基于潜在分数的贝叶斯克拉美-罗界估计用于高维成像系统

中文摘要 AI 辅助

我们提出了一种数据驱动的框架，用于在高维成像系统中估计贝叶斯克拉美-罗界（CRB），该系统具有复杂、解析上难以处理的先验。在此设置中，直接计算CRB具有挑战性，因为需要对先验分数进行建模，并在非常高维中形成和求逆贝叶斯Fisher信息矩阵。为解决这些问题，我们首先在预训练变分自编码器的潜在空间中重新表述逆问题，从而显著降低界估计问题的维度，同时保留图像的空间结构。贝叶斯CRB在此潜在空间中形成，并使用变量变换公式映射回原始参数空间。其次，为了学习潜在先验分数，我们引入了一种新的切片分数匹配目标，该目标定义在具有空间$H^1(\Omega)$ Sobolev范数的Bochner空间中。这种“Bochner空间切片分数匹配”目标与标准切片分数匹配一致，但惩罚了分数空间梯度中的误差，抑制了否则会污染所得CRB估计的高频伪影。我们在一个风格化的定量光声计算机断层扫描（qPACT）乳腺成像问题上验证了该方法，该问题具有超过一百万个未知参数，使用基于Stable Diffusion的基础模型自编码器。所提出的方法产生了稳定、无伪影的贝叶斯CRB估计，这些估计反映了学习先验的高度非高斯结构，并揭示了先验对竞争性qPACT设计方案相对性能的显著影响。

英文摘要

We propose a data-driven framework for estimating the Bayesian Cramér-Rao bound (CRB) in high-dimensional imaging systems with complex, analytically intractable priors. Direct CRB computation is challenging in this setting due to the need to model the prior score and to form and invert the Bayesian Fisher information matrix in very high dimensions. To address these issues, we first reformulate the inverse problem in the latent space of a pre-trained variational autoencoder, thereby dramatically reducing the dimensionality of the bound estimation problem while preserving the spatial structure of the images. The Bayesian CRB is formed in this latent space and mapped back to the native parameter space using a change-of-variables formula. Second, to learn the latent prior score, we introduce a new sliced score matching objective defined in a Bochner space endowed with an $H^1(Ω)$ Sobolev norm in space. This "Bochner-space sliced score matching" objective is consistent with standard sliced score matching, but penalizes errors in the spatial gradients of the score, suppressing high-frequency artifacts that otherwise contaminate the resulting CRB estimates. We validate the approach on a stylized quantitative photoacoustic computed tomography (qPACT) breast imaging problem with over one million unknown parameters, using a foundation-model autoencoder derived from Stable Diffusion. The proposed method yields stable, artifact-free Bayesian CRB estimates that reflect the highly non-Gaussian structure of the learned prior and reveal the substantial impact of the prior on the relative performance of competing qPACT design schemes.

发表机构

• Oden Institute for Computational Engineering and Sciences, the University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学研究所）
• Graduate School of Biomedical Sciences at UT Southwestern Medical Center（德克萨斯大学西南医学中心生物医学科学研究生院）
• Mallinckrodt Institute of Radiology at Washington University in St. Louis（圣路易斯华盛顿大学马林克罗特放射学研究所）

机构由 AI 辅助整理，请以论文原文为准。