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.

中文翻译：

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用于断层弹性成像中剪切波速度重建的 SNR 加权。

在断层弹性成像中，为了通过组合从所有空间方向和激励频率获得的重建来获得最终的波速图，不可避免地要使用权重。在这里，提出了一种新的加权方案，可以最大化最终波速图的信噪比（SNR）。为了最大化最终波速图的 SNR，已提出使用重建的单个图的估计 SNR 值的平方。因此，推导重建的波速图的 SNR 变得必要。考虑到复杂 MRI 信号上的噪声，通过假设高 SNR 的分析方法制定了重构波速图的 SNR，并使用蒙特卡罗模拟 (MCS) 验证了结果。尽管断层弹性成像反演中存在非线性操作，但已经假设当图像 SNR 足够高时噪声保持近似高斯。因此，通过比较 MCS 和解析近似计算的 SNR 来确定 SNR 阈值。在模拟体模上评估了加权方案的准确性、空间分辨率和 SNR 性能。对两种不同的体模进行了 MR 弹性成像 (MRE) 实验。为模拟 3D 人体腹部 MRE 数据和实验人体腹部 MRE 数据生成波速图。仿真结果表明，与原始（即幅度加权）重建的性能相比，SNR 加权反演将波速图的 SNR 性能提高了两倍。在低 SNR 的情况下，使用 SNR 加权时波速图中没有出现偏差，而使用原始加权（即幅度加权）时出现 10% 的偏差。因此，在不使用所提出的加权方法改变波速图的精度或空间分辨率的同时，波速图的 SNR 得到了显着提高。