Data approximation by neural nets for the MRE inverse problem in the frequency and time domains

'Stacked' matrix approximation methods for computing the shear modulus in the magnetic resonance elastography (MRE) inverse problem have been shown to work well in both the frequency and time domain formulations, and are robust to moderate levels of noise. However, when finite differences are used to approximate derivatives of the measured displacement, the algorithms can break down at high noise levels. Here we show that if instead a neural network is used to approximate the derivatives of the noisy displacement data, then the overall MRE algorithms become much more robust to noise pollution. Extensive tests indicate that the new methods perform extremely well even in the presence of very high levels of noise, and no additional processing or smoothing of the data is required.