Bates Oscar, Guasch Lluis, Strong George, Robins Thomas Caradoc, Calderon-Agudo Oscar, Cueto Carlos, Cudeiro Javier, Tang Mengxing
Department of Bioengineering, Imperial College London, SW7 2AZ, United Kingdom.
Earth Science and Engineering Department, Imperial College London, SW7 2AZ, United Kingdom.
Inverse Probl. 2022 Mar 14;38(4):045008. doi: 10.1088/1361-6420/ac55ee.
Bayesian methods are a popular research direction for inverse problems. There are a variety of techniques available to solve Bayes' equation, each with their own strengths and limitations. Here, we discuss stochastic variational inference (SVI), which solves Bayes' equation using gradient-based methods. This is important for applications which are time-limited (e.g. medical tomography) or where solving the forward problem is expensive (e.g. adjoint methods). To evaluate the use of SVI in both these contexts, we apply it to ultrasound tomography of the brain using full-waveform inversion (FWI). FWI is a computationally expensive adjoint method for solving the ultrasound tomography inverse problem, and we demonstrate that SVI can be used to find a no-cost estimate of the pixel-wise variance of the sound-speed distribution using a mean-field Gaussian approximation. In other words, we show experimentally that it is possible to estimate the pixel-wise uncertainty of the sound-speed reconstruction using SVI and a common approximation which is already implicit in other types of iterative reconstruction. Uncertainty estimates have a variety of uses in adjoint methods and tomography. As an illustrative example, we focus on the use of uncertainty for image quality assessment. This application is not limiting; our variance estimator has effectively no computational cost and we expect that it will have applications in fields such as non-destructive testing or aircraft component design where uncertainties may not be routinely estimated.
贝叶斯方法是反问题研究的一个热门方向。有多种技术可用于求解贝叶斯方程，每种技术都有其自身的优缺点。在此，我们讨论随机变分推断（SVI），它使用基于梯度的方法来求解贝叶斯方程。这对于有时间限制的应用（如医学断层扫描）或求解正向问题成本高昂的情况（如伴随方法）很重要。为了评估SVI在这两种情况下的应用，我们将其应用于使用全波形反演（FWI）的脑部超声断层扫描。FWI是一种用于求解超声断层扫描反问题的计算成本高昂的伴随方法，并且我们证明SVI可用于使用平均场高斯近似来找到声速分布的逐像素方差的无成本估计。换句话说，我们通过实验表明，使用SVI和其他类型迭代重建中已经隐含的一种常见近似来估计声速重建的逐像素不确定性是可能的。不确定性估计在伴随方法和断层扫描中有多种用途。作为一个说明性示例，我们专注于将不确定性用于图像质量评估。这个应用并不局限于此；我们的方差估计器实际上没有计算成本，并且我们预计它将在无损检测或飞机部件设计等领域得到应用，在这些领域中不确定性可能不会被常规估计。
