New statistical approaches to inverse problems in biomedicine

该项目的目的是开发新的计算工具来解决生物医学应用中出现的逆问题。计算框架基于贝叶斯统计范式，将反问题重新表述为统计推理问题，并以先验概率分布的形式引入补充稀缺和噪声数据的信息。这个项目的方法论重点是结构的、层次的和动态的先验模型的发展。结构先验模型使得结合不同的成像模式成为可能，这种方法通常被称为数据同化。另一方面，密切相关的层次模型允许先验模型本身存在不确定性，让数据指导先验。特别是，该方法有助于实现本质上是定性的先验信息，重要的例子是解决方案的稀疏性或局部性。动态先验模型在时间相关问题中是必不可少的，它通常涉及结构元素。本项目解决的另一个中心问题是开发有效的计算策略来探索后验概率分布。特别是，基于使用快速约简正演模型的顺序方法将被探索。还将讨论成像应用中从蒙特卡罗样品中提取的不确定度的可视化。由此产生的算法将应用于生物医学逆问题，包括电阻抗断层扫描（EIT），脑磁图（MEG），正电子发射断层扫描（PET）和神经电图（ENG），使用已经建立的合作者网络提供的数据。目前生物医学研究的趋势是开发新的微创成像方式、临床程序和技术。与其使用可能构成健康风险的电离辐射，不如使用弱电流或人体本身的电磁场。电流/电压测量可用于识别乳腺组织中潜在的恶性肿瘤；癫痫发作位点的定位是控制屈光性癫痫的脑外科手术前的一个重要步骤，可以通过测量大脑活动引起的弱磁场来完成。同样，在设计帮助脊髓损伤患者恢复对肌肉的控制，或截肢患者控制假肢的技术时，开发了记录非侵入性神经信号的新方法。这些方法的一个共同特点是，它们所依赖的信号很弱，被噪声干扰，难以识别。此外，计算模型是不完整的，因为描述设置的一些细节是未知的。研究者和他的同事一起开发了克服上述困难的计算方法。该方法依赖于信号的概率建模和模型中的不确定性。补充信息增强了不完整的数据，并特别强调了如何将未知的定性信息转化为定量形式，以便将其输入计算模型的问题。

The aim of the project is to develop new computational tools for solving inverse problems arising in biomedical applications. The computational framework is based on the Bayesian statistical paradigm, in which the inverse problem is reformulated as a statistical inference problem, and information complementing the scarce and noisy data is imported in the form of prior probability distribution. The methodological emphasis of this project is the development of structural, hierarchical and dynamic prior models. Structural prior models make it possible to combine different imaging modalities, an approach often referred to as data assimilation. The closely related hierarchical models, on the other hand, allow uncertainties in the prior model itself, letting the data guide the prior. In particular, the approach facilitates the implementation of prior information that is qualitative in nature, important examples being sparsity or locality of the solution. Dynamic prior models are essential in time dependent problems, and they often involve structural elements. Another central question addressed in this project is the development of efficient computational strategies to explore the posterior probability distributions. In particular, sequential methods based on the use of fast reduced forward models will be explored. The visualization of uncertainties drawn from a Monte Carlo sample in imaging applications will also be addressed. The resulting algorithms will be applied to biomedical inverse problems, including Electrical Impedance Tomography (EIT), MagnetoEncephaloGraphy (MEG), Positron Emission Tomography (PET) and ElectroNeuroGraphy (ENG), using data provided by an already established network of collaborators.The current trend in biomedical research is to develop new imaging modalities, clinical procedures and technologies that are minimally invasive. Instead of using ionizing radiation that may constitute a health risk, methods that use weak electric currents or the electromagnetic fields of the body itself are preferable. Electric current/voltage measurements can be used to identify potential malignant tumors in breast tissue; localization of the onset loci of epileptic seizures, an essential procedure before brain surgery to gain control of refractive epilepsy, can be done by measuring the weak magnetic fields due to the brain activity. Similarly, in designing technologies that help patients with spinal cord trauma to regain control of their muscles, or patients with an amputated limb to control a prosthetic arm, new methods of recording non-invasively the nerve signals are developed. A common feature of these methods is that the signals that they rely on are weak, cluttered by noise, and hard to identify. In addition, the computational models are incomplete, since several details describing the setting are unknown. The investigator, together with his colleagues, develops computational methods to overcome the aforementioned difficulties. The methodology relies on probabilistic modeling of the signal and uncertainties within the model. The incomplete data is augmented by complementary information, and a particular emphasis is on the question, how to translate qualitative information about the unknowns into a quantitative form so that it can be entered in the computational model.