Bernard Simon, Monteiller Vadim, Komatitsch Dimitri, Lasaygues Philippe
Aix Marseille University, CNRS, Centrale Marseille, LMA, Marseille, France.
Phys Med Biol. 2017 Aug 9;62(17):7011-7035. doi: 10.1088/1361-6560/aa7e5a.
We introduce an ultrasonic quantitative imaging method for long bones based on full-waveform inversion. The cost function is defined as the difference in the L -norm sense between observed data and synthetic results at a given iteration of the iterative inversion process. For simplicity, and in order to reduce the computational cost, we use a two-dimensional acoustic approximation. The inverse problem is solved iteratively based on a quasi-Newton technique called the Limited-memory Broyden-Fletcher-Goldfarb-Shanno method. We show how the technique can be made to work fine for benchmark models consisting of a single cylinder, and then five cylinders, the latter case including significant multiple diffraction effects. We then show pictures obtained for a tibia-fibula bone pair model. Convergence is fast, typically in 15 to 30 iterations in practice in each frequency band used. We discuss the so-called 'cycle skipping' effect that can occur in such full waveform inversion techniques and make them remain trapped in a local minimum of the cost function. We illustrate strategies that can be used in practice to avoid this. Future work should include viscoelastic materials rather than acoustic, and real data instead of synthetic data.
我们介绍一种基于全波形反演的长骨超声定量成像方法。代价函数定义为在迭代反演过程的给定迭代中观测数据与合成结果在L范数意义上的差异。为简单起见并降低计算成本，我们采用二维声学近似。基于一种称为有限内存布罗伊登-弗莱彻-戈德法布-香农方法的拟牛顿技术迭代求解反问题。我们展示了该技术如何适用于由单个圆柱体以及随后的五个圆柱体组成的基准模型，后一种情况包括显著的多次衍射效应。然后我们展示了从胫腓骨对模型获得的图像。收敛速度很快，在每个使用的频带中实际通常在15到30次迭代内。我们讨论了在这种全波形反演技术中可能出现的所谓“周期跳跃”效应，以及如何使它们陷入代价函数的局部最小值。我们说明了在实践中可用于避免此问题的策略。未来的工作应包括使用粘弹性材料而非声学材料，以及使用实际数据而非合成数据。
