## Abstract

In this dissertation, we are interested in solving a linear inverse problem: inverse electrophysiological (EP) imaging, where our objective is to computationally reconstruct personalized cardiac electrical signals based on body surface electrocardiogram (ECG) signals. EP imaging has shown promise in the diagnosis and treatment planning of cardiac dysfunctions such as atrial flutter, atrial fibrillation, ischemia, infarction and ventricular arrhythmia.

Towards this goal, we frame it as a problem of learning a function from the domain of measurements to signals. Depending upon the assumptions, we present two classes of solutions: 1) Bayesian inference in a probabilistic graphical model, 2) Learning from samples using deep networks. In both of these approaches, we emphasize on learning the inverse function with good generalization ability, which becomes a main theme of the dissertation. In a Bayesian framework, we argue that this translates to appropriately integrating different sources of knowledge into a common probabilistic graphical model framework and using it for patient specific signal estimation through Bayesian inference. In learning from samples setting, this translates to designing a deep network with good generalization ability, where good generalization refers to the ability to reconstruct inverse EP signals in a distribution of interest (which could very well be outside the sample distribution used during training). By drawing ideas from different areas like functional analysis (e.g. Fenchel duality), variational inference (e.g. Variational Bayes) and deep generative modeling (e.g. variational autoencoder), we show how we can incorporate different prior knowledge in a principled manner in a probabilistic graphical model framework to obtain a good inverse solution with generalization ability. Similarly, to improve generalization of deep networks learning from samples, we use ideas from information theory (e.g. information bottleneck), learning theory (e.g. analytical learning theory), adversarial training, complexity theory and functional analysis (e.g. RKHS). We test our algorithms on synthetic data and real data of the patients who had undergone through catheter ablation in clinics and show that our approach yields significant improvement over existing methods. Towards the end of the dissertation, we investigate general questions on generalization and stabilization of adversarial training of deep networks and try to understand the role of smoothness and function space complexity in answering those questions.

We conclude by identifying limitations of the proposed methods, areas of further improvement and open questions that are specific to inverse electrophysiological imaging as well as broader, encompassing theory of learning and generalization.

## Library of Congress Subject Headings

Electrophysiology--Data processing; Diagnostic imaging--Data processing; Bayesian statistical decision theory; Machine learning; Neural networks (Computer science)

## Publication Date

10-2020

## Document Type

Dissertation

## Student Type

Graduate

## Degree Name

Computing and Information Sciences (Ph.D.)

## Department, Program, or Center

Computer Science (GCCIS)

## Advisor

Linwei Wang

## Advisor/Committee Member

Nathan Cahill

## Advisor/Committee Member

Rui Li

## Recommended Citation

Ghimire, Sandesh, "On Learning and Generalization to Solve Inverse Problem of Electrophysiological Imaging" (2020). Thesis. Rochester Institute of Technology. Accessed from

https://repository.rit.edu/theses/10601

## Campus

RIT – Main Campus

## Plan Codes

COMPIS-PHD