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arXiv 2501.07348physics.med-ph
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使用概率反演的超声医学组织成像:利用变分推断进行速度重建与不确定性量化

Ultrasonic Medical Tissue Imaging Using Probabilistic Inversion: Leveraging Variational Inference for Speed Reconstruction and Uncertainty Quantification

Qiang Li, Heyu Ma, Chengcheng Liu, Dean Ta

AI总结:

本研究将SVGD算法集成至FWI框架,用于医学超声成像的速度重建与不确定性量化,实验表明该方法提升了反演质量、收敛速度及不确定性估计的可靠性。

摘要:

全波形反演(FWI)是医学超声中实现高分辨率成像的一种极具前景的技术。然而,传统的FWI方法存在计算效率低、依赖初始模型以及无法量化不确定性等问题。本研究旨在提升反演性能,并为医学FWI成像提供一种可靠的不确定性量化方法。本研究通过推导概率反演的后验梯度,将Stein变分梯度下降(SVGD)算法集成到FWI框架中。为评估所提出的方法,在合成数据集上进行了数值实验,包括具有真实解剖结构的乳腺组织模型。通过评估成像精度和不确定性量化,比较了基于SVGD的FWI与传统FWI及随机变分推断(SVI)方法的性能。同时,实现了马尔可夫链蒙特卡洛(MCMC)作为基准,以评估不确定性估计的质量。对于合成数据,基于SVGD的FWI框架在感兴趣区域(ROI)内产生了更精确的估计,并且与传统FWI相比展现出更快的收敛速度。在解剖结构真实的乳腺组织模拟中,SVGD在ROI内的最大相对误差为1.10%,平均相对误差为0.09%。估计的不确定性在空间上是一致的,大多数值低于0.01,平均值约为0.003。与SVI相比,SVGD提供了更好的结构分辨率,并且与MCMC基准有更强的一致性,表明其具有更可靠的不确定性量化能力。基于SVGD的FWI方法提高了反演质量,增强了不确定性量化。这些发现表明,概率反演是一种极具前景的工具,可用于解决传统FWI方法在医学组织超声成像中的局限性。

英文摘要:

Full Waveform Inversion (FWI) is a promising technique for achieving high-resolution imaging in medical ultrasound. However, conventional FWI methods suffer from issues related to computational efficiency, dependence on initial models, and the inability to quantify uncertainty. This study aims to enhance inversion performance and provide a reliable method for uncertainty quantification in medical FWI imaging. This study integrates the Stein Variational Gradient Descent (SVGD) algorithm into the FWI framework by deriving the posterior gradient for probabilistic inversion. To evaluate the proposed method, numerical experiments are conducted on synthetic datasets, including a breast tissue model with realistic anatomical structure. Imaging accuracy and uncertainty quantification are assessed to compare the performance of SVGD-based FWI with conventional FWI and Stochastic Variational Inference (SVI) methods. Markov Chain Monte Carlo (MCMC) is implemented as a benchmark to evaluate the quality of uncertainty estimates. For synthetic data, the SVGD-based FWI framework yields more precise estimates in the region of interest (ROI) and demonstrates faster convergence compared to the conventional FWI. For the anatomically realistic breast tissue simulation, SVGD produces a maximum relative error of 1.10\% and a mean relative error of 0.09\% in the ROI. The estimated uncertainty is spatially consistent, with most values below 0.01 and a mean of approximately 0.003. Compared to SVI, SVGD provides improved structural resolution and stronger agreement with the MCMC benchmark, indicating more reliable uncertainty quantification. The SVGD-based FWI method improves inversion quality, enhances uncertainty quantification. These findings indicate that probabilistic inversion is a promising tool for addressing the limitations of traditional FWI methods in ultrasonic imaging of medical tissues.

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