基于动量方程的正则化与图像配准用于二维超声弹性成像
Momentum Equation-Based Regularization and Image Registration for Two-Dimensional Ultrasound Elasticity Imaging
AI总结：
本研究在超声弹性成像配准中比较四种正则化，发现基于动量方程（尤其平面应力假设）的方法误差最低、对比度最高，优于传统应变方法，并提升了对噪声和模型失配的鲁棒性。
摘要：
目的：在准静态超声弹性成像的变分图像配准框架内，评估并比较多种基于力学和传统的正则化策略。方法：我们将先前提出的基于动量方程的后处理方法（SPREME）重新表述为正则化项，直接集成到图像配准能量泛函中。实现并比较了四种正则化类型：应变幅度（$\R_ε$）、带不可压缩约束的应变幅度（$R_{εi}$）、以及平面应变（$R_{Pε}$）和平面应力（$R_{Pσ}$）假设下的基于动量的正则化。每种方法均在通过高斯-牛顿优化求解的变分框架中进行评估。数据：使用由二维和三维有限元模拟生成的合成超声图像序列以及实验体模数据来评估配准性能。比较基于位移和应变场误差、应变对比度以及对比度噪声比（CNR）。结果：基于动量的正则化，特别是在平面应力假设（$R_{Pσ}$）下，在单帧和累积测量中均实现了最低的应变误差和最高的应变对比度，即使底层组织变形违反了二维假设。相比之下，带不可压缩约束的应变幅度正则化（$R_{εi}$）在三维和累积位移场景中产生了不稳定的结果。结论：结合动量守恒的基于力学的正则化在弹性成像图像配准中优于基于应变的技术，尤其是在直接应用于优化框架时。该方法提高了对噪声和模型失配的鲁棒性，为未来基于位移的逆成像方法提供了有前景的方向。
英文摘要：
Objective: Evaluate and compare multiple mechanics-based and traditional regularization strategies within a variational image registration framework for quasi-static ultrasound elastography. Methods:We reformulate a previously proposed momentum-equation-based post-processing method (SPREME) as a regularization term directly integrated into an image registration energy functional. Four regularization types are implemented and compared: a strain magnitude ($\R_ε$), a strain magnitude with incompressibility constraint ($R_{εi}$), and a momentum-based regularization under plane strain ($R_{Pε}$) and plane stress ($R_{Pσ}$) assumptions. Each is evaluated in a variational framework solved via Gauss-Newton optimization. Data:Registration performance is assessed using synthetic ultrasound image sequences generated from 2D and 3D finite element simulations, as well as experimental phantom data. Comparisons are based on displacement and strain field errors, strain contrast, and contrast-to-noise ratio (CNR). Results: Momentum-based regularization, particularly under plane stress assumptions ($R_{Pσ}$), achieved the lowest strain errors and highest strain contrast across both single-frame and accumulated measurements, even when the underlying tissue deformation violated 2D assumptions. In contrast, strain magnitude regularization with an incompressibility constraint ($R_{εi}$) produced unstable results in 3D and accumulated displacement scenarios. Conclusions: Mechanics-based regularization that incorporates momentum conservation outperforms strain-based techniques in elastographic image registration, particularly when applied directly in the optimization framework. This approach improves robustness to noise and model mismatch, offering a promising direction for future displacement-based inverse imaging methods.
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