Thesis
Local monotone operator learning using non-monotone operators for inverse problems in imaging
University of Iowa
Master of Science (MS), University of Iowa
Spring 2024
DOI: 10.25820/etd.007752
Abstract
Magnetic resonance imaging (MRI) is an imaging modality widely used in clinical practice. MRI images are reconstructed from spatial frequency measurements that are acquired sequentially by an MRI scanner. Due to the sequential acquisition, MRI is a relatively slow imaging modality, and significant research efforts have been devoted to reducing the acquisition time. One approach for accelerated MRI is undersampling the measurements. However, image reconstruction from undersampled measurements is an ill-posed inverse problem.
Recovering images from sparse measurements is a problem that arises in several medical imaging modalities. Following recent advances in machine learning, unrolled model-based deep learning algorithms have been introduced for solving such inverse problems. Unrolled algorithms offer state-of-the-art performance, but are impractical for challenging high-dimensional settings such as 3D imaging. Disadvantages of unrolled algorithms include a lack of guarantees on the convergence of the algorithm or robustness to input perturbations, and high GPU memory usage during training. One recently introduced alternative to unrolling is monotone operator learning (MOL), a model-based deep equilibrium framework which is memory-efficient and provides theoretical convergence and robustness guarantees. However, the monotone constraint required by MOL results in reduced performance compared to unrolled methods.
In this work, inspired by convex-non-convex regularization strategies, we introduce local monotone operator learning using non-monotone operators (MnM-MOL). This deep equilibrium framework utilizes a relaxed monotone constraint, which is only enforced in a local neighborhood around the image manifold. We introduce novel theoretical guarantees on the convergence and robustness of this approach, similar to those of MOL. We focus on MRI reconstruction from undersampled measurements, and compare the proposed approach to unrolled methods and MOL methods on multiple datasets. Our experimental results show that relaxing the monotone constraint leads to improved image quality, while still providing robustness to input perturbations.
Details
- Title: Subtitle
- Local monotone operator learning using non-monotone operators for inverse problems in imaging
- Creators
- Maneesh John
- Contributors
- Mathews Jacob (Advisor)Kishlay Jha (Committee Member)Hans Johnson (Committee Member)
- Resource Type
- Thesis
- Degree Awarded
- Master of Science (MS), University of Iowa
- Degree in
- Electrical and Computer Engineering
- Date degree season
- Spring 2024
- Publisher
- University of Iowa
- DOI
- 10.25820/etd.007752
- Number of pages
- viii, 32 pages
- Copyright
- Copyright 2024 Maneesh John
- Language
- English
- Date submitted
- 04/22/2024
- Description illustrations
- images, graphs, tables
- Description bibliographic
- Includes bibliographical references (pages 29-32).
- Public Abstract (ETD)
- Magnetic resonance imaging (MRI) is an imaging technique widely used in clinical practice. MRI images are generated from measurements obtained by an MRI scanner. However, MRI is a relatively slow imaging modality, and the clinical applications are limited by the long scan time required. One approach for accelerated MRI is taking fewer measurements during the scan. However, recovering an image from a few noisy measurements is a challenging problem. Following recent advances in machine learning, many deep learning algorithms have been introduced for solving such inverse problems. One class of deep learning methods is unrolled algorithms. Unrolled approaches offer state-of-the-art performance, but do not provide guarantees on the convergence or robustness of the algorithm, qualities which are especially important in medical imaging. Moreover, unrolled methods are impractical for settings such as 3D imaging, as they are not memory-efficient. One recently introduced alternative to unrolled methods is monotone operator learning (MOL), a framework which is memory-efficient and provides theoretical convergence and robustness guarantees. However, MOL requires an additional constraint that unrolled methods lack, which results in reduced image quality compared to unrolled methods. In this work, we introduce local monotone operator learning using non-monotone operators (MnM-MOL), which is a deep equilibrium framework similar to MOL. However, this framework requires a weaker constraint than MOL, and the constraint is enforced locally instead of globally. Our theoretical results show that this approach offers guarantees of convergence and robustness similar to those of MOL. We focus on the reconstruction of MR images from undersampled measurements, and compare the proposed approach to unrolled methods and MOL methods on multiple datasets. Our experimental results demonstrate that relaxing the constraint leads to improved image quality, while still providing robustness similar to MOL.
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9984647355902771
Metrics
3 File views/ downloads
8 Record Views