We develop a computational framework to quantify uncertainty in shear elastography imaging of anomalies in tissues. We adopt a Bayesian inference formulation. Given the observed data, a forward model and their uncertainties, we find the posterior probability of parameter fields representing the geometry of the anomalies and their shear moduli. To construct a prior probability, we exploit the topological energies of associated objective functions. We demonstrate the approach on synthetic two dimensional tests with smooth and irregular shapes. Sampling the posterior distribution by Markov Chain Monte Carlo (MCMC) techniques we obtain statistical information on the shear moduli and the geometrical properties of the anomalies. General affine-invariant ensemble MCMC samplers are adequate for shapes characterized by parameter sets of low to moderate dimension. However, MCMC methods are computationally expensive. For simple shapes, we devise a fast optimization scheme to calculate the maximum a posteriori (MAP) estimate representing the most likely parameter values. Then, we approximate the posterior distribution by a Gaussian distribution found by linearization about the MAP point to capture the main mode at a low computational cost.

翻译：我们开发了一种计算框架，用于量化组织中异常区域剪切弹性成像的不确定性。采用贝叶斯推断方法，基于观测数据、正演模型及其不确定性，我们求解代表异常区域几何形状及其剪切模量的参数场的后验概率。为构建先验概率，我们利用了相关目标函数的拓扑能量。通过合成二维测试（含光滑与不规则形状）验证该方法。采用马尔可夫链蒙特卡洛（MCMC）技术对后验分布进行采样，获取剪切模量及异常区域几何特性的统计信息。对于由低至中维参数集表征的形状，通用仿射不变集成MCMC采样器适用。但MCMC方法计算成本较高。针对简单形状，我们设计了一种快速优化方案，计算最大后验概率（MAP）估计以表示最可能参数值；随后通过MAP点线性化近似后验分布为高斯分布，以低计算成本捕获主模态。