The precision of TR extrapolation in magnetic resonance image synthesis

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 TR1 and TR2 are used to generate synthetic images at arbitrary repetition times TR. 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 TR1 + TR2 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 TR1 + TR2, for contrast optimization. If T1 = 800 ms, and TR1 + TR2 = 2000 ms, the optimum combination of TR1, TR2 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.