标题： 基于物理知识的西尔维斯特规范化流在磁共振光谱中的贝叶斯推理应用 显示英文标题

标题： Physics-Informed Sylvester Normalizing Flows for Bayesian Inference in Magnetic Resonance Spectroscopy

摘要： 磁共振波谱（MRS）是一种非侵入性技术，用于测量组织的代谢组成，为神经性疾病、肿瘤检测及其他代谢功能障碍提供有价值的见解。然而，准确的代谢物定量受到诸如光谱重叠、低信噪比和各种伪影等挑战的阻碍。传统方法如线性组合模型容易出现歧义，并且通常只能以克拉默-拉奥界的形式提供估计精度的理论下限。本工作引入了一种使用赛尔维斯特规范化流（SNFs）的贝叶斯推理框架，以近似代谢物浓度的后验分布，从而增强定量的可靠性。基于物理学的解码器结合了有关MRS信号形成的先验知识，确保了现实分布的表示。我们在模拟的7特斯拉质子MRS数据上验证了该方法，展示了准确的代谢物定量、良好的不确定性校准以及对参数相关性和多模态分布的洞察。 显示英文摘要

摘要： Magnetic resonance spectroscopy (MRS) is a non-invasive technique to measure the metabolic composition of tissues, offering valuable insights into neurological disorders, tumor detection, and other metabolic dysfunctions. However, accurate metabolite quantification is hindered by challenges such as spectral overlap, low signal-to-noise ratio, and various artifacts. Traditional methods like linear-combination modeling are susceptible to ambiguities and commonly only provide a theoretical lower bound on estimation accuracy in the form of the Cram\'er-Rao bound. This work introduces a Bayesian inference framework using Sylvester normalizing flows (SNFs) to approximate posterior distributions over metabolite concentrations, enhancing quantification reliability. A physics-based decoder incorporates prior knowledge of MRS signal formation, ensuring realistic distribution representations. We validate the method on simulated 7T proton MRS data, demonstrating accurate metabolite quantification, well-calibrated uncertainties, and insights into parameter correlations and multi-modal distributions.