Scalable Uncertainty Quantification for Data-Driven PET Image Reconstruction

本计画系关于正电子发射断层摄影（PET）影像重建之不确定度量化（UQ）。PET是现代诊断成像的支柱，允许非侵入性，敏感和特异性检测许多疾病的功能变化。因此，可靠的PET图像重建具有重要的实际意义，并且在过去的几十年中已经开发了大量的重建算法。大多数传统算法依赖于惩罚最大似然估计，使用手工制作的先验（例如，总变异和解剖学先验），或者最近的基于学习的方法，例如，展开的深度迭代网络。虽然这些技术已经非常成功，但它们缺乏提供不确定性估计的能力，即使这样的估计对于下游决策是非常可取的。首先，噪声模型通常是泊松型的，对浓度具有非负性约束，这排除了将已建立的统计程序应用于泊松回归。其次，真实的PET成像涉及大量数据和高维参数空间。在这个项目中，我们建议利用机器学习的通用工具，例如，高斯过程和变分自动编码器（VAE），用于PET重建的可扩展UQ。

This project is concerned with uncertainty quantification(UQ)for image reconstructions in positron emission tomography (PET). PETis a pillar of modern diagnostic imaging, allowing non-invasive, sensitive and specific detection of functional changes in a number of diseases. Hence, reliable PETimage reconstruction is of great practical importance and a large number of reconstruction algorithms have been developed duringthe last few decades. Mosttraditionalalgorithms rely on penalized maximum likelihood estimates, usingahand crafted prior(e.g., total variation and anatomical priors), or more recently learning based approaches, e.g., unrolled deep iterative networks, have been proposed. While these techniques have been very successful, theylack the capability to provide uncertainty estimates, even though such estimatesare highly desirable for downstream decision making.There are two notable challenges associated with uncertainty quantification (UQ)for PET imaging. First, the noise model is often of Poisson type, with nonnegativity constraint on the concentration, which precludes applying established statistical proceduresfor Poisson regression. Second, realistic PET imaging involves a large volume of data and a high-dimensional parameter space.In this project, we propose to exploit the versatile tools from machine learning, e.g., Gaussian processes and variational autoencoder (VAE), for scalable UQ for PET reconstruction.