate to accurately predict noise performance of the algorithm when SNR is low.

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