SNR Weighting for Shear Wave Speed Reconstruction in Tomoelastography

In tomoelastography, to achieve a final wave speed map by combining reconstructions obtained from all spatial directions and excitation frequencies, the use of weights is inevitable. Here, a new weighting scheme, which maximizes the signal-to-noise ratio (SNR) of the final wave speed map, has been proposed. To maximize the SNR of the final wave speed map, the use of squares of estimated SNR values of reconstructed individual maps has been proposed. Therefore, derivations of the SNR of the reconstructed wave speed maps have become necessary. Considering the noise on the complex MRI signal, the SNR of the reconstructed wave speed map was formulated by an analytical approach assuming a high SNR, and the results were verified using Monte Carlo simulations (MCSs). It has been assumed that the noise remains approximately Gaussian when the image SNR is high enough, despite the nonlinear operations in tomoelastography inversion. Hence, the SNR threshold was determined by comparing the SNR computed by MCSs and analytical approximations. The weighting scheme was evaluated for accuracy, spatial resolution and SNR performances on simulated phantoms. MR elastography (MRE) experiments on two different phantoms were conducted. Wave speed maps were generated for simulated 3D human abdomen MRE data and experimental human abdomen MRE data. The simulation results demonstrated that the SNR-weighted inversion improved the SNR performance of the wave speed map by a factor of two compared to the performance of the original (i.e., amplitude-weighted) reconstruction. In the case of a low SNR, no bias occurred in the wave speed map when SNR weighting was used, whereas 10% bias occurred when the original weighting (i.e., amplitude weighting) was used. Thus, while not altering the accuracy or spatial resolution of the wave speed map with the proposed weighting method, the SNR of the wave speed map has been significantly improved.