Khorashadizadeh, AmirEhsan. Injectivity and locality: robust deep learning for bayesian imaging. 2024, Doctoral Thesis, University of Basel, Faculty of Science.
![]()
|
PDF
26Mb |
Official URL: https://edoc.unibas.ch/96769/
Downloads: Statistics Overview
Abstract
Imaging inverse problems are crucial in exploring and understanding various phenomena in our universe. Astronomers decode light signals from distant galaxies, physicians use imaging to reveal the internal body structures for clinical analysis, and geophysicists process seismic waves to model the Earth's interior. Each case involves reconstructing images of hidden objects from observed data. Recently, data-driven methods based on deep learning have shown great success in solving various imaging inverse problems resulting in high-quality and fast image reconstruction with fewer noisy observations. One major concern when solving inverse problems with deep learning is generalization; we expect the deep neural network to perform well on data other than training samples. Lack of generalization may lead to unstable reconstructions and wrong interpretations which is problematic, particularly for medical applications.
In the first part of this thesis, we build deep-learning architectures based on implicit neural representation. We show that these coordinate-based reconstruction pipelines including MLPatch, Glimpse, and FunkNN for various imaging modalities like image denoising, super-resolution, computed tomography, and magnetic resonance imaging can produce high-quality reconstructions with strong generalization.
While deep learning models with strong generalization can improve the reliability of reconstructions and downstream interpretations, the estimated images can significantly deviate from the true image. Moreover, due to the noise and ill-posedness of the forward operator, there may exist many images that align with our observations, each resulting in a different scientific interpretation. One way to address this is to learn a distribution of possible reconstructions instead of computing a single estimate. This strategy can also help us evaluate an uncertainty map to pinpoint the regions of the recovered image estimated with lower confidence.
To this end, in the second part of this thesis, we develop Bayesian frameworks based on injective neural networks to learn the distribution of reconstructions for solving ill-posed inverse problems. We show that our Bayesian architectures can generate multiple high-quality reconstructions and evaluate physically meaningful uncertainty estimates for various imaging problems including inverse scattering and computed tomography.
In the first part of this thesis, we build deep-learning architectures based on implicit neural representation. We show that these coordinate-based reconstruction pipelines including MLPatch, Glimpse, and FunkNN for various imaging modalities like image denoising, super-resolution, computed tomography, and magnetic resonance imaging can produce high-quality reconstructions with strong generalization.
While deep learning models with strong generalization can improve the reliability of reconstructions and downstream interpretations, the estimated images can significantly deviate from the true image. Moreover, due to the noise and ill-posedness of the forward operator, there may exist many images that align with our observations, each resulting in a different scientific interpretation. One way to address this is to learn a distribution of possible reconstructions instead of computing a single estimate. This strategy can also help us evaluate an uncertainty map to pinpoint the regions of the recovered image estimated with lower confidence.
To this end, in the second part of this thesis, we develop Bayesian frameworks based on injective neural networks to learn the distribution of reconstructions for solving ill-posed inverse problems. We show that our Bayesian architectures can generate multiple high-quality reconstructions and evaluate physically meaningful uncertainty estimates for various imaging problems including inverse scattering and computed tomography.
Advisors: | Dokmanić, Ivan |
---|---|
Committee Members: | Roth, Volker and Konukoglu, Ender |
Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Informatik > Biomedical Data Analysis (Roth) 05 Faculty of Science > Departement Mathematik und Informatik > Informatik > Signal and Data Analytics (Dokmanic) |
UniBasel Contributors: | Roth, Volker |
Item Type: | Thesis |
Thesis Subtype: | Doctoral Thesis |
Thesis no: | 15563 |
Thesis status: | Complete |
Number of Pages: | g, 174 |
Language: | English |
Identification Number: |
|
edoc DOI: | |
Last Modified: | 04 Feb 2025 05:30 |
Deposited On: | 12 Dec 2024 08:24 |
Repository Staff Only: item control page