Solving Inverse Problems in Medical Imaging Using Statistical Signal Processing and Deep Learning

Abstract

Solving inverse problems remain an active research area in various fields to study the cause of a phenomenon by observing the effects. In particular, such efforts are well grounded in medical imaging applications where inverse problems naturally arise due to the imaging target being either inaccessible or invisible to human eyes. Non-regularity or ill-conditioning is a major challenge in such situations which is a direct consequence of limited observations/measurements being available. Medical imaging applications have classically incorporated domain-specific knowledge about the forward encoding operator to regularize the pertaining inverse problem. Deep learning has recently received high interest as an alternative approach for data-driven regularization. In principle, such regularization can be achieved by acquiring more measurements. However, sufficient measurements are usually unavailable due to practical considerations. For instance, in electromagnetic source imaging (ESI) using electroencephalography (EEG), number of recording electrodes can not be excessively increased due to subsequent distortions that electrodes contacts can cause in the medium. This limitation adversely affects the spatial resolution of EEG-based ESI. Another example is magnetic resonance imaging (MRI) where increasing imaging resolution trades off with noise properties, temporal resolution and scan duration. High-resolution MRI can become prohibitively long especially when a sequence of images need to be obtained. Thus, accelerated MRI techniques are required to reconstruct high-resolution images using less data. The present thesis contributes to solving regularization issues pertaining to inverse problems in medical imaging with a focus on high-resolution electromagnetic source imaging (ESI) using electroencephalography (EEG) and accelerated high resolution magnetic resonance imaging (MRI) with high fidelity. The ESI spatial resolution and the brain full coverage is shown to significantly improve when simultaneous scalp EEG and intracranial EEG recordings are jointly utilized. Additionally, a new ESI technique is proposed that incorporates forward modeling uncertainties into inverse problem formulations, considerably improving localization accuracy and recovering underlying source dynamics and extents when such uncertainties are properly determined and modeled. A novel deep learning-based reconstruction technique is proposed for accelerated MRI using a recurrent neural network architecture that offers desired noise properties compared to conventional techniques, particularly at higher acceleration rates. Furthermore, a new deep learning methodology is developed that unrolls inverse problem optimization algorithms into dense recurrent neural networks for improved reconstruction performance without requiring extra computational power or increasing reconstruction time.