New statistical approaches to inverse problems in biomedicine

Case Western Reserve University, Cleveland OH

Investigators

Abstract

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.