{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/117659"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/117659","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Towards geometry-aware and learning-based solutions for inverse problems","abstract":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-12-01","abstract_html":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-12-01","abstract_has_math":false,"creators":["Zehni, Mona"],"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":["Zhao, Zhizhen","Do, Minh N","Bresler, Yoram","Liang, Zhi-Pei"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-12","date_published":"2022-12","updated_at":"2026-07-22T22:24:56Z","subjects":["Inverse Problems","Geometry Aware","Machine Learning"],"languages":["en","eng"],"rights":["Copyright 2022 Mona Zehni"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/117659","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Zhao, Zhizhen","Do, Minh N","Bresler, Yoram","Liang, Zhi-Pei"]},{"key":"dc:creator","label":"Author","values":["Zehni, Mona"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-12","2022-11-28"]},{"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":["Inverse Problems","Geometry Aware","Machine Learning"]}]},{"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 2022 Mona Zehni"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/117659"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-12-01","The student, Mona Zehni, accepted the attached license on 2022-11-23 at 13:34.","The student, Mona Zehni, submitted this Dissertation for approval on 2022-11-23 at 13:36.","This Dissertation was approved for publication on 2022-11-28 at 09:06.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18621 on 2023-04-12 at 08:11:21","In this dissertation, we develop geometry-aware and learning-based solutions for various inverse problems. First, we study multi-segment reconstruction (MSR). We introduce MSR-SWD, a distribution matching approach that recovers a signal such that the distribution of its synthesized measurements matches that of the given observations, in a sliced Wasserstein distance sense. Our numerical results reveal the robustness of MSR-SWD against several benchmarks, especially when the segment lengths are short. Second, we turn to the 2D unknown view tomography (2D UVT) problem. We introduce a geometric-invariant based solution for 2D UVT of point-source images. In addition, we propose an adversarial learning based method to recover a generic image and the viewing angle distribution by matching the empirical distribution of the tomographic observations with the generated data, using the notion of Gumbel-Softmax reparameterization. Our theoretical analysis and numerical experiments showcase the potential of our method to accurately recover the image and the viewing angle distribution. Third, we direct our attention to 3D ab-initio reconstruction and refinement in cryo-electron microscopy (cryo-EM). We start by introducing an ab-initio moment-based approach for the 3D UVT task for 3D point-source models. We also introduce CryoSWD, a 3D cryo-EM ab-initio solution. CryoSWD, inspired by CryoGAN, recovers a 3D map such that the distribution of its synthesized measurements matches the observations, in a sliced Wasserstein sense. Next, we investigate the problem of 3D refinement in cryo-EM. We propose a new approach that refines the projection angles on the continuum, jointly with the 3D map. Finally, we describe DeepSharpen, our deep-learning based solution for cryo-EM map sharpening. Numerical results demonstrate the feasibility and performance of our solutions compared to several baselines. Finally, we focus on 3D human pose estimation from video data. More specifically, we study a pose lifter architecture with kinematic pose representation. We show the advantages of the kinematic representation in semi-supervised settings with scarce labeled data and improved generalization on challenging camera view videos. We also discuss an application -- namely digital neurological examination (DNE). We demonstrate the effectiveness of DNE in capturing digital biomarkers from the extracted 2D/3D pose given recordings of subjects performing neurological examinations."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Towards geometry-aware and learning-based solutions for inverse problems"]}]}],"canonical_facts":{"dc:contributor":["Zhao, Zhizhen","Do, Minh N","Bresler, Yoram","Liang, Zhi-Pei"],"dc:creator":["Zehni, Mona"],"dc:date":["2022-12","2022-11-28"],"dc:description":["Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-12-01","The student, Mona Zehni, accepted the attached license on 2022-11-23 at 13:34.","The student, Mona Zehni, submitted this Dissertation for approval on 2022-11-23 at 13:36.","This Dissertation was approved for publication on 2022-11-28 at 09:06.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18621 on 2023-04-12 at 08:11:21","In this dissertation, we develop geometry-aware and learning-based solutions for various inverse problems. First, we study multi-segment reconstruction (MSR). We introduce MSR-SWD, a distribution matching approach that recovers a signal such that the distribution of its synthesized measurements matches that of the given observations, in a sliced Wasserstein distance sense. Our numerical results reveal the robustness of MSR-SWD against several benchmarks, especially when the segment lengths are short. Second, we turn to the 2D unknown view tomography (2D UVT) problem. We introduce a geometric-invariant based solution for 2D UVT of point-source images. In addition, we propose an adversarial learning based method to recover a generic image and the viewing angle distribution by matching the empirical distribution of the tomographic observations with the generated data, using the notion of Gumbel-Softmax reparameterization. Our theoretical analysis and numerical experiments showcase the potential of our method to accurately recover the image and the viewing angle distribution. Third, we direct our attention to 3D ab-initio reconstruction and refinement in cryo-electron microscopy (cryo-EM). We start by introducing an ab-initio moment-based approach for the 3D UVT task for 3D point-source models. We also introduce CryoSWD, a 3D cryo-EM ab-initio solution. CryoSWD, inspired by CryoGAN, recovers a 3D map such that the distribution of its synthesized measurements matches the observations, in a sliced Wasserstein sense. Next, we investigate the problem of 3D refinement in cryo-EM. We propose a new approach that refines the projection angles on the continuum, jointly with the 3D map. Finally, we describe DeepSharpen, our deep-learning based solution for cryo-EM map sharpening. Numerical results demonstrate the feasibility and performance of our solutions compared to several baselines. Finally, we focus on 3D human pose estimation from video data. More specifically, we study a pose lifter architecture with kinematic pose representation. We show the advantages of the kinematic representation in semi-supervised settings with scarce labeled data and improved generalization on challenging camera view videos. We also discuss an application -- namely digital neurological examination (DNE). We demonstrate the effectiveness of DNE in capturing digital biomarkers from the extracted 2D/3D pose given recordings of subjects performing neurological examinations."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/117659"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Mona Zehni"],"dc:subject":["Inverse Problems","Geometry Aware","Machine Learning"],"dc:title":["Towards geometry-aware and learning-based solutions for inverse problems"],"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":"2026-07-22T22:24:56Z"}