{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/125526"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/125526","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Spatio-temporal tomographic imaging","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms","abstract_has_math":false,"creators":["Iskender, Berk"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Bresler, Yoram","Do, Minh","Kamalabadi, Farzad","Zhao, Zhizhen","Gupta, Saurabh"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-06-24","date_published":"2024-06-24","updated_at":"2026-07-22T22:25:02Z","subjects":["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"],"languages":["en","eng"],"rights":["Copyright 2024 Berk Iskender"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/125526","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bresler, Yoram","Do, Minh","Kamalabadi, Farzad","Zhao, Zhizhen","Gupta, Saurabh"]},{"key":"dc:creator","label":"Author","values":["Iskender, Berk"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-06-24","2024-08"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["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"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2024 Berk Iskender"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/125526"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms","The student, Berk Iskender, accepted the attached license on 2024-06-18 at 14:35.","The student, Berk Iskender, submitted this Dissertation for approval on 2024-06-18 at 14:59.","This Dissertation was approved for publication on 2024-06-24 at 11:52.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20847 on 2025-02-04 at 21:03:46","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."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Spatio-temporal tomographic imaging"]}]}],"canonical_facts":{"dc:contributor":["Bresler, Yoram","Do, Minh","Kamalabadi, Farzad","Zhao, Zhizhen","Gupta, Saurabh"],"dc:creator":["Iskender, Berk"],"dc:date":["2024-06-24","2024-08"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms","The student, Berk Iskender, accepted the attached license on 2024-06-18 at 14:35.","The student, Berk Iskender, submitted this Dissertation for approval on 2024-06-18 at 14:59.","This Dissertation was approved for publication on 2024-06-24 at 11:52.","DSpace SAF Submission Ingestion Package generated from Vireo submission #20847 on 2025-02-04 at 21:03:46","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."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/125526"],"dc:language":["en","eng"],"dc:rights":["Copyright 2024 Berk Iskender"],"dc:subject":["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"],"dc:title":["Spatio-temporal tomographic imaging"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:02Z"}