Spatio-temporal tomographic imaging

Spatio-temporal imaging (also known as dynamic imaging) refers to the inverse problem of the recovery of an underlying time-varying object $f$ at each time instant $t$ from its undersampled measurements $g$ obtained by a known and possibly time-varying measurement operator R_t. The problem appears in various imaging modalities, such as computed tomography (CT) and magnetic resonance imaging (MRI). In this thesis, we particularly focus on the problem of dynamic tomography with time-sequential measurements, which is significantly ill-posed due to only having a single projection for each time instant $t$. Performing a direct recovery using this inconsistent set of projections is not possible. Also, the acquisition strategy (also called the angular sampling order) is another design parameter that plays an important role in the accuracy and stability of the developed methods. We formulate various methods to tackle this problem. Several of the proposed methods employ partially-separable models (PSM) to represent the underlying spatio-temporal object. PSM representation introduces a particular low-rank structure, leading to the factorization of the spatial and temporal effects. It is also parsimonious and preserves interpretability. Firstly, we propose a projection-domain PSM and analyze conditions for a unique and stable solution to this ill-posed inverse problem. The special projection-domain PSM also allows a quantitative analysis and prediction of the performance of different time-sequential acquisition schemes. Then, to enable the incorporation of a spatial regularizer, we propose an object-domain recovery algorithm using a variational formulation with PSM enforced as a soft constraint. This method uses the temporal components of the PSM recovered by the fast projection-domain method for initialization to improve and accelerate convergence. Thirdly, we propose another object-domain method that efficiently combines the PSM and the popular Regularization-by-Denoising (RED) frameworks for the first time. Convergence of the proposed algorithm is improved and accelerated by initializing the method with the spatial and temporal components of the fast projection-domain PSM. The method includes a convergence analysis. Finally, the last method proposed in this thesis combines the neural fields (NFs), or implicit neural representations (INR), with the RED framework for the first time to recover the underlying spatio-temporal object with improved accuracy compared to its low-rank alternative, and another deep-prior-based method. The proposed optimization algorithm avoids costly gradient computations through the deep denoiser for RED updates.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Iskender, Berk

Contributors dc:contributor

• Bresler, Yoram
• Do, Minh
• Kamalabadi, Farzad
• Zhao, Zhizhen
• Gupta, Saurabh

• Dynamic Imaging
• Low Rank Modeling
• Partially Separable Models
• Bilinear
• Unique Recovery
• Regularization By Denoising
• Neural Fields
• Spatio-temporal Regularization
• Dynamic Reconstruction
• Pre-learned Spatial Prior

Statement dc:rights

• Copyright 2024 Berk Iskender

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/125526

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F125526