Waves, rays, and manifolds: physics-driven deep learning for imaging

Kothari, Konik

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https://hdl.handle.net/2142/120315 Copy

Description

Title

Waves, rays, and manifolds: physics-driven deep learning for imaging

Author(s)

Kothari, Konik

Issue Date

2023-04-28

Director of Research (if dissertation) or Advisor (if thesis)

Dokmanic, Ivan

Doctoral Committee Chair(s)

Dokmanic, Ivan

Committee Member(s)

• de Hoop, Maarten
• Anastasio, Mark
• Bresler, Yoram
• Schwing, Alexander

Department of Study

Electrical & Computer Eng

Discipline

Electrical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

inverse problems, machine learning, imaging, signal processing, ill-posedness

Abstract

Imaging inverse problems help us understand our universe. From exploring small molecules to super massive black holes, imaging is ubiquitous. The enormous success of deep learning in recent years has led to an exciting promise for inverse problems---allowing for cheaper measurement setups and faster reconstruction algorithms without sacrificing and, in fact, often improving image reconstruction quality. It is hard therefore, to overstate the importance of deep learning for imaging. While the advances in deep learning are fairly recent, understanding and analyzing imaging physics has a rich and long history of developing insights into the stability of imaging operators. In this thesis, we seek to benefit from both areas of research with an aim to merge them into a symbiotic framework. Many imaging modalities exploit wave phenomena, from seismic reflection tomography to medical ultrasound tomography. The wave equation and its solution operators have been extensively studied in mathematical physics. We take inspiration from their uniqueness and stability theorems to design training algorithms and new neural architectures not only to solve wave imaging inverse problems but also provide a tool for theorists to further probe their conjectures. Throughout this thesis we consider many challenges that appear when applying machine learning to inverse problems, especially in exploratory imaging. An image reconstructed from measurements gathered in exploratory imaging often leads to a high-stakes decision---drilling part of the planet for a mineral or preparing a patient for a biopsy due to a suspicious lump on a scan. These decisions therefore place a higher responsibility on us to not only provide a reconstruction given some measurements but build a more trustworthy system that can foster trust. Often this involves providing multiple possible reconstructions or uncertainty estimates when there is no single unique solution or build interpretable neural architectures that can be related to physical phenomena even in cases where unique solutions exist. The latter can help understand why the network gives a certain estimate given some measurements. Moreover, in imaging scenarios ground-truth data is often scarce. Therefore a robustness to distribution shift ``in-the-wild'' is highly beneficial. We show that many of the aforementioned challenges can be tackled by incorporating ideas from mathematical physics into deep learning on a variety of ill-posed inverse problems.

Graduation Semester

2023-05

Type of Resource

Thesis

Copyright and License Information

Copyright 2023 Konik Kothari

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