The precision of T R extrapolation in magnetic resonance image synthesis

We present a model of noise propagation from acquired magnetic resonance (MR) images to T R ‐extrapolated synthetic images. This model assumes that images acquired at two repetition times T R1and T R2are used to generate synthetic images at arbitrary repetition times T R . The predictions of the model are compared with experimentally acquired phantom data, and show excellent agreement. The model is utilized in an analysis of two applications of MR image synthesis: scan time reduction and multiple‐image synthesis. Scan time is reduced by acquiring data at two short repetition times, and synthesizing at a longer repetition time, with T R1+T R2less than T R . For T 1 =800 ms, a reduction of 20% in scan time results in a 45% reduction in signal‐to‐noise ratio SNR, when compared to direct acquisition. Reducing scan time by much more than 20% produces large noise levels in the synthetic image, and is unlikely to be useful. In multiple‐image synthesis, images are synthesized at any repetition time in the range 0 to T R1+T R2 , for contrast optimization. If T 1 =800 ms, and T R1+T R2 =2000 ms, the optimum combination of T R1, T Rresults in synthetic images whose SNR is at worst 22% less than the SNR of directly acquired images. For many values of T R , the synthetic images have SNR superior to that obtainable by direct acquisition.