The precision of TR extrapolation in magnetic resonance image synthesis

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Abstract
We present a model of noise propagation from acquired magnetic resonance (MR) images to TR -extrapolated synthetic images. This model assumes that images acquired at two repetition times and are used to generate synthetic images at arbitrary repetition times . 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 less than TR. For T1=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 , for contrast optimization. If =800 ms, and =2000 ms, the optimum combination of results in synthetic images whose SNR is at worst 22% less than the SNR of directly acquired images. For many values of TR, the synthetic images have SNR superior to that obtainable by direct acquisition.