Abstract
This work presents an analytical relationship between gradient-spoiled and RF-spoiled steady-state signals. The two echoes acquired in double-echo in steady-state scans are shown to lie on a line in the signal plane, where the two axes represent the amplitudes of each echo. The location along the line depends on the amount of spoiling and the diffusivity. The line terminates in a point corresponding to an RF-spoiled signal. In addition to the main contribution of demonstrating this signal relationship, we also include the secondary contribution of preliminary results from an example application of the relationship, in the form of a heuristic denoising method when both types of scans are performed. This is investigated in simulations, phantom scans, and in vivo scans. For the signal model, the main topic of this study, simulations confirmed its accuracy and explored its dependency on signal parameters and image noise. For the secondary topic of its preliminary application to reduce noise, simulations demonstrated the denoising method giving a reduction in noise-induced standard deviation of about 30%. The relative effect of the method on the signals is shown to depend on the slope of the described line, which is demonstrated to be zero at the Ernst angle. The phantom scans show a similar effect as the simulations. In vivo scans showed a slightly lower average improvement of about 28%.